Q. 8.35

Question

Calculate the final temperature, in degrees Celsius, for each of the following, if $V, n$ do not change:

a. A sample of xenon gas at $25 ° C$ and $740 m m H g$ is cooled to give a pressure of $620 m m H g$ .

b. A tank of argon gas with a pressure of $0950 a t m$ at $- 18 ° C$ is heated to give a pressure of $1250 T o r r .$

Step-by-Step Solution

Verified

Answer

a. The final temperature of xenon gas is $- 23.32 ° C$ .

b. The final temperature of argon gas is $167.2 C °$ .

1Part (a) step 1: Given Information

We need to find the final temperature of the xenon gas.

2Part (a) 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.

$\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}} . . . (1)$

3Part (a) step 3: Calculation

Here we have the quantities available, that is

the initial temperature $T_{1} = 25 ° C = (25 + 273) K = 298 K$

initial pressure $P_{1} = 740 m m H g$

the final pressure $P_{2} = 620 m m H g$

Now, calculating the final temperature $T_{2}$ :

$T_{2} = (T_{1}) \times (P_{2}) \div (P_{1}) T_{2} = (298 K) \times (620 m m H g) \div (740 m m H g) T_{2} = 249.67 K = (249.67 - 273) ° C = - 23.32 ° C$