# What is the density of 5.0 L of NO_2 gas at 1.0 atm at 0.0°C?

Jul 5, 2017

$2.1$ $\text{g/L}$

#### Explanation:

We're asked to find the density of ${\text{NO}}_{2}$ at a certain temperature and pressure.

To do this, we can use the equation

$d = \frac{M P}{R T}$

where

• $M$ is the molar mass of ${\text{NO}}_{2}$, which is $46.01$ $\text{g/mol}$

• $P$ is the pressure of the gas, in $\text{atm}$, given as $1.0$ $\text{atm}$

• $R$ is the universal gas constant, equal to $0.082057 \left(\text{L"•"atm")/("mol"•"K}\right)$

• $T$ is the absolute temperature of the gas, in $\text{K}$

Notice how the given volume measurement is not needed, because the density of a material does't change by increased volume (because quantity will also have increased).

The given temperature converted to Kelvin is

$T = {0.0}^{\text{o""C}} + 273 = 273$ $\text{K}$

Plugging in known values, we have

d = ((46.01"g"/(cancel("mol")))(1.0cancel("atm")))/((0.082057("L"•cancel("atm"))/(cancel("mol")•cancel("K")))(273cancel("K"))) = color(red)(2.1 color(red)("g/L"

rounded to $2$ significant figures.