Chapter 5: States of matter
An ideal gas will have a volume that varies exactly in proportion to its temperature and exactly in inverse proportion to its pressure. QUESTION 4 Some chemical reactions involving gases are performed in sealed glass tubes that do not melt at high temperatures. The tubes have thin walls and can easily break. Use the kinetic theory of gases to explain why the tubes should not be heated to high temperatures.
pV = nRT p is the pressure in pascals, Pa V is the volume of gas in cubic metres, m3 (1 m3 = 1000 dm3) m n is the number of moles of gas n = ___ Mr
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R is the gas constant, which has a value of 8.31 J K–1 mol–1 T is the temperature in kelvin, K.
Calculations using the general gas equation
If we know any four of the five physical quantities in the general gas equation, we can calculate the fifth.
Limitations of the ideal gas laws
Scientists have taken accurate measurements to show how the volumes of gases change with temperature and pressure. These show us that gases do not always behave exactly as we expect an ideal gas to behave. This is because real gases do not always obey the kinetic theory in two ways: ■ ■
there is not zero attraction between the molecules we cannot ignore the volume of the molecules themselves.
These differences are especially noticeable at very high pressures and very low temperatures. Under these conditions: ■ ■
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the molecules are close to each other the volume of the molecules is not negligible compared with the volume of the container there are van der Waals’ or dipole–dipole forces of attraction between the molecules attractive forces pull the molecules towards each other and away from the walls of the container the pressure is lower than expected for an ideal gas the effective volume of the gas is smaller than expected for an ideal gas.
QUESTION 5 a What is meant by the term ideal gas? b Under what conditions do real gases differ from ideal gases? Give reasons for your answer.
The general gas equation
For an ideal gas, we can combine the laws about how the volume of a gas depends on temperature and pressure. We also know from page 18 that the volume of a gas is proportional to the number of moles present. Putting all these together, gives us the general gas equation:
WORKED EXAMPLES 1 Calculate the volume occupied by 0.500 mol of carbon dioxide at a pressure of 150 kPa and a temperature of 19 °C. (R = 8.31 J K–1 mol–1) Step 1 Change pressure and temperature to their correct units: 150 kPa = 150 000 Pa; 19 °C = 19 + 273 = 292 K Step 2 Rearrange the general gas equation to the form you require: nRT pV = nRT so V = ___ p Step3 Substitute the figures: nRT V = ____ p 0.500 × 8.31 × 292 = _______________ 150 000 = 8.09 × 10–3 m3 = 8.09 dm3 2 A flask of volume 5.00 dm3 contained 4.00 g of oxygen. Calculate the pressure exerted by the gas at a temperature of 127 °C. (R = 8.31 J K–1 mol–1; Mr oxygen = 32.0) Step 1 Change temperature and volume to their correct units and calculate the number of moles of oxygen. 127 °C = 127 + 273 = 400 K 5.00 3 –3 3 5 dm3 = _____ 1000 m = 5.00 × 10 m m n = ___ Mr 4.00 = ____ 32.0 = 0.125 mol
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