The Ten: Concepts you need to know for the AP Chemistry Exam by Edvantage Science

AP Chemistry â&#x20AC;&#x201C; The Ten â&#x20AC;&#x201C; Development Team

Authors

Cheri Smith

Yale Secondary School District 34 Abbotsford Gary Davidson School District 22 Vernon Megan Ryan Walnut Grove Secondary School District 35 Langley Chris Toth St. Thomas More Collegiate Burnaby, British Columbia Program Consultant Lionel Sandner Edvantage Interactive

m=0 y = 100 k = 27

g = 133 b = 63 Hex = # 00553F

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Care has been taken to trace ownership of copyright material contained in this text. The publishers will gladly accept any information that will enable them to rectify any reference or credit in subsequent printings. Vice-President of Marketing: Don Franklin Director of Publishing: Yvonne Van Ruskenveld Design and Production: Donna Lindenberg, Paula Gaube Editorial Assistance: Rhys Sandner Proofreading: Eva van Emden The AP Units at the beginning of each chapter are quoted from AP Chemistry: Course and Exam Description, revised edition, effective Fall 2019, published by the College Board, New York, NY. Advanced Placement, AP, and College Board are registered trademarks of the College Board.

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Contents

– The Ten –

What is the The Ten?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv How can it help me study?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv __________________ Unit 1: Atomic Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Unit 1: Periodic Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Unit 2 and 3: VSEPR and IMF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Unit 3: Spectroscopy (PES). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Unit 3 Gases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Unit 4 Solutions and Titrimetry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Unit 5: Kinetics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Unit 6: Thermochemistry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Unit 7: Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Unit 7: Solubility Equilibrium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Introduction iii

What is the The Ten? Before you start looking at this book, please take a few minutes and read this. It will save you time. There are many different AP Chemistry review books available that provide you with thousands of questions. The design of these books is to give you so many questions that as you solve them you gain a false sense of confidence that you understand the material. This book does not do that. This book is created specifically for students of the Edvantage Science program. Their teachers recognize how to best prepare their students and we are happy to support both teachers and students where ever we can. We work with teachers who have consistently supported students to be successful in the AP Chemistry exam. These same teachers have produced the Edvantage Science AP Chemistry 1 and 2 program. This program is the only AP Chemistry program written specifically for high school students rather than first year University and College students. As a result, students using this program tend to well in their current AP Chemistry studies. The Ten is a summary of these teachers’ collective knowledge around how to best prepare students for an exam. They have identified key questions in each unit that have traditionally been considered difficult and the type of question you may expect to encounter on the exam.

How can it help me study? This review book identifies key or reference questions that students consistently have troubles solving in AP Chemistry. The goal of this book is simple. If you can do the questions and complete the digital quizzes at Edvantagescience.com, there will be no surprises on the AP Chemistry exam. We by no means can guarantee any given mark, but we are confident that if you can do these questions, you’re ready for the exam. After solving each problem, you can check your answer at Edvantagescience.com. Look for the course called Edvantage Science AP Chemistry Test Prep. This course is organized by units and page number. You will be able to find the worked solution for every question in The Ten book. There will also be other support tools like quizzes that will provide you with addtional review. We realize this is a challenging time and are impressed with your ability to be ready for the exam. It shows your positive attitute, ability to focus and work hard. You should be proud of your accomplishments as you prepare to complete this course. Good luck on the exam and in your future academic endeavors.

For more information on how to purchase your own personal copy info@edvantageinteractive.com

iv Introduction

Unit 1: Atomic Theory This chapter focuses on the following AP Unit from the College Board: Unit 1: Atomic Structure and Properties _______________________________________________________________________________________________________________ Upon completion of the questions in this section and checking the worked solutions at edvantagescience.com, you should be able to: ❑ Describe how radiant energy that is quantized is fundamentally different than radiant energy that travels as waves. ❑ State Bohr’s postulates regarding the behaviour of hydrogen’s electron. Define and use the terms stationary states, quantum number, ground state, and excited states in your description of Bohr’s model of the atom. ❑ Describe Hydrogen’s bright-line emission spectrum and relate this to the stationary states of Bohr’s atomic model. ❑ Given the relevant equations and constants, solve for: ❑ (i) the energy of the photon released when an electron drops from a higher energy orbit to a lower energy orbit in a hydrogen atom. ❑ (ii) the wavelength of the light emitted when an electron drops from a higher energy orbit to a lower energy orbit in a hydrogen atom. ❑ Explain why an electron can have only certain stable orbits. ❑ Use De Broglie’s equation to calculate a particle’s wavelength from its mass and its speed. ❑ State, in general terms, Heisenberg’s uncertainty principle. ❑ Define an atomic orbital and distinguish this from an electron orbit. ❑ Each quantum number (1st, 2nd, 3rd) describes a different feature of an electron’s orbital. Name and provide the orbital feature described by each quantum number. ❑ Relate the total number of orbitals and the number of different orbital shapes to the first (principal) quantum number. ❑ Name the 4th quantum number, provide its two possible values, and state how it is fundamentally different than the first three quantum numbers. ❑ State the Pauli exclusion principle. ❑ For multi-electron atoms, the sublevels of each principal quantum number have different energies. Explain why this is the case and relate a sublevel’s energy to its number of orbitals. ❑ State the Aufbau principle and Hund’s rule. ❑ Provide atoms’ electron configurations and orbital diagrams. ❑ Provide ions’ electron configurations and orbital diagrams.

0 0 0 0

Models of the atom have gradually developed as our understanding of the composition of the atom has increased.

Unit 1 Atomic Theory 1

1. Use the following mass spectrometry data to calculate the atomic mass of magnesium.

Isotope

Mass of Atom in amu (relative to 12C = 12.0000)

Percent Abundance in Nature

magnesium-24

23.9850

78.99

magnesium-25

24.9858

10.00

magnesium-26

25.9826

11.01

2. Silver has two naturally occurring isotopes. Calculate the percent abundances of silver-107 and silver-109 using the following data: Atomic mass of silver

107.87 amu

Isotopic mass of silver-107

106.9051 amu

Isotopic mass of silver-109

108.9045 amu

2â&#x20AC;&#x192; Unit 1 Atomic Theory

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3. Briefly explain why hydrogen’s visible emission spectrum does not resemble a continuous spectrum or rainbow.

4. Describe what you would expect to see if hydrogen’s visible emission and absorption spectra were superimposed upon each other.

5. If hydrogen’s electron exists in a spherical orbital, why doesn’t this mean that the electron moves around the nucleus in a circle?

6. What is the difference between a 1s orbital and a 2s orbital? What does that difference indicate about an electron possessing energy equal to n = 2 as compared to n = 1?

7. Describe the two differences between a 2px orbital and a 3py orbital.

8. The lobes of a p orbital disappear at the nucleus. What does this tell us about electrons in p orbitals?

Unit 1 Atomic Theory 3

9. You may have heard in previous science classes that the maximum numbers of electrons that can exist in the first four energy levels are 2, 8, 8, and 18 respectively. Do you agree with those numbers and if not, what should they be?

10. The electron configuration for phosphorus, written in core notation, is [Ne] 3s2 3p3. What two things does Hund’s rule tell us about the three electrons in the 3p sublevel?

11. Use the periodic table to complete the following table: Atom or Ion

Full Electron Configuration

Core Notation

Ge Zn2+ Sr Br – Sn In3+

4 Unit 1 Atomic Theory

12. (a) Use the periodic table to identify the neutral atoms having the following electron configurations: Electron Configuration

Element Name

[Ne] 3s2 [Ar] 4s2 3d5 [Kr] 5s2 4d10 5p3 [Xe] 6s2 4f 7 (b) Notice where each of these elements is located on the periodic table. Look at the highest energy sublevel being filled (bold type) in each of the atoms in the table, and identify the four different sections of the periodic table associated with each of these four sublevels.

13. Consider the following six stable ions: N 3–, O 2–, F–, Na+, Mg 2+, and Al 3+. (a) How many electrons are present in each ion?

(b) Write a single electron configuration representing all of the ions.

(c) Which neutral atom possesses this electron configuration? What does this suggest about a possible reason for some ion formation?

Unit 1 Atomic Theory 5

14. (a) Complete the following table for some elements in two families of the periodic table. Alkali Metals

Core Notation

# Outer Electrons

Halogens

lithium

fluorine

sodium

chlorine

potassium

bromine

rubidium

iodine

Core Notation

# Outer Electrons

(b) Consider the numbers of outer electrons present and suggest a reason why elements belonging to the same chemical family demonstrate similar chemical behavior.

15. (a) On a separate sheet of paper, draw an orbital diagram for an atom of iron with sublevel energy increasing vertically. Arrange equal energy orbitals in each sublevel horizontally.

(b) Use a highlighter to label the electrons that would be lost when the Fe3+ cation forms.

6â&#x20AC;&#x192; Unit 1 Atomic Theory

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Unit 1: Periodic Trends This chapter focuses on the following AP Unit from the College Board: Unit 1: Atomic Structure and Properties

Upon completion of the questions in this section and checking the worked solutions at edvantagescience.com, you should be able to:

Define a periodic trend. Name and describe the measurements used to indicate the size of a metal and a non-metal atom respectively. Describe two characteristics of atoms that influence their size. Describe and explain the two periodic trends in atomic size. Given any two isoelectronic species (e.g. Na+ and F−), state which is larger and explain why. Define ionization energy. Describe and explain the two periodic trends in ionization energy. Describe one exception to a general periodic trend in ionization energy. Define electronegativity. Describe and explain the two periodic trends in electronegativity.

Unit 1 Periodic Trends 7

1. Which of the two opposing factors that influence atomic size predominates as we move across a chemical period? What is the general result?

2. Which of the two opposing factors that influence atomic size predominates as we move down a chemical family? What is the general result?

3. In general, is “effective shielding” most evident going across a period or down a family? How can you tell?

4. Using only the periodic table, rank the following alphabetical list of elements in order of decreasing first ionization energy. aluminum argon cesium magnesium rubidium silicon sodium sulfu

r 5. Using the periodic table, write the correct number in the space after each statement below: Members of this chemical family have the highest IE1 in their period. ________ Members of this chemical family have the lowest IE1 in their period. ________ Members of this chemical period have the highest IE1 in their family. ________ Members of this chemical period have the lowest IE1 in their family. ________

8 Unit 1 Periodic Trends

6. The nature of the 2s sublevel is such that 2s electrons have a higher probability of being found closer to the nucleus than electrons in the 2p sublevel. Consider this and the following electron configurations:

beryllium: 1s2 2s2

boron: 1s2 2s2 2p1

Suggest a reason why boron’s first ionization energy is less than beryllium’s, even though boron is a smaller atom.

7. One of the three properties discussed shows periodic trends when moving across a period or up a family opposite to the other two properties. Identify this property and the trend observed.

8. Briefly explain why fluorine is a smaller atom than lithium. Consider which factor is predominating across a period.

9. Where are the largest atoms located on the periodic table? Where are the smallest atoms located on the periodic table?

10. The attraction of electrons to the nucleus and repulsion of the electrons between each other both influence the size of an atom or ion. Use this to complete the following statements. (a) A cation will always be ________________ (smaller or larger) than its parent neutral atom because of _________________ (increased or decreased) attraction of the outer electrons for the nucleus and _________________ (increased or decreased) repulsion of the electrons for each other.

(b) An anion will always be ________________ (smaller or larger) than its parent neutral atom because of _________________ (increased or decreased) attraction of the outer electrons for the nucleus and _________________ (increased or decreased) repulsion of the electrons for each other.

Unit 1 Periodic Trends 9

11. What role do inner or core electrons play in determining atomic size and ionization energy?

12. Complete the following table by filling in the words “lower left” or “upper right” in the appropriate spaces. Where on Periodic Table Elements Show: Largest atomic radii Smallest atomic radii Lowest ionization energy Highest ionization energy Lowest electronegativity Highest electronegativity

13. Consider the first two ionization energies for lithium: IE1 = 519 kJ/mol

IE2 = 7 285 kJ/mol

Explain why lithium’s second ionization energy is more than 10 times its first.

10 Unit 1 Periodic Trends

14. Elements with low ionization energies tend to have relatively low electronegativities. What might this indicate about how they will behave when reacting with high IE and EN elements?

15. Elements with high ionization energies tend to have relatively high electronegativities. What might this indicate about how they will behave when reacting with low IE and EN elements?

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Unit 1 Periodic Trendsâ&#x20AC;&#x192; 11

16. What do you think might occur if two non-metal atoms, each with high EN and IE values reacted together? (Hint: Will either have a tendency to give away electrons?)

17. Write the electron configuration for nickel and zinc. Use these to explain why an atom of zinc is larger than an atom of nickel.

12â&#x20AC;&#x192; Unit 1 Periodic Trends

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Unit 2 and 3: VSEPR and IMF This chapter focuses on the following AP Units from the College Board: Unit 2: Molecular and Ionic Compound Structure and Properties Unit 3: Intermolecular Forces and Properties

Upon completion of the questions in this section and checking the worked solutions at edvantagescience.com, you should be able to: Determine the three-dimensional structures of molecules using Valence Shell Electron Pair Repulsion (VSEPR) Theory. Determine whether a molecule is polar or non-polar. Describe, explain, and supply an example of each of the following types of intermolecular forces - dipole-dipole forces, hydrogen bonds, dispersion forces and ion-dipole forces. Name and provide examples of hybrid atomic orbitals. Describe sigma (σ) and pi (π) bonds. Describe single and double bonds in terms of σ and π bonds. Deduce hybridization, molecular shape and the presence of σ and π bonds from a molecular formula. Define formal charge and calculate the formal charge of each atom in a species. Deduce the preferred Lewis structure based on minimizing formal charge.

Unit 2 and 3 VSPER and IMF 13

1. Complete the following table for each of the chemical species. Lewis Structure

AXmEn Notation

Molecular Shape (Name and Diagram)

(a)

O F

F S F

F (b)

F F

2. Complete the following table for each of the chemical species. Chemical Formula

Lewis Structure

AXmEn Notation

Molecular Shape (Name and Diagram)

(a) CCl4

(b) PF3

14â&#x20AC;&#x192; Unit 2 and 3 VSPER and IMF

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3. Draw Lewis structures for each of the following species. a) CH4

b) H3O+

c) OF2

d) HCN

e) SF6

f) SOF4

4. State the shape and the central atom hybridization for each of the structures. 5. Label each molecule as polar or non-polar.

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Unit 2 and 3 VSPER and IMFâ&#x20AC;&#x192; 15

6. Assign formal charges to each atom in each of the following two structures for CO2. Predict which structure is favored.

(a)

(b)

7. Assign formal charges to each atom in each of the following six structures for SCO. Predict which structure is favored. Which is least likely to form?

(a) O

(d) C

(b) C

(e)

(f)

8. Draw two structures for SO3, one with an expanded octet and one without. You do not need to show resonance structures for the non-expanded form. Use formal charges to predict which structure is favored. Check the Internet to see whether you can find any information indicating that the other structure might, in fact, be favored.

16â&#x20AC;&#x192; Unit 2 and 3 VSPER and IMF

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9. Complete the following table:

Lewis Structure

AXmEn Notation

Shape of Molecule (Name and Diagram)

Type of Intermolecular Force Acting Between Molecules

(a)

H H

Cl dichloromethane (b)

O C

phosgene (c)

F S

F F

sulfur hexafluoride (d)

F F

F I

iodine pentafluoride

Unit 2 and 3 VSPER and IMF 17

10. (a) Draw Lewis structures for each of the species below in the space provided. (b)

State the shape and the central atom hybridization for each.

(c)

Consider the polarity of the bonds in each molecule and then determine whether there is a molecular dipole.

(d)

Indicate the number of sigma and/or pi bonds in each molecule or ion.

(e)

Assign formal charges to each atom in each of the species.

SCl2

TeF5−

XeF4

CO3−2

IOF5

IF4+

18 Unit 2 and 3 VSPER and IMF

Unit 3: Spectroscopy (PES) This chapter focuses on the following AP Units from the College Board: Unit 1: Atomic Structure and Properties Unit 3: Intermolecular Forces and Properties

Upon completion of the questions in this section and checking the worked solutions at edvantagescience.com, you should be able to: Describe how wavelength, wave frequency and photon energy vary across the electromagnetic (EM) spectrum and across the visible light portion of the EM spectrum. Describe how nuclear magnetic resonance (NMR) spectroscopy works, e.g. state what each peak in an NMR spectrum represents. Describe how infrared (IR) spectroscopy works, e.g. state what each inverted peak in an IR spectrum represents. Describe how the shielding effect influences the effective nuclear charge and how that in turn affects the force of attraction between a valence electron and the nucleus as described by Coulombs Law. Describe how ultraviolet-visible (UV-Vis) spectroscopy works, e.g. state what each peak in a UV-Vis spectrum represents. Describe how the energy required to eject an electron from its atom is calculated in photoelectron spectroscopy (PES). Describe how PES works, e.g. state what each peak in a PES spectrum represents. Identify the element represented by a given PES. Use PE spectra to illustrate periodic trends in binding energy.

Unit 3 Spectroscopy and IMF 19

Examine the UV/Vis spectrum shown here. (a) and (b) represent two different samples of the same compound in aqueous solution 0.06

Absorbance

(a) 0.04

(b)

0.02

0.00

300

400

500

600 700 Wavelength (nm)

800

900

. 1. Which sample absorbed more light?

2. Which sample transmitted more light?

3. How does sample (a) differ from sample (b)?

4. At what wavelength is maximum absorbance occurring?

20â&#x20AC;&#x192; Unit 3 Spectroscopy and IMF

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Relative number of electrons

Simulated photoelectron spectra of elements 1 through 5 H

100

0.1

Relative number of electrons

100

0.1

100

Binding energy (MJ/mol) Relative number of electrons

1 Binding energy (MJ/mol)

Binding energy (MJ/mol)

10 Binding energy (MJ/mol)

100

0.1

Binding energy (MJ/mol)

5. Draw an orbital diagram for elements 1 through 5 in the periodic table.

Give three points of comparison between the orbital diagram and the PES for boron.

Compare and explain the position of the first peak for each of the elements 1 to 5.

Compare and explain the heights of the final peak (farthest right) for each of the elements 1 to 5.

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Unit 3 Spectroscopy and IMFâ&#x20AC;&#x192; 21

PES spectra for neon, oxygen and carbon.

9. Examine the figure above. Use the Q values in Coulomb’s law to explain why the energy associated with the first peak is larger in neon and smaller in oxygen. Do the same for the third peak referring to both the Q and r values.

10. Examine the figure above. Why are the first and second peaks the same height for all three elements while the third peak heights vary?

11.

Complete the following table: Region of EM Spectrum Radio Waves

Spectroscopic Technique NMR (nuclear magnetic resonance)

Photons Used To Measure energy changes causing nuclear spin to study molecular structure.

Infrared UV/Visible

X-rays

12. The first ionization energies for selected elements from the second period of the periodic table are as follows: Atom 1st IE (kJ/mol)

Li-3 520

Be-4 899

C-6 1086

N-7 1302

F-9 1681

Ne-10 2081

Use Coulomb’s law to explain the trend in ionization energies in terms of the relative location of the electrons and the charge of the nucleus.

22 Unit 3 Spectroscopy and IMF

13. (a) Calculate the photon frequencies in 1/s for each of the following regions of the electromagnetic spectrum. (b) What range of the spectrum does each energy correspond to? (c) What type of spectroscopy might it be useful for? Wavelength Range

(a) Frequency (1/s)

(b) Range

700 nm to 400 nm

400 nm to 10 nm

10 to 0.01 nm

14. What element does each PES spectrum below represent? (a)

Relative number of electrons

(b)

127 125

9 7 5 Ionization energy (MJ/mol)

400

(d)

Relative number of electrons

(c)

200 30 10 3 Ionization energy (MJ/mol)

400

200 160 30 10 Ionization energy (MJ/mol)

3 1

E (MJ/mol)

Unit 3 Spectroscopy and IMF 23

Relative number of electrons

15.(a) Identify the element whose PES spectrum is shown.

208

18.7

13.5

1.95 1.01 E (MJ/mol)

(b) Draw the Bohr diagram for this element.

(c) Sketch the PES spectrum for the atom having 8 fewer protons than this atom. Label the axes clearly and show the approximate energies.

(d) If photons of wavelength 1.25 x 10–8 m bombarded the original element, which, if any, of the electrons could be emitted?

24 Unit 3 Spectroscopy and IMF

Unit 3 Gases This chapter focuses on the following AP Units from the College Board:

Unit 3: Intermolecular Forces and Properties

Upon completion of the questions in this section and checking the worked solutions at edvantagescience.com, you should be able to:

Use Boyle’s Law to calculate the effect of changing the volume of a gas on its pressure or vice-versa (at a constant temperature). Use Charles’ Law to calculate the effect of changing the temperature of a gas on its volume (at a constant pressure). Use Guy Lussac’s Law to calculate the effect of changing the temperature of a gas on its pressure (at a constant volume). Use the Combined Gas Law to calculate a gas’ new temperature, pressure, or volume when the other two are changed. State the conditions of Standard Temperature and Pressure (STP). Use the Ideal Gas Law to calculate the temperature, pressure, moles, or volume of a gas when the other three are given. Derive the other gas laws and the “kitty cat equation” from the Ideal Gas Law. Define a substance’s boiling point in terms of the substance’s vapour pressure. Describe and explain the effect of altitude on boiling point. Describe the effect of intermolecular forces on vapour pressure and boiling point. State Dalton’s Law of Partial Pressures. Calculate the partial pressure of a gas collected over water by correcting for the water vapour present. State 4 postulates of Kinetic Molecular Theory (KMT) pertaining to gases. Calculate the average kinetic energy and the root mean square velocity of a gas particle, given its temperature. Define diffusion and effusion. Use Graham’s law to calculate two gases’ relative rates of diffusion or effusion. Provide two reasons why gases do not exhibit ideal behaviour. Describe and explain the effect of pressure and temperature on gases’ deviation from ideal behaviour. Calculate the partial pressure of a gas from its mole fraction.

In a hot air balloon, a gas burner is used to heat air to a temperature of about 212°F (100°C). Since hot air is lighter and less dense than the cool air around the balloon, the heated air causes the whole balloon to rise.

Unit 3 Gases 25

1. A standard scuba tank holds a volume of 70.0 ft3 of air under SATP conditions (25°C and 1.00 atm). What volume would this air occupy if released under the conditions a diver experiences under 20 m of water on the northwest coast while winter diving? This diver would experience a temperature of 6.5°C and a pressure of 315 kPa.

2. Jo Bob collects a sample of gas from the exhaust pipe of his sister’s car. The sample contains 1.21 x 1023 molecules of gas at a pressure of 775 mm Hg and a temperature of 38°C. What is the volume of the gas sample?

3. A 44.8 L sample of gas weighs 128.2 g at a temperature of 273 K and a pressure of 760.0 torr. What is the molar mass of this gas?

4. A 7.50 g sample of lithium metal is dropped into 25.0 mL of 1.5 M hydrochloric acid. What volume of hydrogen gas would be evolved once the limiting reactant has been consumed? (The reaction is performed at SATP conditions; hence the temperature is 25.0°C and the pressure is 101.3 kPa.)

26 Unit 3 Gases

5. The propane tank by the portable science classroom near the backfield of a typical school has a volume of 2210 L. Assuming the tank contains 3150 moles of propane gas, what is the pressure inside the tank on a nice warm day of 28°C?

6. Bonzo lives on the planet X, which has an atmospheric pressure of 164 kPa. A nice day on planet X has a temperature of –36°C. If Bonzo exhales 11.0 g of carbon dioxide, what is the volume of gas?

7. For an unknown gaseous element, 3.23 g occupy 5.60 L at 153°C and 101.3 kPa. (a) What is the molar mass of the element?

(b) How many atoms are contained in 3.23 g of this element?

Unit 3 Gases 27

8. A 0.65 g sample of powered zinc metal reacts completely in sulfuric acid to produce zinc sulfate and hydrogen gas. The gas is collected over water as shown in the accompanying diagram. Assuming the pressure in the laboratory is 101.3 kPa and the temperature of the gas sample is 20.0°C, what is the volume of the dry H2 gas collected?

H2SO4 (aq) H2

Zinc

9. Nitrogen gas is collected over water at 25.0°C and 14.7 psi. Given that the vapor pressure of water is 23.8 mm Hg at this temperature, what total volume of gas must be collected to obtain 4.10 g of nitrogen?

10. A mixture of 0.50 mol of hydrogen and 0.25 mol of oxygen in a sealed flask has a total pressure of 6.0 × 101 kPa. Calculate the partial pressure exerted by each of the two gases.

11. A mixture of gases contains 5.00 × 1023 molecules of CO2, 6.00 g of CH4, and 0.300 mol of NH3. The total pressure exerted by the gases is 80.0 kPa. What is the partial pressure of each gas? Hint: First change all the quantities given into moles.

28 Unit 3 Gases

12. The following system contains 20.0 psi each of gases A and B in the end bulbs with an evacuated bulb in the centre. Both stopcocks are opened at once. What is the new overall pressure in the system?

13. The following system is equilibrated with an atmospheric pressure of 1.00 atm in all parts. A thin layer of catalyst near the opened valve causes the gases to react to form ammonia. Give the partial pressures of each gas and the total pressure in the system when the reaction is complete.

2.00 L H2

1.00 L N2

14. The penny coin was removed from circulation in Canada In February of 2014. The United States may soon do the same. The major reason for this move was the rising value of copper metal. When copper’s value increased, pennies were produced as a zinc slug with a thin layer of copper plated over top. Zinc reacts readily with hydrochloric acid, while copper does not. A triangular file is used to nick the edge of a penny to expose the zinc slug below the layer of copper. The zinc reacts with the acid releasing bubbles from the nicked area until nothing remains but a thin shell of copper. If 0.948 L of hydrogen gas is collected over water at 20.0°C and a total pressure of 752 mm Hg, determine the percentage by mass of the copper in the 2.586 g penny.

Unit 3 Gases 29

15. A 239.4 mg sample of a drug designed to treat malaria was run through a series of reactions to convert all the nitrogen in the compound into N2(g). The gas collected over water at 23.8°C and a pressure of 755.5 torr had a volume of 18.66 mL. The vapor pressure of water at this temperature is 22.11 torr. (a) Calculate the percent by mass of nitrogen in the sample.

(b) A 3.239 mg sample of the drug is combusted in air to produce 8.785 mg of CO2(g) and 2.160 mg of water vapor. Determine the percent by mass of carbon and hydrogen in the sample. Assume that any remaining element is oxygen and calculate the empirical formula.

16. Deep sea scuba divers breathe a gas mixture called heliox. Under very high pressures, the nitrogen in air enters the blood stream and causes a drunken type of state called nitrogen narcosis. The lack of nitrogen allows divers to descend to very deep depths without worrying about nitrogen toxicity. A 12.5 L scuba tank contains a helium-oxygen mixture containing 250.0 g of helium and 47.5 g of oxygen at 25°C. Calculate the partial pressure of each of the gases in the tank and determine the total pressure exerted by the heliox.

30 Unit 3 Gases

17. Examine the graphs in Figure 8.4.8 and Figure 8.4.9. (a) Which particle deviates the most from ideal behavior? Give two reasons for this behavior.

(b) What temperature provides the most ideal behavior? Explain.

18. Explain the general pattern for the values of a and b moving down the noble gas family. (A simple statement of the trend is not an adequate answer.)

19. Explain the same pattern moving from N2 to CO2 to CCl4.

20. Explain the same pattern moving from N2 to CO to HCl to H2O.

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Unit 3 Gasesâ&#x20AC;&#x192; 31

32 Unit 3 Gases

Unit 4 Solutions and Titrimetry This chapter focuses on the following AP Units from the College Board: Unit 4: Chemical Reactions.

Upon completion of the questions in this section and checking the worked solutions at edvantagescience.com, you should be able to:

Describe what “like dissolves like” means and provide several examples. List 3 criteria required for a substance to dissolve. Explain why vitamin A is fat-soluble and vitamin C is water-soluble. Describe how soaps work. Calculate the concentration of a solution after it is diluted. Write dissociation equations for ionic solids. When an ionic solid is dissolved, relate the concentrations of the dissolved ions to each other and to the concentration of their parent compound. Calculate the resulting ion concentrations when solutions are mixed. Define electrolyte, non-electrolyte, strong electrolyte, and weak electrolyte. Describe and explain the electrical conductivity of soluble salts, salts with low solubility, weak acids and bases, and strong acids and bases. Define a titration. Perform a titration calculation, e.g. calculate a base’s concentration by knowing the volume and concentration of an acid required to react completely with a given volume of the base. Label the burette, the standardized solution (or titrant), the Erlenmeyer flask, the solution of unknown concentration (or analyte) and the indicator on a diagram of a titration apparatus.

The interactions of solutes and solvents create solutions with a wide range of useful properties.

Unit 4

Solution and Titrimetry 33

1. What is “like” between NaCl and H2O? Why do they interact as they do?

2. Explain why water molecules will not surround I2 molecules? What forces must be overcome between each water molecule?

3. Would you expect NaCl to dissolve in oil, which is a non-polar solvent? Explain.

4. Predict whether NaCl would dissolve in NH3 liquid. Draw a diagram to show the forces acting within the solute, the solvent, and the resulting mixture.

5. Will ammonia dissolve in water? Explain.

6. Is ethanol soluble in hexane, C6H14? Explain.

7. Which is more soluble in water: C2H6 or CH3OH? Explain.

8. Octanol has the formula C8H17OH. Explain why octanol does not dissolve in water.

34 Unit 4 Solution and Titrimetry

9. Paint thinner is a non-polar covalent solvent. Is iodine soluble in paint thinner? Explain.

10. Mothballs are made of naphthalene, C10H8. Will a mothball dissolve better in water or paint thinner? Explain.

11. A student places 10 mL of water and 10 mL of CCl4 into a beaker. Solid iodine is added to the beaker. Explain what you would see and sketch a diagram of it.

12. Why can a molecule of CCl4 not come between water molecules?

13. Explain why NH3 is very soluble in water, but NCl3 is not.

14. When I2 is added to water, it does not dissolve. However, if I2 is added to an aqueous solution of KI, it will dissolve. Use the following reaction, and your understanding of intermolecular forces to explain the above observations. I2(s) + I-(aq) ➝ I3-(aq)

15. Which is more soluble in water? Explain. (a) C4H10 or C3H6OH

(b) MgCl2 or toluene (C7H8)

Unit 4

Solution and Titrimetry 35

16. Glycerin is a common solvent and is found in many skin care products. A student mixed 10 mL of water, 10 mL of glycerin and 10 mL of carbon tetrachloride together. A small amount of CuCl2 was added to the mixture. Explain what you would see.

Glycerin 17. Ethylene glycol is commonly used as antifreeze. Underline the solvent in which it would be most soluble in each pair below.

H H

OH H

H Ethylene glycol

(a) water or paint thinner (a non-polar covalent solvent)

(b) ammonia or carbon tetrachloride

18. List the intermolecular forces present between the following solutes and solvents:

(a) CsCl in H2O

(b) CH3OH in glycerin

(d) acetone in ammonia

Acetone

36â&#x20AC;&#x192; Unit 4 Solution and Titrimetry

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19. A student titrates a standardized solution of H2C2O4 to determine the concentration of NaOH. The indicator used was phenolphthalein. Draw an apparatus used for the titration. Label all glassware and their contents. Describe what color the solution would be in the flask at the beginning of the titration and at the end of the titration.

20. A student titrated 10.00 mL HCl with 0.050 M Sr(OH)2. The table below shows the data collected. Calculate the [HCl]. Molarity of Sr(OH)2 = 0.050 M

Trial #1

Trial #2

Trial #3

Initial burette reading (mL)

0.00

16.05

32.93

Final burette reading (mL)

16.05

32.93

49.68

Volume of Sr(OH)2 added (mL) Average volume Sr(OH)2 (mL)

21. A 25.00 mL sample of 0.20 M H2CO3 was titrated with 0.50 M NaOH. What volume of NaOH was required to reach the equivalence point?

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Unit 4

Solution and Titrimetryâ&#x20AC;&#x192; 37

22. A 10.00 mL sample of vinegar (CH3COOH) was titrated with 18.20 mL of 0.50 M NaOH. Calculate the [CH3COOH].

23. In order to standardize a solution of NaOH, 0.18 g of oxalic acid, H2C2O4· 2H2O, was dissolved to make 250.00 mL of solution. A 25.00 mL sample of this solution was titrated against 15.25 mL NaOH. Calculate the [NaOH].

24. Aspirin has the formula C9H8O4. Only one of the H atoms is released when it acts as an acid. An aspirin tablet with a mass of 0.50 g was dissolved in water, and titrated with 18.30 mL of 0.10 M NaOH. Calculate the mass of aspirin in the tablet, and then the percent by mass of aspirin in the tablet.

25. A 250.00 mL sample of Ca(OH)2 was titrated with 7.25 mL 0.10 M HCl. Calculate the mass of Ca(OH)2 present in the solution.

26. A student dissolved 0.1915 g of an unknown acid HA in 10.00 mL of water. This solution was then titrated with 0.100 M NaOH. The table below shows the data collected. Calculate the molar mass of the acid HA. Molarity of NaOH = 0.100 M

Trial #1

Trial #2

Trial #3

Initial burette reading (mL)

0.00

15.25

30.47

Final burette reading (mL)

15.25

30.47

45.87

Volume of NaOH added (mL) Average volume NaOH (mL)

38 Unit 4 Solution and Titrimetry

Unit 5: Kinetics This chapter focuses on the following AP Unit from the College Board: Unit 5: Kinetics

Upon completion of the questions in this section and checking the worked solutions at edvantagescience.com, you should be able to:

Define chemical kinetics. Define reaction rate. Given a chemical reaction, describe a method(s) for measuring or monitoring its rate. Calculate reaction rates from both numerical and graphical data. Convert the rate of consumption or production of one species into that of another. Use reaction rates to calculate the amount of reactant consumed or product formed in a given period of time. Describe how the initial rate of a reaction is determined from graphical data. Determine a reaction’s order with respect to each reactant, its overall order, and its rate law expression, from tabular data. Determine a reaction’s rate constant (k) from tabular data. For first-order reactions, use the integrated rate law to calculate the concentration of a reactant after a given time period or viceversa. For second-order reactions, use the integrated rate law to calculate the concentration of a reactant after a given time period or vice-versa. Describe and explain the kinetics of a zero-order reaction. Determine a reaction’s order (zero, first, or second) and its rate constant through graphical analysis. Calculate the half-life (t½) of a first-order reaction, given the rate constant (k) of the reaction. Describe how each half-life of a zero and a second-order reaction contrasts with the previous half-life. Calculate the half-lives of a zero and a second-order reaction, given the rate constants (k) of the reactions and the reactant concentrations. Define reaction mechanism, elementary process, and molecularity (unimolecular, bimolecular, and termolecular steps). Define a reaction intermediate and identify the reaction intermediate(s) in a reaction mechanism. Identify a catalyst in a reaction mechanism and illustrate how a catalyst may affect a reaction’s potential energy diagram. Algebraically sum the elementary processes in a reaction mechanism to provide the overall reaction. Describe and explain the concept of a rate-determining step. Cite four factors that could be responsible for a step being the ratedetermining step in a mechanism. Define heterogeneous catalysis and homogeneous catalysis and give an example of each. Determine the rate law of a reaction from its mechanism.

External tanks of liquid oxygen and hydrogen fuel react to create the energy needed to launch a rocket carrying the space shuttle. © Edvantage Interactive 2020

Unit 5 Kinetics 39

1. Consider the graph for the following reaction: CaCO3(s) + 2 HCl(aq) → CaCl2(aq) + CO2(g) + H2O(l)

Volume of CO₂ (mL)

Volume of CO₂ vs. Time 50 40 30 20 10 0

Time (min)

Recall the discussion of the instantaneous rate earlier in this section. (a) Determine the instantaneous rate at the following times: (i) an instant after 0 min (This is the initial rate.)

(ii) 1 min

(iv) 4 min

(b) How do these rates compare? What do you suppose causes this pattern?

2. The following systems represent gaseous reactants A (symbolized by ¢) and B (symbolized by n) at a fixed temperature and volume. The equation for the reaction is A(g) + B(g) → C(g).

Assume the rate law for the reaction is: rate = k[A][B]3

System 1 represents a reaction with a rate of 0.010 mol/L/s. Complete the diagrams for the other systems as follows: (a) Adding enough particles of A ¢) to System 2 to represent a system that would react with an initial rate of 0.020 mol/L/s. (b) Adding enough particles of B (n) to System 3 to represent a system that would react with an initial rate of 0.080 mol/L/s. System 1

System 2

System 3

Rate = 0.010 mol/L/s

0.020 mol/L/s

0.080 mol/L/s

40 Unit 5 Kinetics

3. Here is a table indicating the volume of gas collected as a disk of strontium metal reacts in a solution of hydrochloric acid for 1 min. Sr(s) + 2 HCl(aq) → SrCl2(aq) + H2(g) Time (seconds)

Volume of Hydrogen at STP (mL)

10.0

22.0

20.0

40.0

30.0

55.0

40.0

65.0

50.0

72.0

60.0 72.0 (a) Calculate the average rate of reaction in moles of HCl consumed/second over the first 50.0 s. (b) Calculate the mass of strontium consumed in this 50.0 s period.

(d) Why did the volume of gas remain unchanged from 50.0 s to 60.0 s?

Unit 5 Kinetics 41

4. The spectrophotometer works by shining a single wavelength of light through a sample of a colored solution. A photocell detects the amount of light that passes through the solution as % transmittance and the amount of light that does not pass through as the absorbance. The more concentrated the solution, the darker the color. Dark color leads to a lower percentage of light transmitted and thus a higher absorbance. There is a direct relationship between absorbance and the concentration of a colored solution. The “calibration curve” (actually a straight line) below was created using solutions of known Cu(NO3)2 concentration.

1.2 1.0

calibration curve

0.8 Digital Output of 0.6 Absorbance 0.4

visible light source ﬁlter or coloured photocell mirrors, diﬀraction solution lenses grating and slit

0.2 0.0

0.00 0.01 0.02 0.03 0.04 0.05 0.06 Concentration of Cu(NO3)2(mol/L)

A simpli�ed diagram of a colorimeter

A copper sample was reacted with 250 mL of nitric acid by the following reaction:

3 Cu(s) + 8 HNO3(aq) → 3 Cu(NO3)2(aq) + 2 NO(g) + 4 H2O(l)

As the reaction proceeded, small aliquots were removed and placed in a cuvette (the special test tube used to hold a sample in the spectrophotometer). The cuvettes were then placed in the instrument and the absorbances were recorded as follows:

Time (seconds)

Absorbances (no unit)

Concentration of Copper(II) Ion (mol/L)

0 mol/L

20.

0.40

40.

0.70

60.

0.90

80.

1.00

Find the absorbances on the standard graph and record the corresponding concentrations of the copper(II) ions (equal to the concentration of Cu(NO3)2) in the table. (a) Calculate the average rate of the reaction from time 0 s to 80. s in units of M of HNO3(aq)/s.

Continued

42 Unit 5 Kinetics

(b) What mass of Cu(s) will be consumed during the 80. s trial?

5. Use the information in the table below to write the rate-law expression for the reaction, and explain how you obtained your answer. Determine the rate constant with units. 2 NO(g) + O2(g) → 2 NO2(g) Experiment Number

Initial [O2] (mol.L–1)

Initial [NO] (mol.L–1)

Initial Rate of Formation of NO2 (mol.L–1.s–1)

0.0010

0.0020

0.0010

0.0020

6. Consider an imaginary reaction: 2 X + Y → Z. Determine the rate law and the rate constant, with units, from the experimental data in the table below. Initial Rate of Formation of Z (mol.L–1.s–1)

Initial [X]o (mol.L–1)

Initial [Y]o (mol.L–1)

7.0 × 10–4

0.20

0.10

1.4 × 10–3

0.40

0.20

2.8 × 10–3

0.40

4.2 × 10–3

0.60

Unit 5 Kinetics 43

7. We can use pseudo integrated rate analysis when a reaction involves more than one reactant. We use a large excess of one of the reactants to manipulate the system so that the change in the concentration of the excess reactant is negligible. The value of the concentration of the excess reactant is subsumed into the rate constant because it barely changes and is therefore constant within the margin of error. We determine the order with respect to the species that is present in a very small concentration. We refer to the absolute value of the slope of the straight line plot as the pseudo rate constant, k’ (k prime). We determine the actual rate constant by dividing k’ by the [excess]. A student collected the following data during a laboratory study of the substitution reaction: (CH3)3CBr + OH– → (CH3)3COH + Br– with a large excess of OH–. [(CH3)3CBr] mol/L

0 30 60 90

0.100 0.074 0.055 0.041

ln [(CH3)3CBr]

1/[(CH3)3CBr] L mol–1s–1

ln Concentration

1/Concentration (L/mol)

Draw graphs of [(CH3)3CBr] vs. time, ln [(CH3)3CBr] vs. time, and 1/[(CH3)3CBr] vs. time. Is the substitution reaction zero, first, or second order with respect to (CH3)3CBr? What is the value of the pseudo rate constant with units?

Concentration (mol/L)

Time (s)

8. The rate constant for the first order conversion of cyclopropane to propene in a laboratory is 9.0 x 10–4 min–1. (a) What is the half-life of the reaction?

(b) Assuming the initial concentration of the cyclopropane is 1.50 mol/L, what concentration will remain after 51.2 h?

44 Unit 5 Kinetics

9. Nitrogen dioxide decomposes as indicated in the following equation: 2 NO2(g) → 2 NO(g) + O2(g) A student collected the following data for the decomposition at an elevated temperature. Time (s) 0 50. 100. 200. 300. 400.

[NO2] (mol/L) 0.0100 0.0079 0.0065 0.0048 0.0038 0.0032

ln [NO2]

1/[NO2] (L/mol·s)

1/Concentration (L/mol)

ln Concentration

Concentration (mol/L)

(a) Draw three graphs and determine the rate law expression and the rate constant with units for the decomposition of nitrogen dioxide.

Time (s)

(b) How would the straight-line graph change (in general) if: (i) the initial concentration of the nitrogen dioxide were increased?

(ii) the temperature of the decomposition were elevated?

10. The half-life for the decomposition of N2O5 under laboratory conditions is 2.0 min. (a) What is the rate constant for the reaction under these conditions?

(b) What is the concentration of N2O5 270 s after the reaction starts, assuming an initial concentration of 0.180 mol/L?

Unit 5 Kinetics 45

For the following reaction mechanisms in question 11, determine the overall reaction and identify all catalysts and intermediates (some may not have catalysts). Then sketch a potential energy diagram for the reaction. Indicate Ea for the overall reaction. A numerical value is not expected. 11. O3(g) → O2(g) + O(g)

(slow)

O(g) + O3(g) → 2 O2(g)

(∆H value for entire reaction = –284.6 kJ/mol)

12. The reaction of the iodide ion and the hypochlorite ion is an oxidation-reduction reaction occurring in basic solution: I–(aq) + OCl–(aq) → IO–(aq) + Cl–(aq) (basic)

The three-step mechanism is represented as follows:

fast-forward reversible: OCl–(aq) + H2O(l)  HOCl(aq) + OH–(aq) 

rate-determining step: I–(aq) + HOCl(aq) → HIO(aq) + Cl–(aq)

HIO(aq) + OH–(aq) → H2O(l) + IO–(aq)

(a) Show how the above steps combine mathematically to give the overall reaction. Identify all intermediates and catalysts. (Show work directly on the mechanism provided.) (b) Show that the mechanism provided gives the rate law: rate = k[I–][OCl–][OH–]–1 (Note: Because this redox reaction is occurring in a basic solution, [OH–] can appear in the rate law expression.)

46 Unit 5 Kinetics

Unit 6: Thermochemistry This chapter focuses on the following AP Unit from the College Board: Unit 6: Thermodynamics

Upon completion of the questions in this section and checking the worked solutions at edvantagescience.com, you should be able to: Differentiate between, and provide examples of, state functions and pathway dependent functions. State the first law of thermodynamics. Calculate the change of internal energy (ΔE) of a system from the heat (q) absorbed or released by the system and the work (w) performed by or on the system. For a chemical system at constant pressure, calculate ΔE from ΔH and values that allow you to calculate pressure-volume work (w). State standard state conditions. Derive a reaction’s ΔH using Hess’ Law of Heat Summation. Derive a reaction’s ΔH using Standard Enthalpies of Formation. Derive a reaction’s ΔH using Average Bond Energies. Define temperature, heat, and specific heat. Name and describe 3 types of intermolecular forces (IMF’s). Define heat of fusion, heat of solidification, heat of vaporization, and heat of condensation. Calculate the heat required to raise the temperature and/or change the state of a given amount of a substance. Calculate the final temperature when a hotter material and a colder material are combined. Calculate the heat released or absorbed in a calorimeter when provided with the calorimetric data. Discuss some advantages and disadvantages of fossil fuels and cite some alternative energy sources. Define entropy. Describe some factors that influence a particle’s or compound’s entropy. Predict whether entropy increases or decreases during certain reactions by using factors that commonly govern entropy change. Cite the two thermodynamic “drives” that determine an equilibrium’s position (far left, somewhat centered, far right) Predict an equilibrium’s position from its thermodynamics and vice-versa. Define a spontaneous process and relate that to chemical equilibrium

Unit 6 Thermochemistry 47

1. The complete decomposition of NOCl gas into its elements occurs by the following reaction:

2 NOCl(g) ➝ N2(g) + O2(g) + Cl2(g)

Use the following two reactions and their enthalpy changes to determine the enthalpy change for the decomposition reaction.

½ N2(g) + ½ O2(g) ➝ NO(g)

ΔHf = 90.3 kJ/molf

NO(g) + ½ Cl2(g) ➝ NOCl(g)

ΔHrxn = –38.6 kJ/molrxn

2. Polyvinyl chloride is commonly referred to as PVC. It is a polymer produced from a monomer formed by the addition of ethylene and chlorine gas. Use the following reactions and their enthalpy changes to determine the overall enthalpy change for the PVC monomer reaction:

H2(g) + Cl2(g) ➝ 2 HCl(g) ΔHf = –184.6 kJ/molrxn C2H4(g) + HCl(g) ➝ C2H5Cl(l) ΔHrxn = –65.0 kJ/molrxn C2H3Cl(g) + H2(g) ➝ C2H5Cl(l) ΔHrxn = –138.9 kJ/molrxn C2H4(g) + Cl2(g) ➝ C2H3Cl(g) + HCl(g) ΔHrxn = (?)

3. Given the following data (all species are gases):

2 O3 ➝ 3 O2 ΔHdiss = –427 kJ/molrxn O2 ➝ 2 O

ΔHdiss = 495 kJ/molrxn

NO + O3 ➝ NO2 + O2 ΔHrxn = –199 kJ/molrxn

Calculate the enthalpy change for the following reaction: NO + O ➝ NO2

48 Unit 6 Thermochemistry

Table: Examples of Heats of Formation

NH3(g) –45.9 kJ/mol C(s) [diamond] 1.896 N2O5(g) 11.0 CO2(g) –393.5 C2H4Cl2(g) –166.8 C2H5Cl(g) –112.2 C2H6(g) –84.7 C2H4(g) 52.5 HCl(g) –92.3 H2S(g) –20.2 CH4(g) –74.9 CH3OH(l) –238.6

NO(g) 90.3 kJ/mol NO2(g) 33.2 C3H8(g) –105.0 PF5(g) –1594.4 NaHCO3(s) –947.4 Na2SO4(aq) –1387.1 SO2(g) –296.8 SO3(g) –396.0 H2SO4(aq) –907.5 H2O(g) –241.8 H2O(l) –285.8 ZnO(s) –348.0

Use the values in the Table Examples of Heats of Formation above to solve the practice problems below:

4. Determine the enthalpy change for each of the following reactions: (a) C3H8(g) + H2(g) ➝ C2H6(g) + CH4(g)

(b) 2 H2S(g) + 3 O2(g) ➝ 2 SO2(g) + 2 H2O(l)

5. Use the following information along with the tabular data to calculate the molar enthalpy of formation of ZnS(s). 2 ZnS(s) + 3 O2(g) ➝ 2 ZnO(s) + 2 SO2(g) ΔH of= – 878.2 kJ/molrxn

Unit 6 Thermochemistry 49

Table: Average Bond Energy (KJ/mol)

Bond

Energy

Bond

Energy

Bond

Energy

Bond

Energy

H–H H–F H–Cl H–Br H–I

432 565 427 363 295

Si–H Si–Si Si–O Si–S Si–F Si–Cl Si–Br Si–I

323 226 368 226 565 381 310 234

347 266 327 271 218 ~170

413 347 301 305 358 264 259 453 339 276 216

391 160 209 201 272 200 243 159

S–H S–S S–F S–Cl S–Br S–I

C–H C–C C–Si C–N C–O C–P C–S C–F C–Cl C–Br C–I

N–H N–N N–P N–O N–F N–Cl N–Br N–I O–H O–P O–O O–S O–F O–Cl O–Br O–I

467 351 204 265 190 203 234 234

P–H P–Si P–P P–F P–Cl P–Br P–I

320 213 200 490 331 272 184

F–F F–Cl F–Br F–I Cl-Cl Cl-Br Cl-I Br–Br Br–I I–I

159 193 212 263 243 215 208 193 175 151

N=N N=O O2

418 607 498

C≡C C≡N C≡O

839 891 1070

N≡N

945

Single Bonds

Multiple Bonds C=C C=N C=O

614 615 745 (799 in CO2)

Use the Table Average Bond Energy (KJ/mol) to produce a full thermochemical equation for each of the molecular representations below. 6.

+ H

➔

H H H H—C—C—C—H + 5 O==O

3 O==C==O + 4 H—O—H

H H H

H H—C—O—H + 1½ O= O H

(g)

50 Unit 6 Thermochemistry

(g)

O=C=O +

(g)

O O

H (g)

9. Aluminum metal is commonly used to determine the temperature of different portions of a Bunsen burner flame. Calculate the heat required to completely melt a 0.325 g piece of aluminum wire beginning at a room temperature of 22.5°C. The melting point of aluminum is 660.3°C and its heat of fusion is 398 J/g. Refer to Table 4.6.1 for the specific heat capacity.

10. A piece of iron metal initially at a room temperature of 21.5°C is left on the window ledge in the lab on a sunny day. It absorbs 862.4 J of heat and warms to 32.5°C. What is the mass of the iron? See Table 4.6.1.

11. A 75.45 g sample of silicon initially at 20.5°C absorbs 1326 J of heat. What is the final temperature of the sample? See Table 4.6.1.

12. Calculate the heat required to change a 55.00 g ice cube at –15.0°C into steam at 125.0°C. (Hint: There should be five different q values in your calculation.)

13. A 29.65 g solid gold earring at 33.5°C falls from your ear into a thermally isolated 245.0 mL cup of 65.5°C coffee. Use information from the Table 4.6.1 to determine the final temperature of the earring and the coffee when they reach the same temperature (thermal equilibrium). Assume the specific heat capacity and the density of the coffee is the same as those of water and that the final temperature will be between the initial temperatures.

Unit 6 Thermochemistry 51

14. A brass ball bearing with an initial temperature of 95.55°C is placed in a thermally insulated beaker containing 125.0 mL of water (assume dwater = 1 g/mL exactly) at 20.50°C. When the two substances reach thermal equilibrium, their final temperature is 26.55°C. What is the mass of the brass ball bearing?

15. What is the final temperature when a 348.00 g block of ice at –44.5°C is added to 95.00 g of steam at 125.5°C in an insulated system? Assume the final result will be liquid water.

16. When 500.0 mL of 2.00 mol/L Ba(NO3)2 solution at 22.50°C is combined in a coffee cup calorimeter with 500.0 mL of 2.00 mol/L Na2SO4 solution also at 22.50°C, a white precipitate forms and the temperature of the mixture rises to 25.60°C. Assume the calorimeter materials absorb only a negligible quantity of heat and the final solution’s density and specific heat capacity are identical to those of water. Calculate the molar enthalpy of precipitation of BaSO4(s).

17. A coffee cup calorimeter contains 50.00 g of water at 20.73°C. When 2.13 g of NH4NO3 pellets are stirred into the water, the temperature falls to 17.41°C. Assume the heat capacity of the resulting solution is the same as that of water and that no energy is absorbed or released from or to the surroundings. Calculate the molar enthalpy of dissolution of ammonium nitrate, a chemical commonly used in the production of cold packs.

18. Given: 2 HCl(aq) + Ba(OH)2(aq) ➝ BaCl2(aq) + 2 H2O(l) + 118 kJ/molrxn. Calculate the heat released when 300.0 mL of 0.500 mol/L hydrochloric acid is combined with 100.0 mL of 1.00 mol/L of barium hydroxide. Assume that the temperature of both solutions is initially 21.55°C. The final mixture has a mass of 400.0 g and a heat capacity the same as that of water with negligible heat “leakage” to or from the system. What is the final temperature of the mixture?

52 Unit 6 Thermochemistry

19. A 3.00 g chunk of coal, C(s), was burned entirely to produce CO2(g) in a copper bomb. The mass of the bomb was 2.000 kg and the mass of water in which the copper bomb was immersed was 2.778 kg. The initial temperature of the system was 21.00°C and the final temperature was 29.30°C. Calculate the heat of formation of CO2(g). See Table 4.6.1 for the specific heat capacity of copper.

20. Toluene, C7H8 may be tri-substituted with nitro groups, –NO2, to form the explosive, trinitrotoluene or TNT. A 750.0 mg sample of toluene liquid was placed in a bomb calorimeter with excess oxygen. The heat capacity of the calorimeter was 22.53 kJ/°C. When the calorimeter was fired, the combustion of the toluene caused the temperature to increase from 23.002°C to 24.415°C. Calculate ΔH for the reaction: C7H8(l) + 9 O2(g) ➝ 7 CO2(g) + 4 H2O(l).

21. (a) A standard calibration reaction is used to determine the heat capacity, C, of a bomb calorimeter. The temperature increases 1.275°C because of the input of 14 580 J of energy. What is the heat capacity of the calorimeter?

(b) Use the data in the table of heats of formation (Table 4.5.1) to calculate the ΔHcombustion of methane, CH4(g).

(c) A sample of 1.754 g of methane is combusted in the calorimeter calibrated in part (a). If the initial temperature of the calorimeter is 20.754°C, what final temperature should be attained?

Unit 6 Thermochemistry 53

22. For each of the following state whether entropy is increasing or decreasing and briefly state your reasoning. (a) 2 NH3(g) → N2(g) + 3 H2(g)

(b) NOCl2(g) + NO(g) → 2 NOCl(g)

(d) H2(g) + Cl2(g) → 2 HCl(g)

(e) WO3(s) + 3 H2(g) → W(s) + 3 H2O(g)

23. State whether each of the following reactions will achieve equilibrium with a reasonable amount of reactants and products, go almost to completion, or virtually not occur. (a) 4 NH3(g) + 5 O2(g) → 4 NO(g) + 6 H2O(g) ΔH = –907.2 kJ/mol

(b) N2(g) + 2 O2(g) → 2 NO2(g)

ΔH = +68 kJ/mol

(d) S(s) + O2(g) → SO2(g) ΔH = –297 kJ/mol

24. For the following reaction, state whether the forward reaction is endothermic or exothermic, given that the two thermodynamic drives are opposed to each other. Explain your reasoning. CaCO3(s)



CaO(s) + CO2(g)

25. Describe the thermodynamics of a reaction that establishes equilibrium so far toward reactants that it is said to virtually not occur.

26. The following equilibrium has a reasonable proportion of reactants and products. State whether entropy is increasing or decreasing during the forward reaction. Explain your reasoning. CO2(g) + NO(g)



NO2(g) + CO(g)

54 Unit 6 Thermochemistry

ΔH = +82 kJ/mol

Unit 7: Equilibrium This chapter focuses on the following AP Unit from the College Board: Unit 7: Equilibrium

Upon completion of the questions in this section and checking the worked solutions at edvantagescience.com, you should be able to:

Use Le Chatelier’s principle to describe how an equilibrium system will respond to changing its volume. Explain in terms of forward and reverse reaction rates how an equilibrium system will respond to changing its volume. Use Le Chatelier’s principle to describe how an equilibrium system will respond to changing its temperature. Explain in terms of forward and reverse reaction rates how an equilibrium shifts in response to changing temperature. Describe the Haber-Bosch Process and discuss how chemists regulate its reacting conditions to optimize its production rate. State the equilibrium law and determine a reaction’s equilibrium constant (Keq) from its equilibrium concentrations. Relate a reaction’s equilibrium constant to its equilibrium position. State the only change of conditions that will change a chemical equation’s equilibrium constant. Determine the equilibrium expression for a chemical equation. Determine the equilibrium constant for a chemical equation given the equilibrium constant for the reverse equation or the same equation with different coefficients. Determine the direction a system will proceed to achieve equilibrium, given its reactant and product concentrations and its Keq. Recognize equilibria that do not strictly abide by Le Chatelier’s principle. Calculate a reaction’s equilibrium constant, given the initial concentrations of the reactants and any one reactant’s or product’s equilibrium concentration. Calculate a reaction’s equilibrium concentrations, given its equilibrium constant and the initial concentrations of its reactants. Calculate a reaction’s initial concentrations, given its equilibrium constant and any one reactant’s or product’s equilibrium concentration. Calculate Kp for a gaseous equilibrium, given the partial pressures of its reactants and products at equilibrium or given its Kc.

When the number of shoppers travelling between the two floors on the escalators is equal, the crowd has reached equilibrium.

Unit 7 Equilibrium 55

1. Complete the following plots. The system below is at equilibrium prior to t1. The system is suddenly cooled at t1. The system responds to this stress between t1 and t2 until it re-equilibrates at t2. N2O4(g) + 57 kJ

1.2 [NO2]



2 NO2(g)

1.0 0.8 0.6

[N2O4] 0.4 0.2 0.0

Time

2. Show how the forward and reverse reaction rates respond to a sudden increase in the temperature of the system below at t1. Use a solid line for the forward rate and a dotted line for the reverse rate. The system restores equilibrium at t2. The arrow diagram on the right is another way of depicting the same information. You may use it to do your rough work. Ni(s) + 4 CO(g)  Ni(CO)4(g) ΔH = –603 kJ/mol

Rate

Ef t1

Time

3. Co(H2O)62+(aq) + 2 Cl−(aq) pink



Co(H2O)4Cl2(aq) + 2 H2O(l) purple

A flask containing the above equilibrium turns from purple to pink when cooled. State whether the forward reaction is endothermic or exothermic. Explain how you arrived at your answer.

56 Unit 7 Equilibrium

4. Explain in terms of forward and reverse reaction rates how the equilibrium below responds to a decrease in temperature: N2(g) + 3 H2(g)  2 NH3(g) ΔH = –92.4 kJ/mol

5. Why is an equilibrium’s endothermic direction more sensitive to temperature changes than its exothermic direction?

6. What conditions of temperature and pressure favor products in the following reaction: PCl5(g)



PCl3(g) + Cl2(g)

ΔH = 238 kJ/mol

7. Briefly describe the conflicting factors that chemists face when choosing a temperature to perform the Haber-Bosch process.

8. Consider the system below. When equilibrium is restored, how will the number of each type of molecule and the concentration of each substance compare to those before the stress was introduced? Complete the following table using the words “decrease,” “same,” or “increase.” 2 NH3(g)



N2(g) + 3 H2(g)

Decrease Volume

ΔH = 92.4 kJ/mol Decrease Temperature

N2 Equilibrium concentration

H2 NH3 N2

Equilibrium number

H2 NH3

Unit 7 Equilibrium 57

9. The graph below shows how forward and reverse reaction rates change as an exothermic reaction goes from initiation to equilibrium. Plot the forward and reverse reaction rates for the same reaction at a higher temperature. Rate (forward and reverse) vs. Time for a Reaction as It Approaches and Achieves Equilibrium

Rate (mol/s)

rr 0

15 20 Time (s)

10. Nitric acid is produced commercially by the Ostwald process. The first step of the Ostwald process is: 4 NH3(g) + 5 O2(g)



4 NO(g) + 6 H2O(g) + energy

In which direction will the above system shift in the following situations: (a) Some NO is added.

(b) Some NH3 is removed.

(d) The temperature of the system is decreased. 11. A piston supported by gas trapped in a cylinder is a fixed pressure apparatus. As long as the gas in the cylinder is supporting the same piston then its pressure must be constant because it is exerting the same force over the same bottom surface of the piston. If the piston weighs more, then the fixed pressure is greater. Consider the following equilibrium system trapped in a cylinder: PCl5(g)  PCl3(g) + Cl2(g) (a) In which direction will the system shift when some weight is added to the piston? (b) How would this shift affect the apparatus?

58 Unit 7 Equilibrium

12. Complete the following review table.

N2(g) + 3 H2(g) Stress Add H2



2 NH3(g)

ΔH = –92.4 kJ/mol

Le Châtelier Predicts Response

Chemical Kinetics Explains Shift

Effect

Net Rx

some of the added H2 removed

Add NH3

left

Remove N2

rf decreases

Decrease volume (compress)

net forward rx rr decreases more than rf

Decrease temperature

13. Holding the temperature and pressure constant when a reactant or product is added to an equilibrium system is easier said than done. Some SO3 is added to the following system. Its temperature and pressure are not fixed. 2 SO2(g) + O2(g)



2 SO3(g) + 198 kJ/mol

(a) In which direction will the system shift in response to the added SO3?

(b) In which direction will the system shift in response to the small change in pressure resulting from the added SO3?

(c) In which direction will the system shift in response to the small change in temperature resulting from the increased pressure?

(d) In which direction will the system's shift in response to the change in temperature resulting from the system’s shift to the added SO3?

Unit 7 Equilibrium 59

14. 2 NOCl(g)



Keq = 8.0 × 10−2 at 462°C

2 NO(g) + Cl2(g)

For each of the following, what is the Keq at 462°C? (a) NOCl(g)



NO(g) + ½ Cl2(g)

(b) 2 NO(g) + Cl2(g)



2 NOCl(g)



NOCl(g)

Concentration

15. A + B



AB + 16.8 kJ/mol

B A t1

t2 Time

(a) In which direction is the equilibrium system shifting?

(b) What specifically was done to this system at t1?

60 Unit 7 Equilibrium

16. How would each of the following stresses affect the equilibrium constant, Keq, for:

2 CO(g) + O2(g)



2 CO2(g)

ΔH = –31 kJ/mol

(a) Add some CO2(g)?

(b) Decrease the volume of the reaction vessel (at a constant temperature)?

(d) Add a catalyst?

17. Can you infer that reactants are favored in the reaction below because Keq < 1? Explain. C(s) + H2O(g)



CO(g) + H2(g)

Keq = 0.16

18. Consider the following two equilibria: (a) 2 SO3(g)  2 SO2(g) + O2(g) Keq = 0.25 (b) PCl5(g)



PCl3(g) + Cl2(g)

Keq = 0.50

Given that their initial reactant concentrations are equal, can you infer from their equilibrium constants that the first equilibrium has a lower percent yield than the second equilibrium? Explain.

Unit 7 Equilibrium 61

19. The following gases were placed in a 4.00 L flask: 8.00 mol N2 and 10.00 mol H2. After equilibrium was achieved, 1.20 M NH3 was found in the flask. Complete the ICE table below and determine the equilibrium constant, Keq. N2(g)

3 H2(g)



2 NH3(g)

I C E

20. Equal volumes of 1.60 M Ag+ and 2.60 M S2O32− were mixed. The [Ag(S2O3)23−] at equilibrium was 0.35 M. Complete the ICE table below and determine Keq. (Reminder: Whenever you mix aqueous solutions, there is a dilution effect. Mixing equal volumes doubles the solution’s volume and halves the concentration of both solutes.) Ag+(aq)

2 S2O32−(aq)



Ag(S2O3)23− (aq)

I C E 21. A sample of 6.0 g of carbon was placed in a 1.0 L flask containing 1.4 mol O2. When equilibrium is established, 1.2 g of carbon remains. Determine Keq. (Note: Because carbon is a solid it is crossed out in the ICE table but the moles of carbon consumed must be calculated — outside the ICE table — to determine the equilibrium concentrations of O2 and CO.) 2 C(s)

O2(g)



2 CO(g)

I C E

62 Unit 7 Equilibrium

22. In the lab, 4.5 mol of HCl(g) are pumped into a 3.00 L flask and heated to 80°C. How many moles of Cl2 will be found in the flask after equilibrium is established? Keq at 80°C = 0.36

2 HCl(g)



H2(g)

Cl2(g)

E 23. As part of an experiment, 4.00 mol H2, 4.00 mol C2N2, and 8.00 mol HCN are injected into a 2.00 L flask where they establish equilibrium. What is the [C2N2] when equilibrium is achieved? Keq = 5.00 H2(g)

C2N2(g)



2 HCN(g)

24. The table below shows the molarity of three gases at equilibrium. The concentration of HCl is then decreased as shown. What is the [HCl] when equilibrium is re-established?

H2(g)

Cl2(g)



2 HCl(g)

6.00

12.0

6.00

5.00

Unit 7 Equilibrium 63

25. NiS reacted with O2 in a 2.0 L flask. When equilibrium was achieved 0.36 mol of SO2 were found in the flask. What was the original [O2] in the flask? Keq = 0.30

2 NiS(s)

3 O2(g)  2 SO2(g) +

2 NiO(s)

26. Some HI is pumped into a flask. At equilibrium, the [HI] = 0.60 mol/L. What was the initial [HI]? Keq = 0.25

2 HI(g)

 H2(g) +

I2(g)

27. Some SO2 and O2 are injected into a flask. At equilibrium, the [SO2] = 0.050 M and the [O2] = 0.040 M. What was the initial [O2]? Keq = 100

2 SO2(g) + O2(g)



2 SO3(g)

64 Unit 7 Equilibrium

Unit 7: Solubility Equilibrium This chapter focuses on the following AP Units from the College Board: Unit 7: Equilibrium.

Upon completion of the questions in this section and checking the worked solutions at edvantagescience.com, you should be able to: Use the Solubility Table to determine whether an ionic solid is soluble or has low solubility. Write the formula equation, complete ionic equation, and net ionic equation for a precipitation reaction. State 3 techniques for identifying ions in solution. Identify what ions might be present in a solution from the results of precipitation trials, e.g. precipitates with SO42− but not with OH−. Devise a selective precipitation scheme to separate different types of ions from solution (e.g. SO42− from S2−) by precipitating them one at a time. Describe a technique that may be used to identify precipitates. Describe possible causes of, harms of, and treatments for hard water. Define the solubility product constant (Ksp). Determine the Ksp of a compound from its solubility. Determine the solubility of a compound from its Ksp. Determine whether a precipitate will form from a solution’s ion concentrations. Calculate the maximum concentration of any ion that can coexist in a solution containing known concentrations of other ions. Describe and explain the common ion effect. Calculate the solubility of a compound in a solution containing a common ion.

A patient must ingest a solution of barium sulfate for the large intestine (shown here) to be visible on an X-ray. The small solubility product, or Ksp , of BaSO4 means humans can safely ingest the suspension.

Unit 7 Solubility Equilibrium 65

1. Describe a process to individually remove the ions Ag+, Ba2+, and Be2+ from a solution. Be sure to list the compounds that you add in order, and the method of removing the precipitate. You may wish to use a flow chart.

2. Describe a process to individually remove the ions Br−, SO42–, and S2– from a solution. Be sure to list the compounds that you add in order, and the method of removing the precipitate.

3. Describe a process to individually remove the ions OH−, PO43–, and S2– from a solution. Be sure to list the compounds that you add in order, and the method of removing the precipitate.

4. Consider a solution that may contain Pb2+, Ag+, and Cu2+. Devise a qualitative analysis scheme to confirm the presence of each ion in solution. Remove each ion individually from solution.

5. A solution contains carbonate and phosphate ions. How could you remove these two ions individually from solution?

66 Unit 7 Solubility Equilibrium

6. Calculate the Ksp for each of the following. (a) CaCO3 has a solubility of 6.1 × 10–5 M.

(b) Mn(OH)2 has a solubility of 3.6 × 10–5 M.

(d) The solubility of silver oxalate is 0.033 g/L.

7. A student prepares a saturated solution by dissolving 5.5 × 10–5 mol of Mg(OH)2 in 500. mL of solution. Calculate the Ksp of Mg(OH)2.

8. A student evaporated 150. mL of a saturated solution of MgC2O4. If 0.16 g of solute remains, calculate the Ksp.

Unit 7 Solubility Equilibrium 67

9. Calculate the solubility of the following: (a) silver chloride in mol/L

(b) iron (II) sulfide in g/mL

(d) strontium fluoride in g/L

10. What is the concentration of hydroxide in a saturated solution of iron(III) hydroxide? Hint: Write out the dissociation equation and Ksp expression first. This example is different than the ones shown.

11. What mass of calcium oxalate is dissolved in 650. mL of saturated solution?

12. Will a precipitate form when 8.5 mL of 6.3 × 10–2 M lead(II) nitrate is added to 1.0 L of 1.2 × 10–3 M sodium iodate?

13. Will a precipitate form when 1.5 mL of 4.5 × 10–3 M ammonium bromate is added to 120.5 mL of 2.5 × 10–3 M silver nitrate?

68 Unit 7 Solubility Equilibrium

14. No precipitate forms when 24 mL of 0.17 M sodium fluoride is added to 55 mL of 0.22 M cadmium nitrate. From this information, what can you conclude about the numerical value for the Ksp of CdF2? (State the Ksp value as a range.)

15. Calculate the maximum [Sr2+] that can exist in solutions of the following: (a) 0.045 M sodium fluoride (Remember to consider the source of the fluoride ion.)

(b) 2.3 × 10–4 M lithium carbonate

16. Sodium carbonate may be added to hard water to remove the Mg2+ ions. What mass of sodium carbonate is required to soften 10.0 L of hard water containing 3.2 × 10–3 M Mg2+? (Assume no volume change occurs.)

17. What is the maximum [Ag+] that can exist in a saturated solution of PbI2?

Unit 7 Solubility Equilibrium 69

18. Consider a saturated solution of AgCl. (a) How can you change the Ksp for AgCl?

(b) How can you change the solubility of AgCl?

19. List two substances that would decrease the solubility of Mg(OH)2. Use Le Châtelier’s principle to explain each.

20. List two substances that would increase the solubility of Mg(OH)2. Use Le Châtelier’s principle and a Ksp expression to explain each.

21. Calculate the molar solubility of silver iodate in 0.12 M sodium iodate.

22. Calculate the molar solubility of lead(II) iodide in 0.10 M KI.

23. Calculate the solubility (in g/L) of barium sulfate in 0.050 M barium nitrate.

70 Unit 7 Solubility Equilibrium