Question

The pressure of a given mass of a gas in a container of volume V at constant temperature is reduced to \( \frac{1}{4} \) of initial value. Calculate the \( \% \) change in volume. 

(1) \( 100 \% \)

(2) \( 200 \% \)

(3) \( 300 \% \)

(4) \( 400 \% \)

Answer 1

The correct option is (3) 300%

In Boyle's Law, which states that for a given mass of gas at constant temperature, the product of pressure and volume is constant. This can be expressed as:

P₁V₁ = P₂V₂

Where:

P₁ = initial pressure

V₁ = initial volume

P₂ = final pressure

V₂ = final volume

Given that the final pressure P₂ is one third of the initial pressure P₁:

\(P_2 = \frac{1}{4} P_1\)

According to Boyle's Law:

P₁V₁ = P₂V₂

Substitute P₂ with \(\frac{1}{4} P_1\):

\(P_1 V_1 = (\frac{1}{4} P_1)V_2\)

Since P₁ is not zero, we can divide both sides by P₁:

\(V_1 = \frac{1}{4}V_2\)

Multiply both sides by 3 to solve for V₂:

\(V_2 = 4V_1\)

The change in volume ΔV is given by:

ΔV = V₂ − V₁ = 4V₁ − V₁ = 3V₁

The percentage change in volume is calculated as:

Percentage Change = \((\frac{\Delta V}{V_1}) \times 100\)

Substitute ΔV:

Percentage Change = \((\frac{3V_1}{V_1}) \times 100 = 3 \times 100 = 300\%\)