**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
n_{1} = original number of moles

n_{2}
= 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, P_{1}
= P_{2} and n_{1} = n_{2}, so those terms would cancel
and leave us with Charles Law, V_{1}/T_{1} = V_{2}/T_{2}.
If volume and temperature are constant, and we want to know how the number of
moles affects pressure, the formula simplifies to P_{1}/n_{1} =
P_{2}/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 ^{o}C, what is the final temperature of the
mixture?

T_{2} = 195 K