Question

A sample of Freon-12 ($\mathit{C}{\mathit{F}}_{\mathbf{2}}\mathit{C}{\mathit{I}}_{\mathbf{2}}$) occupies 25.5 L at 298 K and 153.3 kPa. Find its volume at STP.

Short answer

Answer

The volume at STP is 35.4 L.

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 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)

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 (25.5 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 (273 K).

${\mathit{P}}_{\mathbf{1}}$is the initial pressure (153.3 kPa).

${\mathit{P}}_{\mathbf{2}}$is the final pressure (101.325 kPa).

(As STP means, the temperature is 273 K and the pressure is 101.325 kPa).

$$\begin{gathered} {\mathit{V}}_{\mathbf{2}}\mathbf{=}\frac{{\mathbf{P}}_{\mathbf{1}}{\mathbf{V}}_{\mathbf{1}}}{{\mathbf{T}}_{\mathbf{1}}}\mathbf{=}\frac{{\mathbf{P}}_{\mathbf{2}}{\mathbf{V}}_{\mathbf{2}}}{{\mathbf{T}}_{\mathbf{2}}} \\ {\mathit{V}}_{\mathbf{2}}\mathbf{=}\frac{\mathbf{153}\mathbf{.}\mathbf{3}\mathbf{kPa}\mathbf{\times }\mathbf{25}\mathbf{.}\mathbf{5}\mathbf{L}}{\mathbf{298}\mathbf{K}}\mathbf{\times }\frac{\mathbf{273}\mathbf{K}}{\mathbf{1010}\mathbf{.}\mathbf{325}\mathbf{kPa}} \\ {\mathit{V}}_{\mathbf{2}}\mathbf{=}\mathbf{35}\mathbf{.}\mathbf{4}\mathit{L} \end{gathered}$$

Thus, the final volume at STP is 35.4 L.