The Combined Gas Law

Since PV/nT is a constant, there is another version of the ideal gas law known as the

Combined Gas Law:

where n₁ = original number of moles

n₂ = final number of moles

What's nice about this law is that it simplifies into familiar relationships under special conditions.

For instance under conditions of constant pressure and the same number of moles, P₁ = P₂ and n₁ = n₂, so those terms would cancel and leave us with Charles Law, V₁/T₁ = V₂/T₂. If volume and temperature are constant, and we want to know how the number of moles affects pressure, the formula simplifies to P₁/n₁ = P₂/n_2.

But let's get back to an example where we can use the entire formula:

Example A student injects 2 moles of cold helium into a cylinder originally containing 2.5 moles of helium. As he does this, the piston rises and the volume increases from 0.505 L to 0.539 L. The pressure increases from 80 kPa to 90 kPa. If the gas was originally at 20.0 ^oC, what is the final temperature of the mixture?

T₂ = 195 K