Q5.28P - Chemistry: Molecular Nature Of Matter And Change

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?

Step-by-Step Solution

Answer

Answer

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

Step 1: 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).

Step 2: 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.