Using Graham's Law of Diffusion, determine the molar mass of an unknown gas if ethane (C2H6) diffuses at a rate of 3.6 imes 10⁻⁶ mol/h and the unknown gas diffuses at 1.3 imes 10⁻⁶ mol/h?

Molar mass of Krypton (Kr) = 83.80 g/mol
Molar mass of Oxygen ($O_2$) = $2 \times 16.00 \text{ g/mol} = 32.00 \text{ g/mol}$

The gas with the lower molar mass diffuses more rapidly. Since $M_{O_2}$ (32.00 g/mol) is less than $M_{Kr}$ (83.80 g/mol), oxygen ($O_2$) diffuses more rapidly.

Using Graham's Law:

Oxygen ($O_2$) diffuses more rapidly. The relative rate is $\boxed{\text{1.618}}$.

Molar mass of Nitrogen ($N_2$) = $2 \times 14.01 \text{ g/mol} = 28.02 \text{ g/mol}$
Molar mass of Acetylene ($C_2H_2$) = $(2 \times 12.01 \text{ g/mol}) + (2 \times 1.008 \text{ g/mol})$

The gas with the lower molar mass diffuses more rapidly. Since $M_{C_2H_2}$ (26.036 g/mol) is less than $M_{N_2}$ (28.02 g/mol), acetylene ($C_2H_2$) diffuses more rapidly.

Using Graham's Law:

Acetylene ($C_2H_2$) diffuses more rapidly. The relative rate is $\boxed{\text{1.037}}$.