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Chapter 2

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.

Step-by-Step

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.

ANSWER CHECK

The average mass (atomic weight) should be near the mass of the isotope with greatest abundance: in this case, 51.9405 amu with fractional abundance of 0.8379. This provides a quick check on your answer to this type of problem; any “answer” that is far from this will be incorrect.