Chapter 14 Gas Behavior

Kinetic Molecular Theory Chpt 13 pgs 385-389 Particles in a gas are considered to be small, hard spheres with insignificant volume. The motion of the particles in a gas is rapid, constant, and random. All collisions between particles in a gas are perfectly elastic. The Kelvin temperature of a substance is directly proportional to the average kinetic energy of the particles of the substance.

COMPRESSIBILITY According to KMT, the particles of a gas are very far apart. Between the gas particles, there is mostly empty space. For this reason, gases are COMPRESSIBLE. According to KMT, the particles of a gas move in a constant, random, straight-line motion until they collide with something. When they collide with the walls of the container, PRESSURE results.

kPa, atm, mm Hg, torr, bar, or psi. Pressure is defined as the force exerted over a given area. Pressure can be measured in…. kPa, atm, mm Hg, torr, bar, or psi. Standard pressure at sea level 101.3 kPa = 1 atm = 760 mm Hg

VARIABLES used to describe GASES 1. Amount of gas measured in moles (variable used ‘n’). 2. Volume of the gas measured in liters (variable used ‘V’). 3. Temperature of the gas measured in Kelvin (variable used ‘T’). 4. Pressure of the gas measured in atm or kPa (variable used ‘P’).

How does ‘amount of particles’ affect pressure? If the number of particles is doubled, how is the pressure affected? If the number of particles is tripled, how is the pressure affected?

How does an aerosol can work? What happens if you do not hold the can upright? What happens when the pressure of the propellant equals the air pressure outside the can?

What happens to the gas pressure when the volume of the container is reduced by one-half?

What happens to the pressure of a gas when the temperature of the gas is doubled? What eventually happens if the temperature continues to increase?

The Gas Laws Section 14.2

P1 V1 T1 P2 V2 T2 = Combined Gas Law Describes the relationship among pressure, temperature, and volume of an enclosed gas when the amount of gas is the only variable held constant. P1 V1 T1 P2 V2 T2 =

If n is held constant, there is a direct relationship between PV and T. P x V T

Example: A gas at 155 kPa and 25oC has an initial volume of 1.00 L. The pressure of the gas increases to 605 kPa as the temperature is raised to 125oC. What is the new volume? 0.342 L Example: A 5.00 L air sample has a pressure of 107 KPa at a temperature of -50.0oC. If the temperature is raised to 102oC and the volume expands to 7.00 L, what will the new pressure be? 129 kPa

P1V1 = P2V2 T2 T1 Boyle’s Law If T and n remain the same, P increases as V decreases. P1V1 = P2V2 T1 T2 Pressure and Volume are inversely proportional.

The ‘curve’ shows an inverse relationship.

Example: 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? 6.48 L Example: 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? 68.3 kPa

P1V1 P2V2 T1 T2 Charles’s Law If P and n remain the same, V increases as T increases. P1V1 T1 P2V2 T2 = Volume and temperature are directly proportional.

Example illustrating Charles’s Law

Direct relationship between volume and temperature

Example: If a sample of gas occupies 6.80 L at 325oC, what will its volume be at 25oC if the pressure does not change? 3.39 L Example: Exactly 5.00 L of air at -50.0oC is warmed to 100.0oC. What is the new volume if the pressure remains constant? 8.36 L

P1V1 T1 P2V2 T2 = Gay-Lussac’s Law If V and n remain the same, T increases as P increases. P1V1 T1 P2V2 T2 = Pressure and Temperature are directly proportional.

If the temperature in the container is doubled, what happens to the pressure?

Example: A sample of nitrogen gas has a pressure of 6.58 kPa at 539 K. If the volume does not change, what will the pressure be at 211 K? 2.58 kPa Example: The pressure in a car tire is 198 kPa at 27oC. After a long drive, the pressure is 225 kPa. What is the temperature of the air in the tire? Assume that the volume is constant. 341 K or 68oC.

Ideal Gas Law

“universal gas constant” Ideal Gas Law PV = nRT “R” is called the “universal gas constant”

Volume of 1 mole of gas at STP Standard Temperature and Pressure (STP) Temperature 0oC or 273K Pressure 1 atm Volume of 1 mole of gas at STP 22.4L

Calculating the value of R At STP, 1 mole of a gas has a volume of 22.4L, a temperature of 273K and a pressure of 1 atm.

Using the ideal gas law: PV nT 1.00 atm x 22.4 L 1.00 mol x 273K R = = L atm mol K = 0.0821

Variations of R kPa L mol K R = 8.31451 atm L mol K R = 0.08206

What is the volume (in L) of 2.5 moles of oxygen gas measured at 25oC and a pressure of 104.5kPa? Answer: 59 L

At what temperature will 0.0100 mole of argon gas have a volume of 275 mL at a pressure of 100.0 kPa? Answer: 331 K

The Ideal Gas Law and Stoichiometry

What volume of carbon dioxide forms at 10oC and 99 kPa pressure when 0.50 g of sodium bicarbonate reacts completely with hydrochloric acid? Answer: 0.14 L

Magnesium is one metal that is able to react with nitrogen directly. What volume of nitrogen, measured at a pressure of 102 kPa and a temperature of 27oC, will react with 5.0 g of magnesium? Answer: 1.7 L

Section 14.4 Gases: Mixtures and Movement

Dalton’s Law of Partial Pressure Partial Pressure - In a mixture of gases, the individual pressure of each gas.

Dalton’s Law of Partial Pressure The total pressure of a mixture of gases is the sum of the partial pressures of the individual gases in the mixture.

Dalton’s Law of Partial Pressure In equation form: Ptotal = Pa + Pb + Pc + ...

You collect a sample of oxygen gas by the water- displacement method. If the atmospheric pressure is 99.4 kPa and the water-vapor pressure is 4.5 kPa, then what is the partial pressure of the oxygen gas?

Use Dalton’s Law of Partial Pressures: Ptotal = Pa + Pb Ptotal = Pwater-vapor + Poxygen gas 99.4 kPa = 4.5 kPa + Poxygen gas Poxygen gas = 94.9 kPa

the tendency of molecules to move toward areas of lower concentration Diffusion the tendency of molecules to move toward areas of lower concentration until the concentration is uniform throughout. Effusion when a gas escapes through a tiny hole in its container. Graham’s Law The rate of effusion of a gas is inversely proportional to the square root of the gas’s molar mass.

Compare the rates of effusion = √ Rate A Rate B Molar Mass B Molar Mass A Example: Compare the rates of effusion for helium and argon.

Compare the rates of effusion Example: Compare the rates of effusion for oxygen and radon.