Question

Chlorine has two stable isotopes, C1 and C If Cl has a mass of approximately 34.97 and Cl has a mass of approximately 3697 what percent abundances are each found in?

Answer 1

%C₁ = %C₂ = 50%

Step-by-step explanation:

Set up simultaneous equations to solve for two unknowns,

let f₁ and f₂ = fractional abundances of C₁ and C₂ respectively.

Then f₁ + f₂ = 1.00 and

34.97f₁ + 36.97f₂ = Wt. Avg. Atomic Mass (amu) = (34.97 + 36.97)/2 = 35.97amu

Solve equation 1 for f₂ = 1 - f₁ and substitute into equation 2

=> 34.97f₁ + 36.97(1 - f₁) = 35.97

=> 34.97f₁ + 36.97 - 36.97f₁ = 35.97

=> 2f₁ = 1

=> f₁ = 1/2 = 0.50 => 50% abundance for C₁

=> f₂ = 1 - 0.50 = 0.50 => 50% abundance for C₂