A sealed rigid canister contains a fixed mass of nitrogen gas at an initial pressure of 1.… — JAMB UTME

A sealed rigid canister contains a fixed mass of nitrogen gas at an initial pressure of $1.50 \times 10^5\text{ Pa}$ and a temperature of $27^\circ\text{C}$ . If the gas is heated at constant volume until its temperature reaches $127^\circ\text{C}$ , what is the new pressure of the gas?

$2.00 \times 10^5\text{ Pa}$ Answer
B
$7.06 \times 10^5\text{ Pa}$
C
$1.13 \times 10^5\text{ Pa}$
D
$3.19 \times 10^4\text{ Pa}$

Answer

The new pressure of the gas is

2.00 \times 10^5\text{ Pa}

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

P_1/T_1 = P_2/T_2

). Converting temperatures to Kelvin gives

300\text{ K}

and

400\text{ K}

. Substituting these values yields

P_2 = 1.50 \times 10^5 \times (400/300) = 2.00 \times 10^5\text{ Pa}

Step-by-Step Solution

Convert the initial and final temperatures from degrees Celsius to Kelvin.

T_1 = 27 + 273 = 300\text{ K}

and

T_2 = 127 + 273 = 400\text{ K}

Gas laws require absolute temperature in Kelvin for proportional reasoning.

Apply Pressure Law (Gay-Lussac's Law) for constant volume.

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

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

Substitute the known values into the equation and solve for

P_2

P_2 = 1.50 \times 10^5\text{ Pa} \times \frac{400\text{ K}}{300\text{ K}} = 2.00 \times 10^5\text{ Pa}

Multiplying initial pressure by the temperature ratio gives the final pressure.

Key Concept

Pressure Law (Gay-Lussac's Law) states that at constant volume,

P \propto T

where

T

must be in Kelvin.

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Step-by-Step Solution

Key Concept

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