The physical behaviour of a gas is described using four main variables :

- Temperature
- Pressure
- Volume
- Amount (mol number)

## The combined gas law

By combining Boyle’s, Charles’s and Gay Lussac’s Laws, the following equation is derived:

This is the combined gas law that give the relation between the pressure, the temperature and the volume that are all changing. The mol number of the gas is constant.

## Practice problem – The combined gas law

The volume of a gas-filled balloon is V1=30.0 L at T1 = 313 K and P1= 153 kPa pressure.

What would the volume be at standard temperature and pressure (STP)?

T2 = 273 K P2 = 1atm = 101.325 KPa

**STP** represents **standards temperature and pressure **: The standard temperature is 273 K (0° Celsius), and the standard pressure is 1 atm pressure. P= 1 atm = 101.325 kPa and T= 273 K

## Solution

**1- Analyse : **List the knowns and the unknown**.**

*V*_{1} = 30.0 L *T*_{1} = 313 K *P*_{1} = 153 kPa *T*_{2} = 273 K (standard temperature)

*P*_{2} = 101.325 kPa (standard pressure) V_{2} = ??

**2-** **Calculate : **Solve for the unknown.

State the combined gas law. And rearrange the equation to isolate *V*_{2}.

Substitute the known quantities into the equation and solve.