Q. 8.45 - An Introduction to General, Organic, and Biological Chemistry

Question

A $124 mL$ bubble of hot gas initially at $212 °C$ and $1.80 atm$ is emitted from an active volcano. What is the final temperature, in degrees Celsius, of the gas in the bubble outside the volcano if the final volume of the bubble is $138 mL$and the pressure is $0.800 atm$, if the amount of gas does not change?

Step-by-Step Solution

Answer

The final temperature of the gas is $-33.11°C$.

Step 1: Given Information

We need to find the final temperature of gas.

Step 2: Simplify

The combined gas law is:

$\frac{P_1\times V_1}{T_1}=\frac{P_2\times V_2}{T_2}$

Consider:

initial pressure $P_1=1.8 atm$

initial temperature $T_1=212°C=\left(212+273\right)K=485K$

initial volume $V_1=124 mL$

final  pressure $P_2=0.8 atm$

final volume $V_2=138 mL$

Now, calculating the final temperature $T_2$ is:

$$\begin{gathered} T_2=\left[\left(P_2\right)\times \left(V_2\right)\right]÷\left(\frac{P_1\times V_1}{T_1}\right) \\ {T}_2=\left[\left(0.8 atm\right)\times \left(138 mL\right)\right]÷\left(\frac{1.8 atm\times 124 mL}{485K}\right) \\ {T}_2=239.89K=(239.89-273)°C=-33.11°C \end{gathered}$$