Question

Isotope separation is carried out by a method based on the effusion of isotope-substituted molecules passing through an opening whose diameter is less than the mean free path of gas molecules. The method could be used to separate 35Cl and 37Cl isotopes by taking advantage of the different rates of effusion for their respective compounds in the form of HCl .Calculate the ratio of effusion rates for H35Cl and H37Cl . The atomic mass of Cl -35 is 34.9689 amu and that of Cl -37 is 36.9659 amu .

Answer 1

The ratio of effusion rates for H35Cl and H37Cl is approximately 0.948.

Step-by-step explanation:

The effusion rate of a gas is inversely proportional to the square root of its molar mass according to Graham's law. Therefore, we can calculate the ratio of the effusion rates for H35Cl and H37Cl by finding the square root of the molar masses of their respective compounds.

The molar mass of H35Cl is approximately (1 hydrogen atom + 35 atomic mass units of chlorine) = 36 amu, and the molar mass of H37Cl is approximately (1 hydrogen atom + 37 atomic mass units of chlorine) = 38 amu.

To find the ratio, we divide the square root of the molar mass of H35Cl by the square root of the molar mass of H37Cl:

Ratio = √(36 amu) / √(38 amu)

Simplifying the equation, we get:

Ratio ≈ 0.948