## 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 amuThe 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.