Q. 8.76 - An Introduction to General, Organic, and Biological Chemistry

Question

During laparoscopic surgery, carbon dioxide gas is used to expand the abdomen to help create a larger working space. If $4.80L$ of $C{O}_2$ gas at $18°C$ at $785mmHg$ is used. What is the final volume, in litres, of the gas at $37°C$ and a pressure of $745mmHg$, if the amount of $C{O}_2$ does not change?

Step-by-Step Solution

Answer

The final volume of the $C{O}_2$ gas is $5.38L$.

Step 1: Given Information

We have given the volume of $C{O}_2$ gas is $4.80L$, the temperature is $18°C$ and the pressure is $785mmHg$.

Step 2: Calculation

For determining the final volume of the $C{O}_2$ gas in the given condition, we will use the combined gas law equation

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2} ... \left(1\right)$

Considering the given values

Initial pressure $P_1=785mmHg$,

initial volume $V_1=4.8L$,

initial temperature $T_1=18°C=\left(18+273\right)K=291K$, and

final pressure $P_2=745mmHg$,

final temperature $T_2=37°C=\left(37+273\right)K=310K$

Now, for the final volume using all these values in the equation  $\left(1\right)$

$$\begin{gathered} V_2=\frac{P_1{V}_1{T}_2}{P_2{T}_1} \\ {V}_2=\frac{785mmHg\times 4.8L\times 310K}{745mmHg\times 291K}=\frac{1,168,080}{216795}L \\ {V}_2=5.38L \end{gathered}$$