Gases Chapter 14

Section 14.1 The Gas Laws

Ideal Gas Remember, these gas laws apply to ideal (perfectly behaved) gases. Ideal gases behave according to the five assumptions made by kinetic molecular theory, and are as follows:

Kinetic Molecular Theory Gas particles do not attract or repel each other. Gas particles are much smaller than the spaces between them. Gas particles are in constant, random motion. No kinetic energy is lost when gas particles collide with each other or with the walls of their container. All gases have the same kinetic energy at a given temperature.

Boyle’s Law At constant temperature, the pressure exerted by a gas depends on the frequency of collisions between the particles and the container. If the same # of particles is squeezed into a smaller space, the # of collisions increases, thereby increasing the pressure.

Boyle’s Law Equation The equation that expresses Boyle’s Law is: P1V1 = P2V2

Example A sample of compressed methane has a volume of 648 mL at a pressure of 503 kPa. To what pressure would the methane have to be compressed in order to have a volume of 216 mL?

Reasonableness To determine whether your answer is reasonable, notice that the gas is being squeezed into a smaller volume, which requires that the pressure is increased.

Practice What pressure will be needed to reduce the volume of 77.4 L of helium at 98.0 kPa to a volume of 60.0 L? A 250.0 mL sample of chlorine gas is collected when the barometric pressure is 105.2 kPa. What is the volume of sample after the barometer drops to 100.3 kPa?

Practice (cont’d) A weather balloon contains 59.5 L of helium at sea level, where the atmospheric pressure is 101.3 kPa. The balloon is released from a 4000 m mountaintop where the pressure is 61.7 kPa. What is the volume of the balloon when it is released? Meteorologists want the balloon in problem 3 to float at an altitude of 35,000 m where the pressure is 575 kPa. What volume will the balloon have at that altitude?

Charles’s Law When the temperature of a sample of gas is increased and the volume is free to change, the pressure of the gas does not increase. Instead the volume of the gas increases, with an increase in the Kelvin temperature. Charles’s Law is expressed as: V1 = V2 T1 T2

Example A weather balloon contains 5.30 kL of helium gas when the temperature is 12 degrees celsius. At what temperature will the balloon’s volume have increased to 6.00 kL?

Practice A sample of SO2 gas has a volume of 1.16 L at a temperature of 23 degrees Celsius. At what temperature will the gas have a volume of 1.25 L? A balloon is inflated with 6.22 L of helium at a temperature of 36 degrees celsius. What is the volume of the balloon when the temperature is 22 degrees celsius?

Practice A student collects a 125.0 mL sample of hydrogen. Later, the sample is found to have a volume of 128.6 mL at a temperature of 26 degrees celsius. At what temperature was the hydrogen collected? A balloon has a volume of 10, 500 L if the temperature is 15 degrees celsius. If the temperature is -35 degrees celsius, what will be the volume of the balloon?

Gay-Lussac’s Law Gay-Lussac’s Law says that when volume is constant, that pressure increases as temperature increases. It can be expressed as: P1= P2 T1 T2 15

The combined Gas Law and Avogadro's principle Section 14.2 The combined Gas Law and Avogadro's principle 16

Combined Gas Law The three gas laws can be combined into a single law, called the combined gas law. This relates pressure, volume, and temperature by the following equation: P1 V1 = P2 V2 T1 T2 17

Using the Gas Law Using this equation, you can find any value as long as you know the other five. 18

Example A sample of nitrogen monoxide has a volume of 72.6 mL at a temperature of 16 ̊C and a pressure of 104.1 kPa. What volume will the sample occupy at 24 ̊C and 99.3 kPa? 19

Practice 9. A sample of ammonia gas occupies a volume of 1.58 L at 22 °C and a pressure of 0.983 atm. What volume will the sample occupy at 1.00 atm and 0 °C? 10. A student collects 285 mL of O2 gas at a temperature of 15 °C and a pressure of 99.3 kPa. The next day, the same sample occupies 292 mL at a temperature of 11 °C. What is the new pressure of the gas? 20

Practice 11. A balloon is inflated with 2.42 L of helium at a temperature of 27 °C. Later, the volume of the balloon has changed to 2.37 L at a temperature of 19 ° C and a pressure of 99.7 kPa. What was the pressure when the balloon was inflated? 21

Avogadro’s Principle According to Avogadro’s principle, equal volumes of all gases at the same temperature and pressure, contain the same number of particles. In other words, at standard temperature and pressure (STP) [0 °C and 1.00 atm] gases occupy a volume of 22.4 L. 22

Example What is the volume of 7.17 g of neon gas at 24 °C and 1.05 atm, if the initial is STP. 23

Practice 12. How many moles of acetylene (C2H2) gas occupy a volume of 3.25 L at STP? Determine the volume of 12.3 g of formaldehyde gas (CH2O) at STP. What is the volume of 1.000 kg of helium gas at 36 °C and a pressure of 98.7 kPa? 24

Section 14.3 The ideal gas law 25

Ideal Gas Law The ideal gas law is a simpler, more convenient way of relating pressure, volume, temperature and the number of moles. PV = nRT In this equation, n is the number of moles and R is the Ideal gas constant. 26

R Values R includes the molar volume correction. It depends on the units that you need for it. R= 8.314 L *kPa = 0.0821 L * atm = 62.4 L * mmHg mol * K mol * K mol * K 27

Example What pressure in atmospheres will 18.6 mol of methane exert when it is compressed in a 12.00 L tank at a temperature of 45 °C? 28

Practice What is the pressure in atmospheres of 10.5 moles of acetylene in a 55.0 L cylinder at 37 °C? What volume does 0.056 mol of H2 gas occupy at 25 °C and 1.11 atm? A sample of carbon monoxide has a volume of 344 mL at 85 °C and a pressure of 88.4 kPa. Determine the amount of moles of CO present. 29

Mass and Ideal Gas Law Remember, that it is possible to calculate the number of moles of a sample when you know the mass using the molar mass. We can also use the ideal gas expression to find the mass. PV = mRT or PVM = mRT M . 30

Example Determine the molar mass of an unknown gas if a sample has a mass of 0.290 g and occupies a volume of 148 mL at 13 °C and a pressure of 107.0 kPa. 31

Practice A 250.0 mL sample of a noble gas collected at 88.1 kPa and 7 °C has a mass of 0.378 g. What is the molar mass of the gas? Identify the sample. What volume is occupied by 1.000 g of H2O vapor at a temperature of 134 °C and a pressure of 0.0552 atm? A 5.25 L tank contains 87.0 g of neon gas. At what temperature will the tank have a pressure of 19.0 atm? 32

Section 14.4 Gas stoichiometry 33

Stoichiometry Just like we can use moles to perform stoichiometric calculations, with gases we can use volumes to perform stoichiometric calculations. 34

2NH3 (g) + H2SO4 (aq)  (NH4)2SO4 (aq) Example 2NH3 (g) + H2SO4 (aq)  (NH4)2SO4 (aq) What volume of NH3 gas, measured at 78 ° C and a pressure of 1.66 atm, will be needed to produce 5.00 X 103 g of (NH4)2SO4? 35

2 Al (s) + 6 HCl (aq)  2AlCl3 (aq) + 3H2 (g) Practice A piece of aluminum with a mass of 4.25 g is used to generate hydrogen gas by the following method. 2 Al (s) + 6 HCl (aq)  2AlCl3 (aq) + 3H2 (g) The hydrogen collected at a temperature of 15 °C and a pressure of 94.4 kPa. What volume of hydrogen is produced? 36