# Chapter 14 - Gas Laws

Chapter 14 Gas Laws Jennie L. Borders Section 14.1 Properties of Gases Compressibility is a measure of how much the volume of matter decreases under pressure. Gases are compressible because the particles are far apart. Solids and liquids are not compressible.

Factors Affecting Gas Pressure The amount of gas, volume, and temperature are factors that affect gas pressure. Gas pressure is based on the speed and frequency of collisions between the particles and the walls of a container. Amount of Gas As the amount of gas in a closed container increases, the gas pressure increases because

there are more collisions. (directly proportional) Volume As the volume of a closed container increases, the gas pressure decreases because there is more room for the particles, so they experience less collisions. (indirectly proportional) Temperature As the temperature of a closed container

increases, the gas pressure increases because the particles speed up causing more collisions. (directly proportional) Section 14.1 Assessment 1. Why is a gas easy to compress? 2. List three factors that can affect gas pressure. 3. Why does a collision with an air bag cause less damage than a collision with a steering wheel? 4. How does a decrease in temperature affect the pressure of a contained gas?

5. If the temperature is constant, what change in volume would cause the pressure of an enclosed gas to be reduced to one quarter of its original value? 6. Assuming the gas in a container remains at a constant temperature, how could you increase the gas pressure in the container a hundredfold? Section 14.2 The Gas Laws Poem I wrote to help you remember the gas laws:

Boyle is the VIP. Charles likes direct TV. Gay and Lussac will TP the house directly next to me. Boyles Law Boyle is the VIP. Boyles law states that for a given mass of gas at constant temperature, the volume of the gas varies inversely (indirectly) with pressure. If volume goes down, then pressure goes up. P1V1 = P2V2

P1 = initial pressure V1 = initial volume P2 = final pressure V2 = final volume Sample Problem A balloon contains 30.0L of helium gas at 103 kPa. What is the volume of the helium when the balloon rises to an altitude where the pressure is only 25.0 kPa. 124L

Practice Problems The pressure on 2.50L of N2O changes from 105 kPa to 40.5 kPa. If the temperature does not change, what will the new volume be? 6.48L A gas with a volume of 4.00L at a pressure of 205 kPa is allowed to expand to a volume of 12.0L. What is the pressure in the container if the temperature remains constant?

68.3 kPa Charles likes direc TV. Charles Law Charles law states that the volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept constant. If temperature goes up, then volume goes up.

V1 = V2 T1 T2 V1 = initial volume T1 = initial temperature **Remember the change V2 = final volume temperature to Kelvin T2 = final temperature K = oC + 273 Sample Problem A balloon inflated in a room at 24oC has a

volume of 4.00L. The balloon is then heated to a temperature of 58oC. What is the new volume if the pressure remains constant? 4.46L Practice Problems If a sample of gas occupies 6.80L at 325 oC, what will its volume be at 25oC if the pressure does not change? 3.39L

Exactly 5.00L of air at -50.0oC is warmed to 100.0oC. What is the new volume if the pressure remains constant? 8.36L Gay and Lussac will TP the house directly next to me. Gay-Lussacs law states that the pressure of a

gas is directly proportional to the Kelvin temperature if the volume remains constant. If temperature goes up, then pressure goes up. Gay-Lussacs Law P1 = P2 T1 T2 P1 T1 P2 T2

= = = = initial pressure initial temperature final pressure final temperature Sample Problem

The gas in an aerosol can is at a pressure of 103 kPa at 25oC. If the can is thrown into a fire, what will the pressure be when the temperature reaches 928oC? 415 kPa Practice Problems A sample of nitrogen gas has a pressure of 6.58 kPa at 539K. If the volume does not change,

what will the pressure be at 211K? 2.58 kPa The pressure in a car tire is 198 kPa at 27 oC. After a long drive, the pressure is 225 kPa. What is the temperature of the air in the tire? 341 K Combined Gas Law The combined gas law includes volume, pressure, and temperature.

You can use the combined gas law to help you memorize the other gas laws. P1V1 = P2V2 T1 P1 = initial pressure V1 = initial volume T2 P2 = final pressure V2 = final volume

T1 = initial temperature T2 = final temperature Sample Problem The volume of a gas-filled balloon is 30.0L at 313K and 153 kPa pressure. What would the volume be at standard temperature and pressure (STP)? 39.5L Practice Problems A gas at 155 kPa and 25oC has an initial volume

of 1.00L. The pressure of the gas increases to 605 kPa as the temperature is raised to 125oC. What is the new volume in mL? 342 mL A 5.00L air sample has a pressure of 107 kPa at a temperature of -50.0oC. If the temperature is raised to 102oC and the volume expands to 7.00L, what will the new pressure be in mmHg? 964.2 mmHg

Section 14.2 Assessment 1. How are the pressure and volume of a gas 2. 3. 4. 5. related at constant temperature? If pressure is constant, how does a change in temperature affect the volume of a gas? What is the relationship between the

temperature and pressure of a contained gas at constant volume? In what situations is the combined gas law useful? A given mass of air has a volume of 6.00L at 101 kPa. What volume will it occupy at 25.0 24.2 Ldoes not change? kPa if the temperature Section 14.3 Ideal Gas Law The ideal gas law allows us to calculate volume,

pressure, temperature, or number of moles of gas. PV = nRT P = pressure (kPa) V = volume (L) n = number of moles (mol) R = ideal gas constant (8.31 L.kPa/mol.K) T = temperature (Kelvin) Sample Problem A deep underground cavern contains 2.24 x 10 6

L of methane gas (CH4) at a pressure of 1.50 x 103 kPa and a temperature of 315K. How many grams of CH4 does the cavern contain? 2.05 x107g CH4 Practice Problems When the temperature of a rigid hollow sphere containing 685L of helium gas is held at 621K, the pressure of the gas is 1.89 x 103 kPa. How many moles of helium does the sphere contain?

251 mol He A childs lungs can hold 2200 mL. How many grams of air do her lungs hold at a pressure of 1.007 atm and a body temperature of 37 oC. (Use 29 g/mol as the molar mass for air.) 2.5g air Ideal vs. Real Gases An ideal gas follows rules that scientists have created and remains in a gas at any temperature

and pressure. (These do not exist) A real gas changes into a liquid or solid at low temperatures and high pressures. Real gases differ most from an ideal gas at low temperatures and high pressures. Section 14.3 Assessment 1. Under what conditions do real gases deviate most from ideal behavior? 2. What is an ideal gas? 3. Determine the volume occupied by 0.582 mol

of a gas at 15oC if the pressure is 81.8 kPa. 17L 4. What pressure is exerted by 0.450 mol of a gas at 25oC if the gas is in a 0.650L container? 1714 kPa Section 14.4 Gases: Mixtures and Movements Daltons law of partial pressures states that, at constant volume and temperature, the total

pressure exerted by a mixture of gases is equal to the sum of the partial pressure of the component gases. PT = P 1 + P 2 + P 3 PT = total pressure P1, P2, and P3 = partial pressures of each gas Sample Problem Air contains oxygen, nitrogen, carbon dioxide, and trace amounts of other gases. What is the

partial pressure of oxygen at 101.3 kPa if the partial pressures of nitrogen, carbon dioxide, and other gases are 79.10 kPa, 0.040 kPa, and 0.94 kPa, respectively? 21.22 kPa Practice Problems Determine the total pressure of a gas mixture that contains oxygen, nitrogen, and helium. The partial pressures are PO2 = 20.0 kPa, PN2 = 46.7 kPa, and PHe = 26.7 kPa.

93.4 kPa A gas mixture containing oxygen, nitrogen, and carbon dioxide has a total pressure of 32.9 kPa. If PO2 = 6.6 kPa and PN2 = 23.0 kPa, what is PCO2? 3.3 kPa Diffusion vs. Effusion Diffusion is the tendency of molecules to move toward areas of lower concentration until concentration is uniform throughout.

During effusion, a gas escapes through a tiny hole in its container. Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass. Grahams Law Grahams law of effusion/diffusion states that the rate of effusion of a gas is inversely proportional to the square root of the gass molar mass.

( )1/2 RateA = molar massB RateB = molar massA

B is always the bigger (more massive) gas. Sample Problem Compare the rates of effusion of helium and nitrogen gas. He effuses/diffuses 2.7 times faster than N2. Practice Problems Compare the rates of effusion of sulfur trioxide and bromine gas.

SO3 effuses/diffuses 1.41 times faster than Br2. Compare the rates of effusion of oxygen gas and carbon dioxide gas. O2 diffuses/effuses 1.17 times faster than CO2. Section 14.4 Assessment 1. In a mixture of gases, how is the total pressure determined? 2. What is the effect of molar mass on rates of diffusion and effusion?

3. What distinguishes effusion from diffusion? How are these processes similar? 4. Explain why the rates of diffusion of nitrogen gas and carbon monoxide are almost identical at the same temperature. THE END

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