Q. 8.37 - An Introduction to General, Organic, and Biological Chemistry

Question

A gas sample has a pressure of $744 mmHg$ when the temperature is $22°C$. What is the final temperature, in degrees Celsius, when the pressure is $766 mmHg$, with no change in the volume or amount of gas?

Step-by-Step Solution

Answer

The final temperature of the given gas is $31°C$.

Step 1: Given Information

We need to find the final temperature of the gas. 

Step 2: Simplify

Considering the Gay- Lussac's Law that if a constant volume and amount of gas are maintained, the pressure will be increased. In the temperature-pressure relationship which is known as Gay-Lussac's law, the pressure of a gas decreases, and a decrease in temperature decreases the pressure of the gas till the volume of the gas doesn't change. i.e.   

$\frac{P_1}{T_1}=\frac{P_2}{T_2} ... \left(1\right)$

Step 3: Calculation

Here we have the quantities available, that is   

the initial temperature  $T_1=22°=\left(22+273\right)K=295K$

initial pressure  $P_1=744 mmHg$

the final pressure $P_2=766 mmHg$

Now, calculating the final temperature  $T_2$ from equation $\left(1\right)$

$$\begin{gathered} \frac{P_1}{T_1}=\frac{P_2}{T_2} \\ {T}_2=\frac{P_2\times T_1}{P_1} \end{gathered}$$

Putting the values:

$$\begin{gathered} T_2=\frac{766 mmHg\times 295K}{744 mmHg} \\ {T}_2=\frac{225970K}{744} \\ =304K \end{gathered}$$

The final temperature is $31°C$.$T_2=304 K=\left(304-273\right)°C=31°C$