The Behavior of GasesChapter 5

Kinetic Theory Review

• The following five tenets are the basis for ideal gases

• Gases consist of hard spherical particles

• Particles have insignificant volume

• There are large distances between particles

• There are NO attractive or repulsive forces between particles

• Particles are in constant, random motion with elastic collisions

Variables and Equations

• 4 variables are pressure (P) in kilopascals, temperature (T) in kelvins, volume (V) in liters, and number of moles (n).

• Help to understand everyday applications such as airbags, scuba-diving equipment, and hot-air balloons.

Compressibility

• Why are gases compressed more easily than liquids or solids?

• How does the overall volume of the particles in a gas compare to the overall volume of the gas

• How does an airbag work?

Amount of a Gas

• What happens to the pressure if you double the amount of particles in a rigid container?

• How does an aerosol can work?

Volume

• If you double the volume of a rigid container, what can be said about the pressure?

• What about if you halve the volume?

Temperature

• When you increase the temperature of gas molecules in a container, what happens to the pressure?

• The molecules gain more KE, move faster, and thus create more pressure.

• If you leave a bag of potato chips in the sun, it will bulge at the seams

Gas Laws

• Boyle’s Law

• Charles’ Law

• Gay-Lussac’s Law

• Combined Gas Law

• Ideal Gas Law

• Dalton’s Law

• Graham’s Law

Boyle’s Law

• As volume increases, pressure _________.

• Therefore, volume and pressure are inversely related

• We can show this by P1V1 = P2V2

Charles’ Law

• As temperature increases, volume _________.

• Therefore temperature and volume are directly related.

• We can show this by

Gay-Lussac’s Law

• As the pressure of an enclosed gas increases, the temperature __________.

• Therefore temperature and pressure are directly related.

• We can show this by

The Combined Gas Law

• We can combine the previous three laws into one law that involves P, T and V.

• The combined gas law is written as

The Ideal Gas Law

• To calculate the number of moles of a contained gas, we use the variable ‘n’

• The ideal gas law is PV = nRT

• R is known as the ideal gas constant

• R = 8.31 (if pressure is in kPa)

R = 0.0821 (if pressure is in atm)

Ideal Gas Law

• PV = nRT

• What are the units on R?

• Can we derive the value for R?

• Remember that at STP, T = 273 K, P = 101.3 kPa, n = 1 mol, V = 22.4 L

Ideal vs. Real

• Real gases differ most from an ideal gas at low temperatures and high pressures

• Remember, in reality, there are attractive forces between molecules

Dalton’s Law

• Also known as the law of partial pressures: In a mixture of gases, the total pressure is the sum of the partial pressures of the gases

• Simply, Ptotal = P1 + P2 + P3 + …

• Why would a climber at the top of Mt. Everest care about Dalton’s Law?

Graham’s Law

• Gases with a lower molar mass will diffuse faster than gases with a larger mass

• It makes sense that a lighter object will have to move faster to have the same energy as a larger object moving slowly

• We can show this law as

How to Solve Problems

Here is a sample problem:

5 moles of gas is heated to 400K in a 2.5 L container. What is the pressure of the gas?

• Identify and write down variables.

n = 5, T = 400K, V = 3.5 L

N – 5, T = 5, 400