Ch. 14 The Behavior of Gases -...

Ch. 14 The Behavior of Gases

14.1 PROPERTIES OF GASES

Compressibility● Compressibility: a measure of how much

the volume of matter decreases under pressure

● Gases are easily compressed because of the spaces between gas particles

Factors Affecting Gas Pressure● Amount of gas (moles) n● Volume (liters) V● Temperature (Kelvins) T● Pressure (kilopascals) P

Amount of Gas

Volume

Temperature

14.2 THE GAS LAWS

Boyle’s Law● For a given mass of gas at constant

temperature, the volume of the gas varies inversely with pressure

● P1 x V1 = P2 x V2

Sample Problems● Nitrous oxide (N2O) is used as an

anesthetic. The pressure on 2.50 L of N2O changes from 105 kPa to 40.5 kPa. If the temperature does not change, what will the new volume be?

● A gas with a volume of 4.00 L at a pressure of 205 kPa is allowed to expand to a volume of 12.0 L. What is the pressure in the container if the temperature remains constant?

Charles’ Law● The volume of a fixed mass of gas is

directly proportional to its Kelvin temperature if the pressure is kept constant

● V1/T1 = V2/T2

Sample Problems● If a sample of gas occupies 6.80 L at

325⁰ ⁰

● ⁰

● ⁰⁰

Gay-Lussac’s Law● The pressure of a gas is directly

proportional to the Kelvin temperature if the volume remains constant

● P1/T1 = P2/T2

Sample Problems● The pressure in a sealed plastic container

is 108 kPa at 41⁰⁰

●⁰

The Combined Gas Law●  

Sample Problems● A gas at 155 kPa and 25⁰

⁰

●⁰⁰

14.3 IDEAL GASES

Ideal Gas Law● Combining all four factors● P1 x V1 / T1 x n1 = P2 x V2 / T2 x n2● If you know the values for P, V, T, and n

for one set of conditions, you can calculate a value for a constant

● 1 mol of gas occupies 22.4 L at STP (101.3 kPa and 273 K)

● Plugging in these values, R=P x V/T x n = 8.31 (L • kPa)/(K •mol)

Ideal Gas Law● R is the ideal gas constant ◦8.31 (L • kPa)/(K •mol)

● Ideal gas law is written P x V = n x R x T◦ PV=nRT◦ If the gas behaves ideally, this equation can

be used to calculate any 1 of the four factors (R is a constant)

Sample Problems● At 34°C, the pressure inside a

nitrogen-filled tennis ball with a volume of 0.148 L is 212 kPa. How many moles of nitrogen gas are in the tennis ball?

Sample Problems● When the temperature of a rigid hollow

sphere containing 685 L of helium gas is held to 621 K, the pressure of the gas is 1.89 x 103 kPa. How many moles of helium does the sphere contain?

Sample Problems● What pressure will be exerted by 0.450

mol of gas at 25°C if it is contained in a 0.650-L vessel?

● A helium-filled balloon contains 0.16 mol He at 101 kPa and a temperature of 23°C. What is the volume of gas in the balloon?

Sample Problems● A deep underground cavern contains

2.24 x 106 L of methane gas (CH4) at a pressure of 1.50 x 103 kPa and a temperature of 315 K. How many kilograms of CH4 does the cavern contain?

Sample Problems● A child’s lungs can hold 2.20 L. How

many grams of air do her lungs hold at a pressure of 102 kPa and a body temperature of 37°C? Use a molar mass of 29 g for air, which is about 20% O2 (32 g/mol) and 80% N2 (28 g/mol).

Sample Problems● What volume will 12.0 g of oxygen gas

(O2) occupy at 25°C and a pressure of 52.7 kPa?

● When the temperature of a rigid cylinder containing 235 L of argon gas is held to 365 K, the pressure of the gas is 768 kPa. How many moles of argon does the cylinder contain?

Ideal Gases and Real Gases● Ideal gases do not exist◦ But, at many conditions real gases do

behave similarly to ideal gases● Real gases differ most from an ideal gas

at low temperatures and high pressures

14.4 GASES: MIXTURES AND MOVEMENTS

Dalton’s Law● In a mixture of gases, the total pressure

is the sum of the partial pressures of the gases.

● Ptotal = P1 + P2 + P3 + …● Partial pressure: pressure exerted by one

gas in a mixture● If the % composition of the mixture

does not change, then the fraction of pressure does not change as the total pressure changes

Sample Problems● Air contains oxygen, nitrogen, carbon

dioxide, and trace amounts of other gases. What is the partial pressure of oxygen at 101.30 kPa of total pressure if the partial pressures of nitrogen, carbon dioxide, and other gases are 79.10 kPa, 0.040 kPa, and 0.94 kPa, respectively?

Sample Problems● 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?

● 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.

Graham’s Law● Diffusion: the tendency of molecules to

move toward areas of lower concentration until the concentration is uniform throughout

● Effusion: gas escapes through a tiny hole in a container

● Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass

Graham’s Law●  

Sample Problems● How much faster does helium (He)

effuse than nitrogen (N2) at the same temperature?

● Calculate the ratio of the velocity of hydrogen molecules to the velocity of carbon dioxide molecules at the same temperature.