Question

When the pressure that a gas exerts on a sealed container changes from 893 mm hg to 778 mm hg, the temperature changes from 49.3 degrees C to degrees C?

Answer 1

7.8 degrees Celsius

Answer 2

Answer: The final temperature of the gas is 7.58 °C.

Explanation: We are given initial and final pressure of the system and we need to find the final temperature of the system.

To calculate it, we use the equation given by Gay-Lussac.

His law states that pressure is directly related to the temperature of the gas.

$P\propto T$

Or,

$\frac{P_1}{T_1}=\frac{P_2}{T_2}$

where,

$P_1$ = initial pressure = 893 mmHg = 1.175atm (Conversion factor: 1atm = 760mmHg)

$T_1$ = initial temperature = 49.3°C = [49.3 + 273.15]K = 322.45K

$P_2$ = Final pressure = 778mmHg = 1.023atm

$T_$ = Final temperature = ?°C

Putting values in above equation, we get:

$\frac{1.175atm}{322.45K}=\frac{1.023atm}{T_2}\\\\T_2=280.73K$

Converting Final temperature from kelvin to degree Celsius.

$T_2=280.73K=[280.73-273.15]^oC=7.58^oC$

Hence, the final temperature of the gas is 7.58 °C.