Gases: Chapter 1010.1 – Characteristics of Gases

• Physical properties of gases are all similar.• Composed mainly of nonmetallic elements with

simple formulas and low molar masses.• Unlike liquids and solids, gases expand to fill their containers. are highly compressible. have extremely low densities.• Two or more gases form a homogeneous

mixture.

10.2 -- Pressure

• Pressure = force per unit area (P = F/A)

• SI Unit = N/m2 = 1 pascal (Pa). kPa is more common

• Atmospheric pressure (the force exerted by the atmosphere on a given surface area) -- measured with a barometer:

• 1 atm = 760mmHg = 760 torr = 101.3kPa

• Standard pressure = 1atm

• Manometer – measures the difference in pressure between atmospheric pressure the pressure of a gas in a container.

• Pgas = Patm + h• Note: • h is positive if Pgas > Patm

• h is negative if Pgas < Patm

10.3 – the Gas Laws

• Boyle’s Law: At a constant temp., the pressure and volume of a gas are inversely proportional.

• PV = a constant, or P1 x V1 = P2 x V2

• Charles’s Law: The volume of a fixed amount of gas at constant pressure is directly proportional to its Kelvin temperature

• V1/T1 = V2/T2 • (note: temp must be • in Kelvin)

• Avogadro’s Law: At a fixed T and P, the volume of a gas is directly proportional to the number of moles of gas.

• At STP (1atm and 0°C), 1 mole of a gas = 22.4L (molar volume of a gas at STP)

10.4 – The Ideal Gas Law

• The Ideal Gas Law (an ideal gas is a hypothetical gas that follows the ideal gas law under all pressure, volume, and temperature conditions)

• PV=nRT• R=.0821 L atm/mol K (see other values on page 408)

• The Combined Gas Law

10.5 – Applications of the Ideal Gas Law

• Determination of Gas Densities: using the ideal gas law, set the volume equal to 1L and solve for moles (that gives you moles/L) – then convert to g/L using the molar mass.

• Or use the following equation:• d = MP/RT, where M is the molar mass of the gas• (note: this equation is not on the equation sheet, so

you would have to memorize it)

Determination of the molar mass of a gas: calculate moles with the ideal gas equation, then divide mass/moles• Or use the following equation:• M = mRT/PV, where M is the molar mass.• (note: this equation is also not on the equation

sheet)

• Gases in Reaction Stoichiometry• Law of Combining Volumes: If all the gases in the reaction are at

the same conditions, then the mole ratio is also the volume ratio.

• For other problems, use the ideal gas law to relate the moles of a gas to other gas units, such as volume and pressure (you can’t use the 22.4L/mole conversion if the conditions aren’t STP)

10.6 – Gas Mixtures and Partial Pressures• If two gases that don’t react are combined in a container, they

act as if they are alone in the container.• Dalton’s Law of Partial Pressures:• Ptotal = P1 + P2 + P3 + …

• Mole fraction = moles of one component / total # of moles in mixture.

• For gases in a mixture, the mole fraction = the pressure fraction (Pgas/Ptotal)

• So, PA = Ptot x XA

• Collecting a gas over water:

• -there’s a mixture of the desired insoluble gas and water vapor

• Ptotal = Pbar = Pgas + PH2O

10.7 – The Kinetic-Molecular Theory of Gases1) Gases consist of large numbers of molecules that are in

continuous, random motion.2) The combined volume of all the molecules of the gas is

negligible relative to the total volume in which the gas is contained.

3) Attractive and repulsive forces between gas molecules are negligible.

4) 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.

5) The average kinetic energy of the molecules is proportional to the absolute (kelvin) temperature

• The Maxwell-Boltzmann distribution describes the distribution of particle speeds in an ideal gas. Notice that:

• 1. As the molar mass of the gas increases, the speed of the molecules decreases and the range gets smaller.

• 2. As the temp. increases, the speed increases and the range gets larger.

How Fast Do Gas Molecules Move?• Temperature is related to the average

kinetic energy of the gas molecules.• Individual molecules can have

different speeds of motion.• The figure shows three

different speeds: ump is the most probable speed (most

molecules are this fast). uav is the average speed of the

molecules. urms, the root-mean-square speed, is

the one associated with the average kinetic energy. Molar mass

10.8 – Molecular Effusion and Diffusion

Effusion 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 a second substance.

Graham’s Law of Effusion

• Graham’s Law relates the molar mass of two gases to their rate of speed of travel.

• The “lighter” gas always has a faster rate of speed.

10.9 – Real Gases: Deviations from Ideal Behavior

The assumptions made in the kinetic-molecular model (negligible volume of gas molecules themselves, no attractive forces between gas molecules, etc.) break down at high pressure and/or low temperature.

Real Gases In the real world, the behavior of gases only conforms to the

ideal-gas equation at relatively high temperature and low pressure. This is because real gases do have volumes and do attract one another.

At high pressures, the volumes of the gas molecules are not negligible, so the gas volume would be slightly greater than that predicted by the Ideal Gas Law.

At low temps, the attractive forces are not negligible, which lessens the forces with which gas molecules hit the wall of their container, giving a lower pressure than would be predicted by the Ideal Gas Law