# A sample of nitrogen dioxide has a volume of 28.6 L at 45.3°C and 89.9 kPa. What is its volume at STP?

Jun 11, 2017

$22.1$ $\text{L}$

#### Explanation:

We can solve this problem using the combined gas law:

$\frac{{P}_{1} {V}_{1}}{{T}_{1}} = \frac{{P}_{2} {V}_{2}}{{T}_{2}}$

Standard temperature and pressure conditions are

• $100$ $\text{kPa}$

• ${0}^{\text{o""C}}$

Remember that the temperatures must be in Kelvin, so we must convert the Celsius temperatures:

${0}^{\text{o""C}} = 273.15$ $\text{K}$

${45.3}^{\text{o""C}} = 318.5$ $\text{K}$

Since we're trying to find the volume at stp, let's rearrange this equation to solve for ${V}_{2}$:

${V}_{2} = \frac{{P}_{1} {V}_{1} {T}_{2}}{{T}_{1} {P}_{2}}$

Plugging in known values, we have

V_2 = ((89.9cancel("kPa"))(28.6"L")(273.15cancel("K")))/((318.5cancel("K"))(100cancel("kPa"))) = color(red)(22.1 color(red)("L"

rounded to $3$ significant figures, the amount given in the problem.

The volume of the nitrogen as sample at stp is thus $22.1$ liters.