A sample of oxygen gas occupies a volume of 450\text{ cm}^3 at a temperature of 27^\circ\t… — JAMB UTME

A sample of oxygen gas occupies a volume of $450\text{ cm}^3$ at a temperature of $27^\circ\text{C}$ . If the pressure remains constant, what will be the volume of the gas when its temperature is increased to $207^\circ\text{C}$ ?

$720\text{ cm}^3$ Answer
B
$3450\text{ cm}^3$
C
$281\text{ cm}^3$
D
$630\text{ cm}^3$

Answer

The volume of the gas at

207^\circ\text{C}

720\text{ cm}^3

According to Charles's Law, the volume of a gas is directly proportional to its absolute temperature when pressure remains constant (

V_1/T_1 = V_2/T_2

). Converting the temperatures to Kelvin (

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

and

T_2 = 207 + 273 = 480\text{ K}

) and calculating gives

V_2 = 450 \times (480 / 300) = 720\text{ cm}^3

Step-by-Step Solution

Convert temperatures from Celsius to the absolute (Kelvin) scale.

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

and

T_2 = 207 + 273 = 480\text{ K}

Gas laws require temperatures to be expressed on the absolute temperature scale (Kelvin).

Apply Charles's Law equation.

\frac{V_1}{T_1} = \frac{V_2}{T_2} \implies V_2 = V_1 \times \frac{T_2}{T_1}

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

Substitute the known values and calculate

V_2

V_2 = 450 \times \frac{480}{300} = 450 \times 1.6 = 720\text{ cm}^3

Completing the arithmetic yields the final volume.

Key Concept

Charles's Law states that at constant pressure, the volume of a given mass of gas is directly proportional to its absolute temperature (

V \propto T

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