Q. 8.83 - An Introduction to General, Organic, and Biological Chemistry

Question

A gas sample has a volume of  $4250 mL$ at $15°C$ and $745 mmHg$. What is the final temperature, in degrees Celsius, after the sample is transferred to a different container with a volume of $2.50 L$and a pressure of $1.20atm$ if the amount of gas does not change? $(8.5)$

Step-by-Step Solution

Answer

The final temperature is $65.5°C$.

Step 1: Given Information

We need to find the final temperature.

Step 2: Simplify

Initial conditions as:

$P_1=745 mmHg=098 atm$

$V_1=4250 mL=4.25 L$

$T_1=15°C=(15+273)K=288K$

Final conditions as:

$P_2=1.2 atm$

$V_2=2.5L$

Now, calculating the final temperature $T_2$:

Here,

$$\begin{gathered} \frac{PV}{T}=Cons\tan t \\ {T}_2=\frac{P_1\times V_2\times T_1}{P_1\times V_1} \\ {T}_2=\frac{1.2 atm\times 2.5 L\times 288 K}{0.98 atm\times 4.25 L} \\ {T}_2=207.4K=(207.4-273)°C=65.5°C \end{gathered}$$