Ch. 13: Gas Laws

I. Factors Affecting Gas Pressure A.Amount of Gas 1.↑ molecules = ↑ collisions with walls = ↑ pressure 2.↓ molecules = ↓ collisions with walls = ↓ pressure B.Volume 1.↑ volume = ↑ surface area = ↓ collisions per unit of area = ↓ pressure 2.↓ volume = ↓ surface area = ↑ collisions per unit of area = ↑ pressure

C.Temperature 1.↑ temperature = ↑ molecule speed = ↑ frequent (and harder) collisions = ↑ pressure 2.↓ temperature = ↓ molecule speed = ↓ frequent (and harder) collisions = ↓ pressure

II. Boyle’s Law – Pressure & Volume A.The volume of a fixed mass of gas varies inversely with the pressure at constant temperature 1.Volume ↑ as pressure ↓ 2.volume ↓ as pressure ↑

B.If we know the volume of a gas at a given pressure, we can predict the new volume if the pressure is changed. C.Mathematically: P 1 V 1 = P 2 V 2 D.Can use any units given, as long at the same units are used throughout the problem.

Example: Consider a 1.5 L sample of a gas at a pressure of 56 mmHg. If the pressure is changed to 150 mmHg at a constant temp., a)Will the volume increase or decrease? b)What will the new volume be?

III. Charles’s Law – Temperature & Volume A.Kelvin Temperature Scale (Absolute Scale) 1.K=273 + °C 2.°C = K – K = absolute zero 4.Standard temperature = 0°C = 273K

B.The volume of a fixed mass of gas at constant pressure varies directly with the Kelvin (absolute) temperature 1.Mathematically: V1 V2V1 V2 T1T2T1T2 **Temperatures must be in Kelvin!! Will have to convert Celsius to Kelvin for problems that use Charles’s Law.

Example: A 2.0 L sample of air is collected at 298 K and then cooled to 278 K. The pressure is held constant at 1.0 atm. a)Does the volume increase or decrease? b)Calculate the volume of the air at 278 K.

IV. Combined Gas Laws – combining Boyle’s & Charles Law A.Expresses the relationship between pressure, volume, and temperature of a fixed amount of gas B.Mathematically: ** Temps must be in Kelvin!! P1V1 P2V2P1V1 P2V2 T 1 T 2 C.To find V 2, use STP for P 2 & T 2 (T = 273 K and P = kPa)

Example: What will be the new volume if 125 mL of He gas at 100 o C and atm is cooled to 25 o C and the pressure is increased to 1.15 atm?

V. Ideal Gases - gases that conform to gas laws at all conditions of pressure and temperature A.Ideal gases – (theoretical) do not exist 1.Conform precisely to the kinetic theory Particles have no volume and there is no attraction between particles 2.Real gases differ most from ideal gases at low temperatures and high pressures

B.Ideal Gas Law 1.Mathematically: PV = nRT 2.P = Pressure, V = Volume, n = # of moles, T = Temperature (must be in Kelvin!) 3.Ideal gas constant: R = (L·atm)/(K·mol)

Example: A sample of hydrogen gas, H 2, has a volume of 8.56 L at a temperature of 0C and a pressure of 1.5 atm. Calculate the number of moles of H 2 present in the gas sample.

VI. Dalton’s Law of Partial Pressures A.In a mixture of gases, the total pressure is the sum of the partial pressures of the gases B.Mathematically: P total = P 1 + P 2 + P 3 + … C.Gas pressure depends only on the number of particles in a given volume and on their average kinetic energy

Example: The partial pressure of helium is 10.5 kPa in a mixture of helium, oxygen, and methane gases. If the total pressure is 100 kPa and the partial pressure of oxygen is 30.5 kPa, what is the partial pressure of the methane gas?