Chemistry_Grade_10-12 (1).pdf

Exercise the ideal gas equation 1 an unknown gas has

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Exercise: The ideal gas equation 1. An unknown gas has pressure, volume and temperature of 0.9 atm, 8 L and 120 C respectively. How many moles of gas are present? 2. 6 g of chlorine (Cl 2 ) occupies a volume of 0.002 m 3 at a temperature of 26 C. What is the pressure of the gas under these conditions? 3. An average pair of human lungs contains about 3.5 L of air after inhalation and about 3.0 L after exhalation. Assuming that air in your lungs is at 37 C and 1.0 atm, determine the number of moles of air in a typical breath. 4. A learner is asked to calculate the answer to the problem below: Calculate the pressure exerted by 1.5 moles of nitrogen gas in a container with a volume of 20 dm 3 at a temperature of 37 C. The learner writes the solution as follows: V = 20 dm 3 n = 1.5 mol R = 8.3 J.K 1 .mol 1 T = 37 + 273 = 310 K p = nRT, therefore p = nRV T = 1 . 5 × 8 . 3 × 20 310 = 0.8 kPa (a) Identify 2 mistakes the learner has made in the calculation. (b) Are the units of the final answer correct? (c) Rewrite the solution, correcting the mistakes to arrive at the right answer. 8.7 Molar volume of gases It is possible to calculate the volume of a mole of gas at STP using what we now know about gases. 1. Write down the ideal gas equation 145
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8.8 CHAPTER 8. THERMAL PROPERTIES AND IDEAL GASES - GRADE 11 pV = nRT, therefore V = nRT p 2. Record the values that you know, making sure that they are in SI units You know that the gas is under STP conditions. These are as follows: p = 101.3 kPa = 101300 Pa n = 1 mole R = 8.3 J.K 1 .mol 1 T = 273 K 3. Substitute these values into the original equation. V = nRT p V = 1 mol × 8 . 3 J.K 1 .mol 1 × 273 K 101300 Pa 4. Calculate the volume of 1 mole of gas under these conditions The volume of 1 mole of gas at STP is 22.4 × 10 3 m 3 = 22.4 dm 3 . 8.8 Ideal gases and non-ideal gas behaviour In looking at the behaviour of gases to arrive at the Ideal Gas Law, we have limited our ex- amination to a small range of temperature and pressure. Most gases do obey these laws most of the time, and are called ideal gases , but there are deviations at high pressures and low temperatures . So what is happening at these two extremes? Earlier when we discussed the kinetic theory of gases, we made a number of assumptions about the behaviour of gases. We now need to look at two of these again because they affect how gases behave either when pressures are high or when temperatures are low. 1. Molecules do occupy volume This means that when pressures are very high and the molecules are compressed, their vol- ume becomes significant. This means that the total volume available for the gas molecules to move is reduced and collisions become more frequent. This causes the pressure of the gas to be higher than what would normally have been predicted by Boyle’s law (figure 8.6). ideal gas real gas Volume Pressure Figure 8.6: Gases deviate from ideal gas behaviour at high pressure.
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