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scme1702
The ratio of the rates is equivalent to the square root of the ratio of the molar masses.
Molar mass of chlorine: 71
Molar mass of ethane: 30

V(Cl) / V(C₂H₆) = √(30 / 71)
V(Cl) / V(C₂H₆) = 0.65

The relative rate of diffusion of chlorine to ethane is 0.65
dexteright02

Hello!

Find the relative rate of diffusion for the gases chlorine, CL2 and ethane, C2H6

  • We have the following data:

[tex]R_1\:(rate)[/tex]

[tex]R_2\:(rate)[/tex]

[tex]M_1\:(molecular\:mass\:Cl_2)[/tex]

Cl2 = 2*(35.5u) = 71u → M1 = 71 g/mol

[tex]M_2\:(molecular\:mass\:C_2H_6)[/tex]

C2 = 2*(12u) = 24u

H6 = 6*(1u) = 6u

C2H2 = 24u + 6u = 30u → M2 = 30 g/mol

*** Note: Under Graham's Law, the rate of diffusion and effusion of gases (volume that leaks per unit time, that is, in seconds) is inversely proportional to the square root of your molar masses.

  • We apply the data to Graham's formula (Law of Effusion and Diffusion of gases):

[tex]\dfrac{R_1}{R_2} = \sqrt{\dfrac {M_2}{M_1}}[/tex]

[tex]\dfrac{R_1}{R_2} = \sqrt{\dfrac {30}{71}}[/tex]

[tex]\boxed{\boxed{\dfrac{R_1}{R_2} \approx 0.65}}\:\:or\:\:\boxed{\boxed{\dfrac{R_1}{R_2} \approx 65\%}}\to(relative\:rate)\:\:\:\:\:\:\bf\green{\checkmark}[/tex]

Answer:

The relative rate of diffusion for the gases chlorine and ethane is 65%

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