A sealed rigid glass flask contains carbon dioxide gas at a temperature of 7^\circ\text{C}… — JAMB UTME

A sealed rigid glass flask contains carbon dioxide gas at a temperature of $7^\circ\text{C}$ and a pressure of $1.4\text{ atm}$ . If the flask is heated to a final temperature of $77^\circ\text{C}$ at constant volume, what is the new pressure exerted by the gas?

$1.75\text{ atm}$ Answer
B
$15.4\text{ atm}$
C
$1.12\text{ atm}$
D
$2.10\text{ atm}$

Answer

The new pressure exerted by the gas is

1.75\text{ atm}

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

P_1/T_1 = P_2/T_2

). Converting the temperatures to Kelvin (

T_1 = 7 + 273 = 280\text{ K}

and

T_2 = 77 + 273 = 350\text{ K}

) and solving for

P_2

gives

P_2 = 1.4 \times \frac{350}{280} = 1.75\text{ atm}

Step-by-Step Solution

Convert initial and final temperatures from Celsius to Kelvin.

T_1 = 7 + 273 = 280\text{ K}

and

T_2 = 77 + 273 = 350\text{ K}

Gas laws require absolute temperature in Kelvin for proportional relationship calculations.

Apply the Pressure Law (Gay-Lussac's Law).

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

For a fixed mass of gas at constant volume, pressure is directly proportional to absolute temperature.

Substitute the values to calculate the final pressure

P_2

P_2 = 1.4 \times \frac{350}{280} = 1.4 \times 1.25 = 1.75\text{ atm}

Simplifying the fraction

\frac{350}{280} = \frac{5}{4} = 1.25

gives the final answer.

Key Concept

Pressure Law (Gay-Lussac's Law)

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