Question

12.Lithium forms compounds which are used in dry cells, storage batteries, and in high-temperature lubricants. It has two naturally occurring isotopes, 6Li (isotopic mass = 6.015123 amu)and 7Li (isotopic mass = 7.016005 amu). Lithium has an average atomic mass of 6.9412 amu.

What is the percent abundance of lithium-6?

(a)6.015 %

(b)7.48%

(c)49.47 %

(d)86.65 %

(e)92.53%

The answer is B but how to do this?

Answer 1

Given,

Isotopic mass of Li-6 = 6.015123 amu

Isotopic mass of Li-7 = 7.016005 amu

The average atomic mass of Li = 6.9412 amu

We know, the formula to calculate the average atomic mass,

Average atomic mass = [Fractional abundance of isotope 1 x Isotopic mass of isotope 1] +[Fractional abundance of isotope1 x Isotopic mass of isotope 1]

Assume, Fractional abundance of Li-6 = "a"

Thus, Fractional abundance of Li-7 = ( 1-a)

Now, Substituting the known values in the above formula and solving for "x",

6.9412 amu = [ a x 6.015123 amu] + [ (1-a) x 7.016005 amu]

6.9412 amu = 6.015123 a + 7.016005 - 7.016005 a

1.000 a = 0.0748

a = 0.0748

Now, Converting this fractional abundance to percentage,

= 0.0748 x 100

= 7.48 %

Thus,

Percent abundance of Li-6 = 7.48 %