How to Calculate an Average Atomic Weight

To do these problems you need some information: the exact atomic weight for each naturally-occuring stable isotope and its percent abundance. These values can be looked up in a standard reference book such as the "Handbook of Chemistry and Physics."

This problem can also be reversed. Study the tutorial below and then look at the problems done in the reverse direction.

Example #1: Carbon

To calculate the average atomic weight, each exact atomic weight is multiplied by its percent abundance (expressed as a decimal). Then, add the results together and round off to an appropriate number of significant figures.

This is the solution for carbon:

(12.000000) (0.9890) + (13.003355) (0.0110) = 12.011

Example #2: Nitrogen

This is the solution for nitrogen:

(14.003074) (0.9963) + (15.000108) (0.0037) = 14.007

Video: How to Calculate an Average Atomic Weight.

This type of calculation can be done in reverse, where the isotopic abundances can be calculated knowing the average atomic weight. Go to tutorial on reverse direction.

Example #5: In a sample of 400 lithium atoms, it is found that 30 atoms are lithium-6 (6.015 g/mol) and 370 atoms are lithium-7 (7.016 g/mol). Calculate the average atomic mass of lithium.

Solution:

1) Calculate the percent abundance for each isotope:

Li-6: 30/400 = 0.075
Li-7: 370/400 = 0.925

2) Calculate the average atomic weight:

x = (6.015) (0.075) + (7.016) (0.925)

x = 6.94 g/mol

Calculate the average atomic weight for:

1) magnesium

mass number	exact weight	percent abundance
24	23.985042	78.99
25	24.985837	10.00
26	25.982593	11.01

2) molybdenum

mass number	exact weight	percent abundance
92	91.906808	14.84
94	93.905085	9.25
95	94.905840	15.92
96	95.904678	16.68
97	96.906020	9.55
98	97.905406	24.13
100	99.907477	9.63

3) tin (this one is optional!! Suggestion: set it up as a spreadsheet, take it into class and impress your teacher.)

mass number	exact weight	percent abundance
112	111.904826	0.97
114	113.902784	0.65
115	114.903348	0.36
116	115.901747	14.53
117	116.902956	7.68
118	117.901609	24.22
119	118.903310	8.58
120	119.902200	32.59
122	121.903440	4.63
124	123.905274	5.79

The answers? Look on a periodic table!! Remember that the above is the method by which the average atomic weight for the element is computed. No one single atom of the element has the given atomic weight because the atomic weight of the element is an average, specifically called a "weighted" average.

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