# A gas under a pressure of 74 mmHg and at a temperature of 75°C occupies a 500.0-L container. How many moles of gas are in the container?

Aug 18, 2017

$\text{1.7 mols ideal gas}$.

Anytime you see a bunch of units in a row, it's probably an ideal gas problem. The first order of business is to convert all these to more usual units. Consider the universal gas constant:

$R = \text{0.082057 L"cdot"atm/mol"cdot"K}$.

The units of pressure, volume, and temperature are given directly in the units of $R$!

For the units to work out, the pressure $P$ could be rewritten in $\text{atm}$:

$P = 74 \cancel{\text{mm Hg" xx "1 atm"/(760 cancel"mm Hg") = "0.0974 atm}}$

It is always reasonable to use the temperature $T$ in $\text{K}$ for general chemistry, and in this case it makes the units work out...

${75}^{\circ} \text{C" + 273.15 = "348.15 K}$

The volume $V$ is in normal units. We do want it in $\text{L}$, just as we wanted $P$ in $\text{atm}$. Thus, we can now use the ideal gas law:

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

where $n$ is the mols of ideal gas.

So, to two significant figures, the mols are:

$\textcolor{b l u e}{n} = \frac{P V}{R T}$

$= \left(\text{0.0974 atm" cdot "500.0 L")/("0.082057 L"cdot"atm/mol"cdot"K" cdot "348.15 K}\right)$

$=$ $\textcolor{b l u e}{\underline{\text{1.7 mols ideal gas}}}$