The Combined Gas Law

We have three different relationships among temperature, volume, and pressure of a gas; these are as follows:

Boyle’s Law: PV = k at constant temperature.

Charle’s Law:  at constant pressure.

Gay–Lussac’s Law:  at constant volume.

These three gas laws can be combined in one combined gas law. This law can be expressed as

Example 1.28: A sample of a gas has a volume of 80.0 ml at a pressure of 1 atm and a temperature of 20°C. What volume will the gas occupy at 1.5 atm and 45°C?

Solution:

Given: V₁ = 80 ml; P₁ = 1 atm; T₁ = 273 + 20 = 293 K; P₂ = 1.5 atm; T₂ = 273 + 45 = 318 K; V₂ = ?

1.11.5  Gas Constant

Since 1 mole of a gas occupies 22.4 l at standard temperature (273 K) and pressure (1 atm), it is possible to arrive at a mathematical expression to relate moles, pressure, temperature, and volume. This expression is called the ideal gas law. This law contains an additional term ‘R’ which is called the universal gas constant. In this expression ‘N’ equals the number of moles of a gas, the volume ‘V’ must be expressed in litres, the pressure ‘P’ must be expressed in atmospheres and the temperature must be expressed in degrees Kelvin.

This constant can be calculated by using the above values in this law.

When the values of 22.4 l and 273 degrees Kelvin are applied, the value of R is found to be

If we use CGS units, P will be expressed in dynes per square cm, V is the volume of a mole (i.e., the volume occupied by 6.0221 × 10²³ molecules) and the value of the universal gas constant is 8.3145 × 10⁷ erg/mole K. If we use SI units, P will be expressed in Pascal (N/m²), V will be the volume of a kilomole (i.e., the volume occupied by 6.0221 × 10²⁶ molecules) and the value of the universal gas constant is 8.3145 × 10³ J/kilomole K.