A fixed mass of gas occupies a volume of 800\text{ cm}^3 at a pressure of 1.5\text{ atm} u… — JAMB UTME

A fixed mass of gas occupies a volume of $800\text{ cm}^3$ at a pressure of $1.5\text{ atm}$ under isothermal conditions. What is the final volume of the gas in $\text{cm}^3$ if the pressure is reduced to $570\text{ mmHg}$ ? ( $1\text{ atm} = 760\text{ mmHg}$ )

$1600\text{ cm}^3$ Answer
B
$400\text{ cm}^3$
C
$2.11\text{ cm}^3$
D
$22400\text{ cm}^3$

Answer

The final volume of the gas is

1600\text{ cm}^3

Under isothermal conditions, Boyle's Law applies (

P_1V_1 = P_2V_2

). Converting the initial pressure of

1.5\text{ atm}

\text{mmHg}

gives

1140\text{ mmHg}

. Substituting the values into

1140 \times 800 = 570 \times V_2

yields

V_2 = 1600\text{ cm}^3

Step-by-Step Solution

Convert the initial pressure (

P_1

) to the same unit as the final pressure (

P_2

P_1 = 1.5\text{ atm} \times 760\text{ mmHg/atm} = 1140\text{ mmHg}

Units of pressure must be consistent before applying gas law equations.

Apply Boyle's Law formula for isothermal conditions.

P_1V_1 = P_2V_2 \implies 1140\text{ mmHg} \times 800\text{ cm}^3 = 570\text{ mmHg} \times V_2

Boyle's Law states that for a fixed mass of gas at constant temperature, pressure and volume are inversely proportional.

Rearrange the equation to solve for

V_2

V_2 = \frac{1140 \times 800}{570} = 1600\text{ cm}^3

Calculates the expanded volume resulting from the decrease in pressure.

Key Concept

Boyle's Law (

P_1V_1 = P_2V_2

at constant temperature)

Estimated Time:1m 30s

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