Today, we will explain the relationships between gas volume, temperature and pressure.

Robert Boyle Robert Boyle discovered that gas pressure and volume are related mathematically. The observations of Boyle and others led to the development of the gas laws. The gas laws are simple mathematical relationships between the volume, temperature, pressure and the amount of gas.

Boyle’s Discovery Boyle discovered that doubling the pressure on a sample of gas at constant temperature reduces its volume by one-half. Reducing the pressure on a gas by one half allows the volume of the gas to double. As one variable increases, the other decreases How are they related?

Pressure-Volume Relationship The pressure of a gas is caused by moving molecules hitting the container walls. Suppose the volume of a container is decreased but the same number of gas molecules is present at the same temperature. There will be more molecules per unit volume. The number of collisions with a given unit of wall area per unit time will increase as a result. Therefore pressure will also increase.

Boyle’s Law The general volume-pressure relationship is called Boyle’s Law. Boyle’s Law states that the volume of a fixed mass of gas varies inversely with the pressure at constant temperature. It can be expressed as mathematically: PV = k (P is pressure, V is volume and k is a constatnt)

Boyle’s Law The relationship between changes of pressure and volume can be expressed as: P1V1 = P2V2 P1 and V1 represent initial conditions. P2 and V2 Represent a different set of conditions. Given three of the four values, you can use this equation to calculate the fourth value for a system at constant temperature.

Example: A sample of oxygen gas has a volume of 150.0 mL when its pressure is 0.947 atm. What will the volume of the gas be at a pressure of 0.987 atm if the temperature remains constant? Given: V1 = 150.0 mL P1 = 0.947 atm P2 = 0.987 atm V2 = unknown Since the pressure increased at constant temperature, what should we expect to see happen to volume?

Example: A balloon filled with helium gas has a volume of 500mL at a pressure of 1atm. The balloon is released and reaches an altitude of 6.5 km, where the pressure is 0.5 atm. If the temperature has remained the same, what volume does the gas occupy at this height?

Example: The piston of an internal combustion engine compresses 450mL of gas. The final pressure is 15 times greater than the initial pressure. What is the final volume of the gas, assuming constant temperature?

Example: A helium filled balloon contains 125 mL of gas at a pressure of 0.974 atm. What volume will the gas occupy at standard pressure?