# If chlorine gas has a volume of 465mL at 50°C ,what is the volume if the temperature decreases to 30°C?

Dec 6, 2015

${V}_{2} = 436 m L$

#### Explanation:

To answer this question, we will need to assume the following:

1. Chlorine gas is behaving ideally, so we can use the ideal gas law: $P V = n R T$
2. During the process, the pressure is remaining constant.

Since we are heating the ballon, the number of mole is not changing and therefore, $n$ is constant too.

Thus $V = {\underbrace{\frac{n R}{P}}}_{\textcolor{b l u e}{\text{constant k}}} T \implies \frac{V}{T} = k \implies \frac{{V}_{1}}{{T}_{1}} = \frac{{V}_{2}}{{T}_{2}}$

$\implies {V}_{2} = \frac{{V}_{1}}{{T}_{1}} \times {T}_{2} = \frac{465 m L}{323 \cancel{K}} \times 303 \cancel{K} = 436 m L$

Therefore, chlorine will occupy a volume of $436 m L$ at ${30}^{\circ} C$.