Question

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

Short answer

The final volume is$0.83L$.

Step-by-step solution

Given Information

We need to find the final volume.

Simplify

Initial conditions as;

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

Final conditions as:

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

Now, calculating the final volume $V_2$:

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