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Zorluk: KolayGraham's Law of Diffusion and Effusion

Under the same conditions of temperature and pressure, Gas X has a molar mass of 4 g/mol4\text{ g/mol} and Gas Y has a molar mass of 64 g/mol64\text{ g/mol}. How many times faster will Gas X diffuse compared to Gas Y?

  1. 4 times as fastCevap
  2. B
    16 times as fast
  3. C
    2 times as fast
  4. D
    0.25 times as fast

Cevap

Gas X diffuses 4 times as fast as Gas Y.
According to Graham's Law of Diffusion, the rate of diffusion rr of a gas is inversely proportional to the square root of its molar mass MM. Therefore, rXrY=MYMX=644=16=4\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.

Adım Adım Çözüm

1
State Graham's Law formula for relative rates of diffusion
rXrY=MYMX\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.
2
Substitute the given molar masses into the formula
rXrY=644=16\frac{r_X}{r_Y} = \sqrt{\frac{64}{4}} = \sqrt{16}
Molar mass of Gas Y (MYM_Y) is 64 g/mol64\text{ g/mol} and Gas X (MXM_X) is 4 g/mol4\text{ g/mol}.
3
Simplify the square root expression
rXrY=4\frac{r_X}{r_Y} = 4
The square root of 16 is 4, showing Gas X diffuses 4 times as fast as Gas Y.

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Graham's Law of Diffusion
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Graham's Law of Diffusion and Effusion

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