Chapter 4, Problem 78A

Interpretation Introduction

Interpretation:

Chromium’s atomic mass is to be calculated from the given data.

Concept introduction:

Atomic mass of an element is the weighted average mass of the isotopes of that element.

Answer to Problem 78A

Atomic mass of chromium is 51.996 amu.

Explanation of Solution

Isotope	Percent Abundance	Mass (amu)
Cr50	4.35	49.946
Cr52	83.79	51.941
Cr53	9.50	52.941
Cr54	2.36	53.939

Cr50

Atomic mass − 49.946 amu

Percentage abundance − 4.35%

$\begin{array}{l}{\text{Mass Contribution (M}}_1)=\text{ Atomic mass }\times \text{ Percentage Abundance }\\ \text{ = 49}\text{.946 }\times \text{ 4}\text{.35\%}\\ \text{ = 2}\text{.173 amu}\end{array}$

Cr52

Atomic mass − 51.941 amu

Percentage abundance − 83.79%

$\begin{array}{l}{\text{Mass Contribution (M}}_2)=\text{ Atomic mass }\times \text{ Percentage Abundance }\\ \text{ = 51}\text{.941 }\times \text{ 83}\text{.79\%}\\ \text{ = 43}\text{.521 amu}\end{array}$

Cr53

Atomic mass − 52.941 amu

Percentage abundance −9.50%

$\begin{array}{l}{\text{Mass Contribution (M}}_3)=\text{ Atomic mass }\times \text{ Percentage Abundance }\\ \text{ = 52}\text{.941 }\times \text{ 9}\text{.50\%}\\ \text{ = 5}\text{.029 amu}\end{array}$

Cr54

Atomic mass − 53.939 amu

Percentage abundance − 2.36%

$\begin{array}{l}{\text{Mass Contribution (M}}_4)=\text{ Atomic mass }\times \text{ Percentage Abundance }\\ \text{ = 53}\text{.939 }\times \text{ 2}\text{.36\%}\\ \text{ = 1}\text{.273 amu}\end{array}$

$\begin{array}{l}\text{Atomic mass of silver = Sum of mass contribution}\\ {\text{ = M}}_1{\text{ + M}}_2{\text{ + M}}_3{\text{ + M}}_4\\ \text{ = 2}\text{.173 + 43}\text{.521 + 5}\text{.029 + 1}\text{.273}\\ \text{ = 51}\text{.996 amu}\end{array}$

Conclusion

Thus, chromium atomic mass is 51.996 amu.