Q. 8.84 - An Introduction to General, Organic, and Biological Chemistry

Question

In the fermentation of glucose (winemaking), $780 mL$of $C{O}_2$ gas was produced at $37°C$ and $1.00 atm$. What is the final volume, in liters, of the gas when measured at $22°C$ and $675 mmHg$. If the amount of gas does not change?$(8.5)$

Step-by-Step Solution

Answer

The final volume is $0.83 L$.

Step 1: Given Information

We need to find the final volume.

Step 2: Simplify

Initial conditions as;

$$\begin{gathered} P_1=1 atm \\ {V}_1=780 mL=0.78 L \\ {T}_1=37°C=(37-273)K=310 K \end{gathered}$$

Final conditions as:

$$\begin{gathered} P_2=675 mmHg=0.89 atm \\ {T}_2=22°C=(22+273)K=295K \end{gathered}$$

Now, calculating the final volume $V_2$:

$$\begin{gathered} \frac{PV}{T}=Cons\tan t \\ {V}_2=\frac{P_1\times V_1\times T_2}{T_1\times P_2} \\ {V}_2=\frac{1 atm\times 0.78 L\times 295 K}{310 K\times 0.89 atm}=0.83 L \end{gathered}$$