Question

A sample of chlorine gas is confined in a 5.0-L container at 328 torr and $\mathbf{37}\mathbf{°}\mathit{C}$. How many moles of gas are in the sample?

Short answer

Answer

The number of moles of gas in the sample is 0.085 mol.

Step-by-step solution

Ideal gas law

The ideal gas law equation is,

$\mathit{P}\mathit{V}\mathbf{=}\mathit{n}\mathit{R}\mathit{T}$

The ideal gas law for the given condition can be written as,

$\mathit{n}\mathbf{=}\frac{\mathbf{PV}}{\mathbf{RT}}$

Here,

V is the volume (5.0 L)

T is the temperature ($\mathbf{37}\mathbf{°}\mathit{C}\mathbf{=}\mathbf{310}\mathbf{}\mathit{K}$).

P is the pressure (328 torr).

Determination of moles

Before putting the value in the equation pressure needs to be changes in atm as the value of gas constant used will be in $\mathit{L}\mathbf{}\mathit{a}\mathit{t}\mathit{m}\mathbf{}{\mathit{K}}^{\mathbf{-}\mathbf{1}}\mathit{m}\mathit{o}{\mathit{l}}^{\mathbf{-}\mathbf{1}}$.

$\mathbf{1}\mathbf{}\mathit{t}\mathit{o}\mathit{r}\mathit{r}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{00132}\mathbf{}\mathit{a}\mathit{t}\mathit{m}$

And,

$\mathbf{328}\mathbf{}\mathit{t}\mathit{o}\mathit{r}\mathit{r}\mathbf{\times }\frac{\mathbf{0}\mathbf{.}\mathbf{00132}}{\mathbf{1}\mathbf{}\mathbf{torr}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{433}\mathbf{}\mathit{a}\mathit{t}\mathit{m}$

The number of moles of gas in the sample is,

$$\begin{gathered} \mathit{n}\mathbf{=}\frac{\mathbf{PV}}{\mathbf{RT}} \\ \mathit{n}\mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{433}\mathbf{}\mathbf{atm}\mathbf{\times }\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{L}}{\mathbf{0}\mathbf{.}\mathbf{0821}\mathbf{}{\mathbf{atmLK}}^{\mathbf{-}\mathbf{1}}{\mathbf{mol}}^{\mathbf{-}\mathbf{1}}\mathbf{310}\mathbf{}\mathbf{K}} \\ \mathit{n}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{085}\mathit{m}\mathit{o}\mathit{l} \end{gathered}$$

Thus, the number of moles of gas in the sample are 0.085 mol.