Question

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

Short answer

The final temperature is$65.5°C$.

Step-by-step solution

Given Information

We need to find the final temperature.

Simplify

Initial conditions as:

$P_1=745mmHg=098atm$

$V_1=4250mL=4.25L$

$T_1=15°C=(15+273)K=288K$

Final conditions as:

$P_2=1.2atm$

$V_2=2.5L$

Now, calculating the final temperature $T_2$:

Here,

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