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## Q. 2.2

Determining Atomic Weight from Isotopic Masses and Fractional Abundances

Chromium, Cr, has the following isotopic masses and fractional abundances:

 Mass Number Isotopic Mass (amu) Fractional Abundance 50 49.9461 0.0435 52 51.9405 0.8379 53 52.9407 0.095 54 53.9389 0.0236

What is the atomic weight of chromium?

PROBLEM STRATEGY

The type of average used to calculate the atomic weight of an element is similar to the “average” an instructor might use to obtain a student’s final grade in a class. Suppose the student has a total exam grade of 76 and a total laboratory grade of 84. The instructor decides to give a weight of 70% to the exams and 30% to the laboratory. How would the instructor calculate the final grade? He or she would multiply each type of grade by its weight factor and add the results:

(76 × 0.70) + (84 × 0.30) = 78

The final grade is closer to the exam grade, because the instructor chose to give the exam grade greater weight.

## Verified Solution

Multiply each isotopic mass by its fractional abundance, then sum:

$49.9461 amu \times 0.0435 =2.17 amu \\51.9405 amu \times 0.8379 =43.52 amu \\52.9407 amu \times 0.0950 =5.03 amu \\53.9389 amu \times 0.0236=\underline{1.27 amu} \\ 51.99 amu$

The atomic weight of chromium is 51.99 amu.