A sample of nitrogen gas enclosed in a constant-volume container exerts a pressure of 2.50… — JAMB UTME

A sample of nitrogen gas enclosed in a constant-volume container exerts a pressure of $2.50\text{ atm}$ at a temperature of $-23^\circ\text{C}$ . To what temperature, in degrees Celsius ( $^\circ\text{C}$ ), must the gas be heated so that its pressure increases to $4.00\text{ atm}$ ?

Answer: 127 °C

Answer

The gas must be heated to

127^\circ\text{C}

According to Gay-Lussac's Pressure Law, for a fixed mass of gas at constant volume, pressure is directly proportional to absolute temperature (

P \propto T

). Converting

-23^\circ\text{C}

to Kelvin gives

250\text{ K}

. Solving

\frac{2.50}{250} = \frac{4.00}{T_2}

gives

T_2 = 400\text{ K}

. Converting back to Celsius (

400 - 273

) yields the correct temperature of

127^\circ\text{C}

Step-by-Step Solution

Convert the initial temperature from Celsius to the thermodynamic temperature scale (Kelvin).

T_1 = -23 + 273 = 250\text{ K}

Gas laws strictly require temperature to be expressed in Kelvin.

Use Gay-Lussac's Pressure Law equation

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

to solve for

T_2

T_2 = \frac{P_2 \times T_1}{P_1} = \frac{4.00 \times 250}{2.50} = 400\text{ K}

At constant volume, the pressure of a given mass of gas is directly proportional to its absolute temperature.

Convert the calculated temperature

T_2

back to degrees Celsius.

t_2 = 400 - 273 = 127^\circ\text{C}

The question explicitly requests the final temperature in degrees Celsius.

Key Concept

Pressure Law (Gay-Lussac's Law)

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