# A sample of nitrogen gas has a volume of 32.4 L at 20°C. The gas is heated to 220°C at constant pressure. What is the final volume of nitrogen?

Dec 24, 2015

The volume of nitrogen gas at 493 K will be 54.5 L.

#### Explanation:

This is an example of Charles' law which states that the volume of a gas held at constant pressure is directly proportional to the Kelvin temperature. The equation for Charles' law is ${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$.

Given/Known
${V}_{1} = \text{32.4 L}$
${T}_{1} = \text{20"^"o""C"+273.15="293 K}$
${T}_{2} = \text{220"^"o""C"+273.15="493 K}$

Unknown
${V}_{2} = \text{???}$

Solution
Rearrange the equation to isolate ${V}_{2}$ and solve.

${V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}$

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

V_2=(32.4"L"xx493cancel"K")/(293cancel"K")="54.5 L"