Exploration Sum: The Mole: Conversions, Mass Determination

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Exploration Sum: The Mole: Conversions, Mass Determination, & Hydrates This Exploration contains targeted background content to prepare you for performing the exercises in this lesson.

Learning Objectives Define the concept of a mole.

Distinguish between the terms: atomic mass, molecular mass, and molar mass.

Convert between mass, moles, atoms, and molecules.

Define and name hydrates by the number of moles of water held in a compound.

Explore The Mole A single atom or a single molecule is so small that chemists are seldom able to work with one at a time. Even when weighing the smallest quantities of substances, numerous atoms and molecules are present. A unit of measure called a mole is used to combat this problem, allowing for successful work with defined quantities of atoms and molecules. *****A mole (n) is a unit of measure, describing the amount of a chemical substance that contains as many atoms, molecules, or formula units as there are in exactly 12 grams of pure carbon (12C). This amount of particles (6.022 × 1023) is referred to as Avogadro’s number. *****The atomic masses shown on the periodic table are the average masses of the various isotopes of each element, expressed in atomic mass units, or amu. The atomic mass unit was standardized to be equal to exactly 1/12th the mass of one carbon-12 (12C) atom; thus, one 12C atom has a mass of 12.000 amu. However, carbon has three isotopes (12C, 13C, and 14C) that contain six protons each, but the isotopes vary in the number of neutrons. The different number of neutrons leads to variation in the amu of each isotope. Since natural carbon (C) is composed of some of each isotope, it has an average atomic mass of 12.011 amu, as shown on the periodic table in Figure 1.

Figure 1.

Periodic Table of Elements.******The atomic mass (atomic weight) of an element is equal to the mass in grams required to equal 1 mole of the substance.

Because atomic mass units and the mole are defined from the same reference (carbon-12), the value on the periodic table can represent the mass of a single atom in atomic mass units or the mass of a mole of substance in grams. Thus, the atomic mass units shown on a periodic table are numerically equivalent to the ****** molar masses of the elements or the mass in grams of each element that contains one mole of atoms of that element. For example, the element nitrogen has a molar mass of 14.007 grams, thus 1 mole of nitrogen is equal to 14.007 grams. Likewise, the compound H2O has a molar mass of 18.015 (H + H + O = 1.008 + 1.008 + 15.999), thus 1 mole of H2O is equal to 18.015 grams. The mass of one mole of a substance (molar mass) is equal to either its atomic mass expressed in grams (if it is a monoatomic element) or its ******molecular mass expressed in grams (if it is a diatomic element or compound). *************************************************************************** *************************************************************************** **************************************************************Explore Co nversions Molar mass conversions are common calculations in chemistry laboratories. Example calculations are provided below to further explore the relationships between molar masses, moles, grams, and atoms. For each example, assume that a vial contains 12.5 grams of magnesium chloride (MgCl2), and you need to know how many moles and atoms of magnesium and chlorine are in the vial.

Example #1: Calculating the Molar Mass of a Compound

What is the molar mass of MgCl2?

1. Identify the molar mass of each element in the compound using the periodic table. For MgCl2:

Molar mass of Mg=24.305 g Mg=1 mole Mg Molar mass of Cl=35.453 g Cl=1 mole Cl

2. Add the molar mass of each element in the compound together. *****In the compound MgCl2 there is 1 mole of magnesium and 2 moles of chlorine: Molar mass of MgCl2 = 24.305 g/mol + (2×35.453 g/mol) = 95.211 g/mol The molar mass of MgCl2 is 95.211 g MgCl2: 95.211 g MgCl2 = 1 mole MgCl2.

Example #2: Calculating the Number of Moles of a Compound in a Sample How many moles of MgCl2 are present in a sample weighing 12.5 g?

1. Calculate the molar mass of the compound using the periodic table.

From Example #1, the molar mass of MgCl2 is 95.211 g/mol.

2. Use the molar mass to convert the mass (grams) of the sample to moles.

The mass of the MgCl2 sample in this example is 12.5 g.

12.5 g MgCl2 * 1 mol MgCl2/ (divide) 95.211g MgCl2=0.131 mol of MgCl2 There are 0.131 mol of MgCl2 in 12.5 g of MgCl2 Example #3: Calculating the Number of Moles of an Element in a Sample How many moles of Mg are present in 12.5 g MgCl2? How many moles of Cl are present?

1. Calculate the molar mass of the compound using the periodic table. ***From Example #1, the molar mass of MgCl2 is 95.211 g/mol.

2. Use the molar mass to convert the mass (grams) of the sample to moles. ******From Example #2, there are 0.131 mol MgCl2 in a 12.5 g sample.

3. Calculate how many moles of each element are present in the moles of the compound. *****For MgCl2, calculate the number of moles of Mg present in 0.131 mol MgCl2: 0.131 mol MgCl2 *1 mol Mg/ (divide) 1 mol MgCl2 = 0.131 mol of Mg ******* Calculate the number of moles of Cl present in 0.131 mol MgCl2: 0.131 mol MgCl2* 2 mol Cl/ (divide) 1 mol MgCl2= 0.262 mol Cl There are 0.131 mol of Mg and 0.262 mol of Cl in 12.5 g of MgCl2.

Example #4: Calculating the Number of Atoms of an Element in a Sample How many atoms of Mg are present in 12.5 g MgCl2? How many atoms of Cl are present?

1. Calculate the molar mass of the compound using the periodic table. ******From Example #1, the molar mass of MgCl2 is 95.211 g/mol.

2. Use the molar mass to convert the mass (grams) of the sample to moles. ******From Example #2, there are 0.131 mol MgCl2 in a 12.5 g sample.

3. Calculate how many moles of each element are present in the moles of the compound. ******From Example #3, there are 0.131 mol Mg and 0.262 mol Cl in 0.131 mol MgCl2.

4. Apply Avogadro’s number to convert the moles of each element to numbers of atoms.

# 0.131 mol Mg * 6.022 x10^23 atoms/(divide) 1 mol Mg = 7.89 x 10^22 atoms Mg # 0.262 mol Cl * 6.022x 10^23 atoms/ (divide) 1 mol Cl = 1.58 x 10^23 atoms Cl There are 7.89 x 1022 atoms of Mg and 1.58 x 1023 atoms of Cl present in 12.5 g of MgCl2.

********************************************************************* ********************************************************************* ************ Explore Another Example of Converting Grams to Moles Potassium aluminum sulfate (KAl(SO4)2), commonly referred to as alum, has a wide range of uses in industry, cosmetics, cooking, and even taxidermy. How many moles of potassium aluminum sulfate are in a jar containing 10 g of the substance?

First, determine the molar mass of the compound.

Molar mass of KAl(SO4)2=39.098 g/mol + 26.982 g/mol + 2(32.066 g/mol + (4 ×15.999 g/mol)) Molar mass of KAl(SO4)2=66.080 g/mol + 2(96.062 g/mol) Molar mass of KAl(SO4)2=258.204 g/mol *****Next, use the molar mass to convert the grams to moles.

10.0 g KAl(SO4)2 ×1 mol KAl(SO4)2/(divide) 258.204 g KAl(SO4)2 =0.0387 mol of KAl(SO4)2 ******************** The mole is attributed to an 18th century Italian scientist whose full name, Lorenzo Romano Amedeo Carlo Avogadro di Queregna e di Cerreto, fits the long number that now bears his name. The French chemist and Nobel laureate, Jean Baptiste Perrin, proposed that the quantity of molecules be called "Avogadro's Constant." *************************************************************************** Explore Hydrates Hydrates In the experiment, the mole concept is used to determine how many moles of water are present in a sample of hydrated potassium aluminum sulfate. A hydrate is a compound in which water molecules are a part of the crystalline structure. The water is loosely held in the compound and is easily separated from the compound upon heating.

It is important to note that a hydrate is different than a sample that is merely wet.

Hydrates are named by adding the Greek prefixes mono-, di-, tri-, penta-, hexa-, hepta-, etc., to the end of the standard name of the compound, followed by the word "hydrate," to describe moles of water held in the compound. For example: CuSO4⋅5H2O=Copper(II) sulfate pentahydrate MgSO4⋅7H2O=Magnesium sulfate heptahydrate Heating Hydrates The formulas indicate that 1 mole of CuSO4•5H2O contains 1 mole of CuSO4 and 5 moles of H2O; and 1 mole of MgSO4•7H2O contains 1 mole of MgSO4 and 7 moles of H2O. If we were to heat these two hydrates, the water molecules would be released: CuSO4⋅5H2OUpon heating−−−−−−−−→CuSO4+5H2O MgSO4⋅7H2OUpon heating−−−−−−−−→MgSO4+7H2O As shown in the equations, for each mole of hydrated copper (II) sulfate that is heated, 5 moles of water are released, leaving behind 1 mole of copper (II) sulfate. Likewise, for each mole of hydrated magnesium sulfate that is heated, 7 moles of water are released, leaving behind 1 mole of magnesium sulfate.

Experimentation Preview

In this experiment, the mass of three items will be used to calculate the number of moles and atoms of each element present in the chemical compound. In addition, the chemical formula of a hydrated potassium aluminum sulfate (alum) will be determined. By calculating the mass of water released by the hydrated potassium aluminum sulfate after heating and converting the mass of water to moles of water, the chemical formula of the hydrated compound can be determined. In this experiment the hydrated potassium aluminum sulfate (alum) will be heated multiple times, to ensure that all of the water contained in the sample is released.

When the sample is heated and all of the water has been released, the mass of the sample will not change and will remain constant no matter how many additional times the sample is heated. *************************************************************************** *************************************************************************** Experimentation Summary Learning Objectives Calculate the number of moles, molecues, and atoms of a substance.

Calculate the number of moles of water released by a hydrate.

Determine the empirical formula of the hydrate from the formula of the anhydrous compound and experimental data.

 



A. Calculate the moles of anhydrous (dry) KAl(SO4)2 that were present in the sample.

Step 1: Find the mass of the dry anhydrous salt show work: Final weighing – mass of pan = mass of anhydrous salt  Step 2: Find the molar mass of KAl(SO4)2 and show work here  Step 3: Find the moles with work shown: grams of the dry salt divided by the molar mass = moles B. Calculate the ratio of moles of H2O to moles of anhydrous KAl(SO4)2. Note: Report the ratio to the closest whole number.  Show work here: Take the value of the moles of water and divide by the moles of the salt. Round to the nearest whole number C. Write the empirical formula for the hydrated alum, based on your experimental results and answer to Question B.  Hint: if the ratio of moles of H2O to moles of anhydrous KAl(SO4)2 was 4, then the empirical formula would be: KAl(S04)2•4H20. Show your work. 

a). mass of anhydrous salt = Final weighing – mass of pan = 2.4 - 1.3 = 1.1 Molar mass of KAl(SO4)2= 39 + 27 +2(32+4x16) = 258 moles = mass / RFM = 1.1 / 258 = 0.004264 moles b). moles of water...

Calculate the moles of anhydrous (dry) KAl(SO 4 ) 2 that were present in the sample. Step 1: Find the mass of the dry anhydrous salt show work: *************************************************************************** *************************************************************************** The molar mass of carbon dioxide (CO2) is _____.    

44.0 g/mol 47.0 g/mol 43.0 g/mol 42.5 g/mol FEEDBACK Great job!

2. A mole is a unit of measure, describing the amount of a chemical substance that contains as many atoms, molecules, or formula units as there are in exactly 12 grams of pure oxygen.  

True False FEEDBACK Great! A mole is a unit of measure, describing the amount of a chemical substance that contains as many atoms, molecules, and ions as there are in exactly 12 grams of pure carbon.

3. The molar mass of carbon dioxide (CO2) is _____.    

44.0 g/mol 47.0 g/mol 43.0 g/mol 42.5 g/mol FEEDBACK Great job!

4. A mole is a unit of measure, describing the amount of a chemical substance that contains as many atoms, molecules, or formula units as there are in exactly 12 grams of pure oxygen.  

True False FEEDBACK Great! A mole is a unit of measure, describing the amount of a chemical substance that contains as many atoms, molecules, and ions as there are in exactly 12 grams of pure carbon.

5. The first step when converting between mass of a compound and moles of a compound is to determine the molar mass of the compound.  

True False FEEDBACK The first step when converting between mass of a compound and moles of a compound is to determine the molar mass of the compound.The second step is to use the molar mass to convert grams to moles.

6. Water is released from a hydrate by _____.    

heating the hydrate cooling the hydrate adding water to the hydrate none of the above FEEDBACK Great job!

1. There are _____ atoms in 12 grams of pure carbon (12C).    

12.022 x 10 23 6.022 x 10 23 4.023 x 10 23 1.00 x 10 FEEDBACK

23

This question focuses on Learning Objective 1: Define the concept of the mole.

2. One mole of a compound has the mass that is equal to the molecular mass.  

True False FEEDBACK This question focuses on Learning Objective 2: Distinguish between the terms: atomic mass, molecular mass, and molar mass.

3. The element oxygen has a molar mass of 15.999 grams, thus one mole of oxygen is equal to _____ g/mol.    

31.998 23 15.999 x 10 15.999 23 31.998 x 10 FEEDBACK This question focuses on Learning Objective 2: Distinguish between the terms: atomic mass, molecular mass, and molar mass.

4. A hydrate is a compound in which water molecules are a part of the crystalline structure.  

True False

FEEDBACK This question focuses on Learning Objective 4: Define a hydrate, and name hydrates based on the moles of water held in the compound.

5. When copper sulfate heptahydrate is heated, how many moles of water are available to be released?    

1 4 7 9 FEEDBACK Hepta is the prefix for 7, therefore 7 moles of water are released in from copper sulfate heptahydrate. Review Exploration - Hydrates.

This questions focuses on Learning Objective 4: Define a hydrate and name hydrates based on the moles of water held in the compound.

6. The second step in converting between the mass of a compound and moles of a compound is to use the molar mass to convert grams to moles.  

True False FEEDBACK This question focuses on Learning Objective 3: Convert between mass, moles, atoms, and molecules.

7. Calculate the moles of anhydrous CuSO4 present in a sample with 0.5 g CuSO4 at a molar mass of 159.61 g/mol.    

0.00313 0.00853 0.00710 0.00626 FEEDBACK This question focuses on Learning Objective 5: Calculate the number of moles, molecules, and atoms of a substance.

8. Based on the correct answer to question 7, calculate the ratio of moles of H2O to moles of anhydrous CuSO4 if there were 0.085 mols of released H2O.    

12 10 27 5 FEEDBACK This question focuses on Learning Objective 5: Calculate the number of moles, molecules, and atoms of a substance.

9. After heating a sample of hydrated CuSO4, the mass of released H2O was found to be 2.0 g. How many moles of H2O were released if the molar mass of H2O is 18.016 g/mol?    

0.004 0.111 9.031 0.222 FEEDBACK This question focuses on Learning Objective 6: Calculate the number of moles of water released by a hydrate.

10. Based on the correct answer to question 8, what is the empirical formula for hydrated CuSO4?    

CuSO4●27H2O CuSO4●12H2O CuSO4●10H2O CuSO4●H2O FEEDBACK This question focuses on Learning Objective 7: Determine the empirical formula of a hydrate from the formula of an anhydrous compound and experimental data.

Cu (II) sulfate exists as a hydrate. It has many practical uses including use as a fungicide and pesticide. When mixed with chromium and arsenic it forms the wood preservative called CCA. CCA was used in pressure treated wood to protect wood from rotting due to insects and microbial agents. Because CCA treated wood contains toxic heavy metals, its use has been discontinued for home use and children’s play sets.

1. A chemist is given a sample of the CuSO4 hydrate and asked to determine the empirical formula of it. The original sample weighed 42.75 g. After heating to remove the waters of hydration, the sample weighed 27.38 g. Determine the formula for this hydrate.

Expected Answer Mass of water removed = 42.75 g – 27.38 g = 15.37 g Moles of water removed = 15.37 g x 1 mol/18.0 g = 0.854 mols Mass of anhydrous copper sulfate = 27.38 g Moles of anhydrous copper sulfate = 27.38 g x 1 mol/159.55 g = 0.172 mols Moles H2O/mols CuSO4 = 0.854/0.172 = 4.96 = 5 (rounded to whole number) Formula = CuSO4 • 5H2O