Problem :
3.0 moles of gas at 300 K and 1.0 atm have a volume of 15 smoots. What is
R in ?
Rearrange
PV = nRT to solve for
R:
= R. Plug in the values
of
P,
V,
n, and
T to solve for
R.
R = 0.017 .
Problem :
A sample of gas at 1.0 atm and 298 K has a volume of 8.7 L. How much gas does
the sample contain?
Rearrange
PV = nRT to solve for
n.
= n. Let's try
converting everything to SI units so that we can used the gas constant value
of
8.314 . 1.0 atm converts to
1.0×10^{5} Pa. There are
10^{3} m
^{3} in a liter, so 8.7 L converts to
8.7×10^{3} m
^{3}. Plugging in these values, we find that
n = 0.35
mol.
Problem :
You are the head engineer at a chemical plant. Sam Yagan, the summer intern,
has just broken the cooling system to the main helium tank. Sam tells you not
to be worried; the tank can withstand up to 40.0 atm of pressure before
exploding. Before Sam's accident, the tank was subjected to 10.0 atm. The tank
was originally at 250 K, but it's a hot summer day, and you fear its temperature
may rise to 350 K. Should you believe Sam?
The key to this problem is to realize which values are constant.
V,
n, and
R do not change.
P and
T do. Rearrange
PV = nRT so that the variables
and constants are on opposite sides of the "=" sign:
= = C 

Since the
C is constant regardless of
P and
T, we can rearrange the
equation in to a more useful form:
= 

Plug in the given values for
P and
T. The pressure in the tank will only
rise to 14 atm. Sam is correct; there is no immediate danger from the rise in
temperature. That coolant system must have had a purpose, though, and you
should repair it ASAP.
Problem :
A race of purely gasbased aliens inhabits Jupiter (P = 808 kPa, T = 600 K).
On Jupiter, each alien occupies a volume of one cubic meter. The aliens decide
to visit Earth. They board their climate controlled gascraft, make the long
journey to Earth, and land in a cornfield in southern Idaho (P = 101 kPa,
T = 300 K ). When they disembark, how big will they be? Assume that the
aliens' innards do not diffuse or burst in the Earth's atmosphere.
P,
T, and
V are the variables in this problem.
n is constant. Place
the constants and variables on opposite sides of the "=" sign:
= n 

We can rearrange this equation:
Solving for
V_{2}, we find that the aliens will have a volume of four cubic
meters.