# If I have 21 moles of gas held at a pressure of 3800 torr and a temperature of 627°C what is the volume of the gas?

Aug 12, 2016

The gas has a volume of $310 L$

#### Explanation:

Because we are given the pressure, number of moles, and temperature, we will have to use the ideal gas law equation:

Based on the units that are associated with each variable, the number of moles have good units. The temperature has to be converted to Kelvins; we can do this by adding $273$ to the temperature given in degrees Celsius:

Therefore, ${627}^{o} C + 273 = 900 K$

The next issue is that pressure has units of torr instead of atmospheres; we can use the following relationship to give the correct units:

Thus, 3800cancel"torr"xx(1atm)/(760cancel"torr") = 5atm

R has the same value no matter what chemical species you are dealing with.

Now we know P,T, n, and R.

All we have to do is rearrange the equation to solve for V. We can do this by dividing by the pressure on both sides of the equation:

$\frac{\cancel{P} V}{\cancel{P}} = \frac{n R T}{P}$

$V = \frac{n R T}{P}$

Finally, plug in your known values like so:

$V = \left(21 \cancel{\text{mol"xx0.08206Lcancel"atm"/cancel"molK"xx900cancelK)/(5cancel"atm}}\right)$

$V = 310 L$