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Gas Laws – The combined gas law

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

  1. Temperature
  2. Pressure
  3. Volume
  4. Amount (mol number)

The combined gas law

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

Gas Laws - The combined gas law

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.

V1 = 30.0 L T1 = 313 K P1 = 153 kPa T2 = 273 K (standard temperature)

P2 = 101.325 kPa (standard pressure) V2 = ??

2- Calculate : Solve for the unknown.

State the combined gas law. And rearrange the equation to isolate V2.

Gas Laws - The combined gas law

Substitute the known quantities into the equation and solve.

Gas Laws - The combined gas law