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/n2.
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