Answer to Question #107208 in General Chemistry for Jake

Question

Germanium has 5 common isotopes, a sample contains the following:

70Ge (57.4%), 72Ge (75.9%), 73Ge (21.3%), 74Ge (100%), 76Ge (21.0%) What is the average atomic mass of the sample?

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

57.4%(70Ge) + 75.9%(72Ge) + 21.3%(73Ge) + 100%(74Ge) + 21.0%(76Ge) = 275.6%.

Then,

f(70Ge) = 57.4 / 275.6 = 0.20827;

f(72Ge) = 75.9 / 275.6 = 0.27540;

f(73Ge) = 21.3 / 275.6 = 0.07730;

f(74Ge) = 100 / 275.6 = 0.36284;

f(76Ge) = 21 / 275.6 = 0.07620.

Therefore,

The average atomic mass of germanium (Ge) = 0.20827*70 + 0.27540*72 + 0.07730*73 + 0.36284*74 + 0.07620*76 = 14.5789 + 19.8288 + 5.6429 + 26.85016 + 5.7912 = 72.69196

The average atomic mass of germanium (Ge) = 72.69196

Checking:

Let's compare with table values:

70Ge (20.84%), 72Ge (27.54%), 73Ge (7.73%), 74Ge (36.28%), 76Ge (7.61%).(https://www.britannica.com/science/isotope)

Consequently,

The average atomic mass of germanium (Ge) = 0.2084*70 + 0.2754*72 + 0.0773*73 + 0.3628*74 + 0.0761*76 = 14.588 + 19.8288 + 5.6429 + 26.8472 + 5.7836 = 72.6905.

Table values are well consistent with the values ​obtained.

Answer: The average atomic mass of germanium (Ge) = 72.69196.