Chapter 4, Problem 77A

.

Interpretation Introduction

Interpretation:

Silver has two isotopes: $\text{A}\text{g}$ with a mass of 106.905 amu and 52.00% of abundance, and $\text{A}\text{g}$ with a mass of 108.905 amu and 48.00% of abundance. Atomic mass of silver is to be calculated.

Concept introduction:

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

Answer to Problem 77A

Atomic mass of silver is 107.864 amu.

Explanation of Solution

$\text{A}\text{g}$

Atomic mass − 106.905 amu

Percentage Abundance − 52.00%

$\begin{array}{l}{\text{Mass contribution (M}}_1)\text{ = Atomic mass }\times \text{ Percentage abundance}\\ \text{ = 106}\text{.905 }\times \text{ 52\%}\\ \text{ = 55}\text{.590}\end{array}$

$\text{A}\text{g}$

Atomic mass − 108.905 amu

Percentage Abundance − 48.00%

$\begin{array}{l}{\text{Mass contribution (M}}_2)\text{ = Atomic mass }\times \text{ Percentage abundance}\\ \text{ = 108}\text{.905 }\times \text{ 48\%}\\ \text{ = 52}\text{.274}\end{array}$

$\begin{array}{l}\text{Atomic Mass = Sum of mass contribution}\\ {\text{ = M}}_1{\text{ + M}}_2\\ \text{ = 55}\text{.590 + 52}\text{.274}\\ \text{ = 107}\text{.864 amu}\end{array}$

Conclusion

Atomic mass of silver with isotopes $\text{A}\text{g}$ and $\text{A}\text{g}$ is 107.864amu.