Q. 8.81 - An Introduction to General, Organic, and Biological Chemistry

Question

Your spaceship has docked at a space station above Mars. The temperature inside the space station is carefully controlled $24°C$ at a pressure of $745 mmHg$. A balloon with a volume of $425 mL$drifts into the airlock where the temperature is $-95°C$ and the pressure is $0.115 atm$. What is the final volume, in milliliter, of the balloon if $n$ does not change and the balloon is very elastic?$\left(8.5\right)$

Step-by-Step Solution

Answer

The final volume is $2221.6 mL$.

Step 1: Given Information

We need to find the final volume.

Step 2: Simplify

We consider:

Initial pressure is $P_1=745 mmHg=098 atm$

Initial volume is $V_1=435$

Initial temperature is $T_1=24°C=(24+273)K=297K$

Final pressure is $P_2=0.115 atm$

Final temperature is $T_2=-95°C=\left(-95+273k\right)=178K$

Now, the calculating the final volume $V_2$is:

$$\begin{gathered} \frac{PV}{T}=Cons\tan t \\ {V}_2=\frac{P_1\times V_1\times T_2}{T_1\times P_2} \\ {V}_2=\frac{0.98\times 435 mL\times 178 K}{297K\times 0.115 atm} \\ {V}_2=2221.6 mL \end{gathered}$$