Gas Laws

1. Kinetic Molecular Theory Ideal Gases :  Gas particles do not attract or repel each other.  Gas particles are much smaller than the distances between them. They are mostly empty space.  Gas particles are in constant, random motion.  No kinetic energy is lost when gas particles collide with each other or with the walls of their container.

 All gases have the same average kinetic energy at a given temperature. (note not the same velocity!) Real gases behave like ideal gases except at high pressures and low temperatures. At high pressures or low temperatures the particles are closer together and are effected by the intermolecular forces.

Temperature – average kinetic energy of the gas particles.  Gas laws require temperature to be in units of Kelvin.  No negative temperatures  Does not have zero as a temperature except at absolute zero.  Kelvin = ºC  0ºC = 273 K  100ºC = 373 K  26ºC = 299 K  379 K = 106ºC  318 K = 45ºC

STP – standard temperature and pressure  0ºC, 1 atm  0ºC, kPa  273 K, 760 mmHg  273 K, kPa Gases are described by the :  Number of molecules (moles)  Pressure  Temperature  Volume

2. Boyle’s Law The volume of a given amount of gas, held at constant temperature varies inversely with the pressure. Constant temperature, constant number of particles. Pressure ↑ Volume ↓ (inverse relationship) Pressure ↓ Volume ↑ PV = constant

When collecting gases in the lab, we use the technique of water displacement. The product gases bubble into a container filled with water. The collected gas is “wet” because it contains water vapor. The water vapor exerts a partial pressure. To determine the pressure exerted by the gas, you subtract the pressure of the water vapor. The vapor pressure exerted by water depends on the temperature of the gas. P dry gas = P wet gas – P water

3. Charles’s Law The volume of a given amount of gas, held at constant pressure, varies directly with the Kelvin temperature. Constant pressure, constant number of particles. Temperature ↑ Volume ↑ (direct relationship) Temperature ↓ Volume ↓ Constant = Temperature MUST be in Kelvin!

4. Gay-Lussac’s Law The pressure of a given amount of gas, held at constant volume, varies directly with the Kelvin temperature. Constant volume, constant number of particles. Pressure ↑ Temperature ↑ (direct relationship) Pressure ↓ Temperature ↓ Constant = Temperature MUST be in Kelvin!

5. Combined Gas Law States the relationship among pressure, volume, and Kelvin temperature of a fixed amount of gas. 1 = before 2 = after Can determine the pressure, volume, or temperature should the other variables change! Always convert temperature to Kelvin!!!!! Always convert temperature to Kelvin!!!!!

Constant Temperature, T 1 = T 2  So P 1 V 1 = P 2 V 2 Constant Pressure, P 1 = P 2  So Constant Volume, V 1 = V 2  So

6. Example Problems A gas occupies a volume of 2.45 liters at a pressure of kPa and a temperature of 20°C. What volume will the gas occupy if the pressure changes to 99.3 kPa and the temperature remains at 20°C?

A 525 ml sample of hydrogen gas is collected over water at 80.0°C. The pressure of the wet hydrogen gas is 95.0 kPa. What volume will the dry hydrogen gas occupy at kPa pressure? The vapor pressure of water at 80.0°C is 47.3 kPa.

A 325 ml sample of gas is collected over water at 27°C. The pressure in the container is 68 kPa. What would the pressure be if the sample was dried and placed into a ml container at 27°C? The vapor pressure of water at 27°C is 3.6 kPa.

A tank of compressed carbon dioxide has a temperature of 23.6°C and a volume of 31.4 liters. The carbon dioxide is completely transferred into a smaller tank that has a volume of 25.0 liter. Assuming none of the carbon dioxide escapes during the transfer, what is the temperature, in °C, of the carbon dioxide in the smaller tank if the temperature is lowered to achieve the same pressure as in the large tank?

The pressure in a bicycle tire is 1.34 atm at 33.0°C. At what temperature will the pressure inside the tire be 1.60 atm? Assume the volume is constant.

What volume will a 8.6 liter sample of gas at kPa, 25°C occupy at kPa and 0°C?

A gas balloon is sitting in the freezer at -5°C, 3.25 liters, and a pressure of kPa. The balloon is moved to the counter where the temperature is 28°C and the pressure is kPa. What is the volume of the balloon after sitting on the counter several hours?

Hydrogen gas at a temperature of 22.0°C that is confined in a 5.00 L cylinder exerts a pressure of 4.20 atm. What is the volume of the gas at STP?

Homework Gas Laws