Question

20 mL of gas \(A\) and 10 mL of gas \(B\) diffuse through a porous membrane separately in 1 minute. If the vapor density of \(B\) is \(X\), what is the vapor density of \(A\)?

• A. \(2X\)
• B. \(4X\)
• C. \(\dfrac{X}{4}\)
• D. \(\dfrac{X}{2}\)

Hint:

According to Graham's law, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass or vapor density: \[ r\propto \frac{1}{\sqrt{VD}}. \]

Answer 1

The Correct Option is C

Step 1: Apply Graham's law.
\(\frac{r_A}{r_B} = \frac{20}{10} = 2 = \sqrt{\frac{M_B}{M_A}} = \sqrt{\frac{VD_B}{VD_A}}\).

Step 2: Solve for VD of A.
Squaring: \(4 = \frac{X}{VD_A}\), so \(VD_A = \frac{X}{4}\).
\[ \boxed{\frac{X}{4}} \]