Q. 8.82 - An Introduction to General, Organic, and Biological Chemistry

Question

You are doing research on the planet $X$. The temperature inside the space station is carefully controlled $24°C$ and the pressure is $775 mmHg$. Suppose that a balloon, which has a volume of $850 mL$inside the space station, is placed into the airlock, and floats out to planet $X$. If the planet $X$ has an atmospheric pressure of $0.150 atm$ and the volume of the balloon changes to $3.22L$, what is the temperature, in degree Celsius,  on the planet $X$( $n$ does not change)?$(8.5)$

Step-by-Step Solution

Answer

On the planet $X$, the temperature is $103°C$.

Step 1: Given Information

We need to find the temperature, on the planet $X$.

Step 2: Simplify

Here,

initial pressure is $P_1=0.99 atm$

initial volume is $V_1=0.85L$

initial temperature is $T_1=297K=(297-273)°C=24°C$

final pressure is $P_2=0.15 atm$

final volume is$V_2=3.22 L$

Now, calculating the final temperature $T_2$ is:

$$\begin{gathered} T_2=\frac{P_2\times V_2\times T_1}{P_1\times V_1} \\ =\frac{0.15 atm\times 3.22 L\times 297 K}{0.99 atm\times 0.85L} \\ =170K=(170-273)°C=103°C \end{gathered}$$