Under the same conditions of temperature and pressure, Gas X has a molar mass of 4\text{ g… — JAMB UTME

Under the same conditions of temperature and pressure, Gas X has a molar mass of $4\text{ g/mol}$ and Gas Y has a molar mass of $64\text{ g/mol}$ . How many times faster will Gas X diffuse compared to Gas Y?

4 times as fastAnswer
B
16 times as fast
C
2 times as fast
D
0.25 times as fast

Answer

Gas X diffuses 4 times as fast as Gas Y.

According to Graham's Law of Diffusion, the rate of diffusion

r

of a gas is inversely proportional to the square root of its molar mass

M

. Therefore,

\frac{r_X}{r_Y} = \sqrt{\frac{M_Y}{M_X}} = \sqrt{\frac{64}{4}} = \sqrt{16} = 4

. This means Gas X diffuses 4 times faster than Gas Y.

Step-by-Step Solution

State Graham's Law formula for relative rates of diffusion

\frac{r_X}{r_Y} = \sqrt{\frac{M_Y}{M_X}}

The rate of diffusion is inversely proportional to the square root of molar mass.

Substitute the given molar masses into the formula

\frac{r_X}{r_Y} = \sqrt{\frac{64}{4}} = \sqrt{16}

Molar mass of Gas Y (

M_Y

) is

64\text{ g/mol}

and Gas X (

M_X

) is

4\text{ g/mol}

Simplify the square root expression

\frac{r_X}{r_Y} = 4

The square root of 16 is 4, showing Gas X diffuses 4 times as fast as Gas Y.

Key Concept

Graham's Law of Diffusion

Estimated Time:45s

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