Question

At constant temperature, a gas is at a pressure of 940 mm of Hg. At what pressure, its volume decreases by 40%.

• A. 564 mm of Hg
• B. 1860 mm of Hg
• C. 2350 mm of Hg
• D. 1567 mm of Hg

Answer 1

The correct option is D

1567 mm of Hg

Explanation for the correct option:

Boyle's law: At constant temperature, for a given mass of a gas, Volume (V) is inversely proportional to Pressure (P).

$V\propto \frac{1}{P}$

Therefore, for a gas at two different conditions of temperature and pressure follow the relationship given below:

$P_1{V}_1=P_2{V}_2$

P₁ =940 mm of Hg (given)

P₂ = Pressure at which volume is reduced by 40%

V₂ = Volume decreased by 40%

$V_2=V_1-\frac{40}{100}{V}_1=\frac{60}{100}{V}_1$

V₁= Volume at pressure P₁

$$\begin{gathered} 940\times V_1=P_2\times \frac{60}{100}{V}_1 \\ {P}_2=\frac{940\times 100}{60}=1566.5\approx 1567mmofHg \end{gathered}$$

Hence, option (d) is correct.