Chapter 4, Problem 67A

Interpretation Introduction

Interpretation : The weighted average atomic mass of nitrogen is to be calculated.

Concept Introduction : The weighted average mass of the atoms in a naturally occurring sample of an element is the atomic mass. The formula of weighted atomic mass is given as:

  $\text{weighted atomic mass}\text{=}\text{atomic mass}\times \text{Natural percent abundance}$

Answer to Problem 67A

The weighted average atomic mass of nitrogen is $14.01\text{amu}$ .

Explanation of Solution

Given information :

The isotope N-14 has an atomic mass of 14.003 amu with 99.67% abundance.

The isotope N-15 has an atomic mass of 15.000 amu with 0.37% abundance.

The weighted average mass of the atoms in a naturally occurring sample of an element is the atomic mass.

The mass and relative abundance of isotopes as they appear in nature are both reflected in the weighted average mass.

The formula of weighted atomic mass is given as:

  $\text{weighted atomic mass}\text{=}\text{atomic mass}\times \text{Natural percent abundance}$

To calculate the weighted atomic mass of N-14, substitute the values in the above formula:

  $\begin{array}{c}\text{weighted atomic mass}\text{=}\text{atomic}\text{mass×Natural percent abundance}\\ \text{=14}\text{.003}\text{amu}\text{×0}\text{.9963}\\ \text{=13}\text{.95}\text{amu}\end{array}$

To calculate the weighted atomic mass of N-15, substitute the values in the above formula:

  $\begin{array}{c}\text{weighted atomic mass}\text{=}\text{atomic}\text{mass×Natural percent abundance}\\ \text{=15}\text{.000}\text{amu}\text{×0}\text{.37}\\ \text{=0}\text{.0555}\text{amu}\end{array}$

The weighted average atomic mass is the average of the weighted atomic masses of N-14 and N-15.

  $\begin{array}{c}\text{weighted}\text{average}\text{atomic}\text{mass}\text{=}\frac{\left(13.95+0.0555\right)\text{amu}}{2}\\ =14.01\text{amu}\end{array}$

The weighted average atomic mass of nitrogen is $14.01\text{amu}$ .