Answer to Question #165578 in Chemistry for Cleopatria

Question

Suppose that an element has two isotopes. The average atomic mass of the element is  49.237 u. One isotope has a mass of 41.834 u

 and an abundance of 35.94%.

Calculate the mass of the second isotope.

Answer 1

Solution:

The average atomic mass of an element is the sum of the masses of its isotopes, each multiplied by its natural abundance.

Average atomic mass = f₁M₁ + f₂M₂ +… + f_nM_n,

where f is the fraction representing the natural abundance of the isotope and M is the mass number (weight) of the isotope.

The average atomic mass of the element is 49.237 u.

f₁ = 0.3594 (35.94%)

M₁ = 41.834 u

f₂ = 1 - 0.3594 = 0.6406 (64.06%)

M₂ = unknown

Hence,

The average atomic mass of the element = f₁M₁ + f₂M₂

49.237 = 0.3594 × 41.834 + 0.6406 × M₂

34.202 = 0.6406 × M₂

M₂ = 53.390 u

Answer: The mass of the second isotope is 53.390 u.