# Question #da497

Mar 23, 2016

You need a container that can hold $\text{1.04 L}$ of nitrogen gas.

#### Explanation:

The problem essentially wants you to determine the volume of $0.0459$ moles of nitrogen gas at STP.

As you know, the volume a gas occupies depends on the conditions for pressure and temperature. Changing one or both of the parameters will result in a change in volume.

STP conditions are defined as a pressure of $\text{100 kPa}$ and a temperature of ${0}^{\circ} \text{C}$. What's special about these conditions is that one mole of any ideal gas occupies $\text{22.7 L}$.

This is known as the molar volume of a gas at STP.

So, every time you're at STP conditions, you know that one mole of an ideal gas will occupy a volume of $\text{22.7 L}$. This means that you an use the molar volume of the gas as a conversion factor to go from moles to liters and vice versa

$0.0459 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{moles"))) * overbrace("22.7 L"/(1color(red)(cancel(color(black)("mole")))))^(color(purple)("molar volume of a gas at STP")) = color(green)(|bar(ul(color(white)(a/a)"1.04 L} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

The answer is rounded to three sig figs, the number of sig figs you have for the number of moles of gas.

SIDE NOTE More often than not, STP conditions will be given to you as a pressure of $\text{1 atm}$ and a temperature of ${0}^{\circ} \text{C}$.

Under these conditions, one mole of any ideal gas occupies $\text{22.4 L}$. If this is the value given to you for the molar volume of a gas at STP, simply redo the calculation using $\text{22.4 L}$ instead of $\text{22.7 L}$.

$0.0459 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{moles"))) * overbrace("22.4 L"/(1color(red)(cancel(color(black)("mole")))))^(color(purple)("molar volume of a gas at STP")) = color(green)(|bar(ul(color(white)(a/a)"1.03 L} \textcolor{w h i t e}{\frac{a}{a}} |}}}$