Question

The density of a gas A is thrice that of a gas B at the same temperature. The molecular weight of gas B is twice that of A. What will be the ratio of pressure acting on B and A?

• A. \(\frac{1}{4}\)
• B. \(\frac{7}{8}\)
• C. \(\frac{2}{5}\)
• D. \(\frac{1}{6}\)

Hint:

In questions about gas density, pressure, and molecular weight, use the ideal gas law to relate these quantities.

Answer 1

The Correct Option is D

By the ideal gas law, pressure \(P\) is related to density \(d\) by the formula: \[ P = \frac{dRT}{M} \] where: - \(d\) is the density, - \(R\) is the universal gas constant, - \(T\) is the temperature, and - \(M\) is the molecular weight. Since density of gas A is three times that of gas B and the molecular weight of gas B is twice that of gas A, the ratio of pressures is given by: \[ \frac{P_B}{P_A} = \frac{d_B \cdot M_A}{d_A \cdot M_B} = \frac{3 \cdot M_A}{1 \cdot 2 M_A} = \frac{3}{6} = \frac{1}{6} \] Thus, the correct answer is Option (D).