# How many mols of nitrogen gas are contained in a "8.349 L" container held at "200.6 torr" and 64^@ "C"?

May 13, 2017

The Good Chemist thinks for a moment, pondering why the volume $V$, pressure $P$, and temperature $T$ were all given in a single sentence. He comes to realize that the only equation from general chemistry that contains all three such variables is the ideal gas law!

$P V = n R T$

He pulls out his trusty pencil and pocket calculator, and performs the following calculation, perhaps rashly assuming that nitrogen gas is ideal, disregarding its identity.

Too lazy to look up the universal gas constant in units of $\text{L"cdot"torr/mol"cdot"K}$, he decides to use units of $\text{atm}$ for pressure instead.

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

$= \left(\left(2.006 \times {10}^{2} \text{torr" xx "1 atm"/"760 torr")("8.349 L"))/(("0.082057 L"cdot"atm/mol"cdot"K")(64 + "273.15 K}\right)\right)$

$=$ $\textcolor{b l u e}{\text{0.080 mols ideal gas}}$