GAS LAWSChapter 5

Pressure

Temperature

STP

Combined Gas Law

Boyle’s Law PV = k

Charles’ LawV = kT

Gay-Lussac’s LawP = kT

Avogadro’s LawThe ____________ of a gas at constant temperature and pressure is directly proportional to the ___________________ of the gas.

Do equal volumes of gases under the same conditions of temperature and pressure have the same MASS? Why or why not?

Ideal Gas equation PV=nRT R, the gas constant

****Temperature must be ______________

Molar VolumeVolume that 1 mole of gas occupies

Practice1. Suppose we have a gas confined to a cylinder. How will each of these changes

affect the average distance between molecules, the pressure of the gas, and the number of moles of gas present in the cylinder :

(a) Heat the gas from 298 K to 360 K, while maintaining the piston in the same position.

(b) Move the piston to reduce the volume of gas from 1 L to 0.5 L.

(c) Inject additional gas through the gas inlet valve.

2. Calcium carbonate, CaCO3(s), decomposes upon heating to give CaO(s) and CO2(g). A sample of CaCO3 is decomposed, and the carbon dioxide is collected in a 250-mL flask. After the decomposition is complete, the gas has a pressure of 1.3 atm at a temperature of 31 °C. How many moles of CO2 gas were generated?

3. Tennis balls are usually filled with air or N2 gas to a pressure above atmospheric pressure to increase their “bounce.” If a particular tennis ball has a volume of 144 cm3 and contains 0.33 g of N2 gas, what is the pressure inside the ball at 24 °C?

4. The gas pressure in an aerosol can is 1.5 atm at 25 °C. What would the pressure be if the can were heated to 450 °C?

Further Applications of the Ideal Gas LawMolecular mass

Density

Practice5. What happens to the density of a gas as

(a) the gas is heated in a constant-volume container; (b) the gas is compressed at constant temperature; (c) additional gas is added to a constant-volume container?

6. Calculate the average molar mass of dry air if it has a density of 1.17 g/L at 21 °C and 740.0 torr.

Partial pressureThe total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone.

Ptotal =

When one collects a gas over water, there is water vapor mixed in with the gas

Practice7. The table below shows the constituents of air at standard pressure.

The % of gases in air Partial pressure (STP) 78.08% N2 593.4 mm Hg20.95% O2 x mm Hg

0.94% Ar 7.1 mm Hg 0.03% CO2 0.2 mm Hg

What is the partial pressure of oxygen in atm?

Mole FractionThe mole fraction of an individual gas component in an ideal gas mixture can be expressed in terms of the component's partial pressure or the moles of the component:

xi = Pi = ni xi= mole fraction of any individual gas component in a gas mixture P n Pi= partial pressure of any individual gas component in a gas mixture

ni= moles of any individual gas component in a gas mixturen= total moles of the gas mixtureP= pressure of the gas mixture

The partial pressure of an individual gas component in an ideal gas can be obtained using this expression:

Pi = xi P

Practice8. What is the mole fraction for oxygen in problem #7?

KMTGas particles are in ______________________________ motion

The combined volume of all the molecules of the gas is _____________ relative to the total volume in which the gas is contained.

Attractive and repulsive forces between gas molecules are _______________.

Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant.

Maxwell-Boltzman DistributionAn increase in temperature spreads out the distribution and the mean speed is shifted upward

Velocity of a GasThe distribution of speeds for The distribution of speeds of threenitrogen gas molecules at three different gases at the same temperaturedifferent temperatures

urms = 3RT√ M

Practice9. A sample of O2 gas initially at STP is compressed to a smaller volume at constant

temperature. What effect does this change have on (a) the average kinetic energy of O2 molecules,

(b) the average speed of O2 molecules,

(c) the total number of collisions of O2 molecules with the container walls in a unit time,

(d) the number of collisions of O2 molecules with a unit area of container wall per unit time?

Molecular Effusion and DiffusionEffusion is the escape of gas molecules through a tiny hole into an evacuated space.

Diffusion is the spread of one substance throughout a space or throughout a second substance.

Graham’s law governs effusion and diffusion of gas molecules.Rate of effusion is inversely proportional to its _____________________

Real Gases: Deviations from Ideal BehaviorAn ideal gas is like an ideal vacation!

_________ temperature and ________ pressure