Q5.27P - Chemistry: Molecular Nature Of Matter And Change

Question

A sample of carbon monoxide occupies 3.65 L at 298 K and 745 torr. Find its volume at $\mathbf{-}\mathbf{14}\mathbf{°}\mathit{C}$ and 367 torr.

Step-by-Step Solution

Answer

Answer

The final volume is 6.44 L.

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 can also be written as,

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

(Moles of the sample are fixed)

Step 2: Determination of final volume

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

Here,

${\mathit{V}}_{\mathbf{1}}$ is the initial volume (3.65 L).

${\mathit{V}}_{\mathbf{2}}$ is the final volume.

${\mathit{T}}_{\mathbf{1}}$ is the initial temperature (298 K).

${\mathit{T}}_{\mathbf{2}}$ is the final temperature (259 K).

${\mathit{P}}_{\mathbf{1}}$ is the initial pressure (745 torr).

${\mathit{P}}_{\mathbf{2}}$ is the final pressure (367 torr).

The final volume of the given sample at STP is,

$$\begin{gathered} {\mathit{V}}_{\mathbf{2}}\mathbf{=}\frac{{\mathbf{P}}_{\mathbf{1}}{\mathbf{V}}_{\mathbf{1}}}{{\mathbf{T}}_{\mathbf{1}}}\mathbf{=}\frac{{\mathbf{P}}_{\mathbf{2}}{\mathbf{V}}_{\mathbf{2}}}{{\mathbf{T}}_{\mathbf{2}}} \\ {\mathit{V}}_{\mathbf{2}}\mathbf{=}\frac{\mathbf{745}\mathbf{ }\mathbf{torr}\mathbf{\times }\mathbf{3}\mathbf{.}\mathbf{65}\mathbf{ }\mathbf{L}}{\mathbf{298}\mathbf{K}}\mathbf{\times }\frac{\mathbf{259}\mathbf{K}}{\mathbf{367}\mathbf{torr}} \\ {\mathit{V}}_{\mathbf{2}}\mathbf{=}\mathbf{6}\mathbf{.}\mathbf{44}\mathit{L} \end{gathered}$$

Thus, the final volume is 6.44 L.