Q. 8.75 - An Introduction to General, Organic, and Biological Chemistry

Question

A weather balloon has a volume of $750L$ when filled with helium  at $8°C$ at a pressure of $380Torr$. What is the final volume, in liters, of the balloon, where the pressure is $0.20atm$ and the temperature is $-45°C$, when $n$ does not change?

Step-by-Step Solution

Answer

The final volume of the balloon is $1521.35L$.

Step 1: Given Information

We have given the volume of weather balloon is $750L$, the temperature is $8°C$ and the pressure is $380Torr$.

Step 2: Simplify

For determining the final volume of the ballon 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 $P_1=380 torr=\left(\frac{380}{760}\right)torr=0.5atm$,

initial volume $V_1=750L$,

initial temperature $T_1=8°C=\left(8+273\right)K=281K$, and

final pressure $P_2=0.20atm$,

final temperature $T_2=-45°C=\left(-45+273\right)K=128K$

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

$$\begin{gathered} V_2=\frac{P_1{V}_1{T}_2}{P_2{T}_1} \\ {V}_2=\frac{0.5atm\times 750L\times 228K}{0.20atm\times 281K}=\frac{85500}{56.2}L \\ {V}_2=1521.35L \end{gathered}$$