Chapter 4, Problem 115A

Interpretation Introduction

Interpretation:

The reason for the atomic mass of sulfur or chlorine is not a whole number needs to be explained.

Concept introduction:

The isotope contains different numbers of neutron and same number of protons. So, the atomic mass of the isotope is different. The calculation of the atomic mass of elements is termed as the average atomic mass.

$\text{Average}\text{atomic}\text{mass}\text{=}\text{(}\text{mass}\text{of}\text{isotope×relative}\text{abundance)}$

Explanation of Solution

The weighted average of the atomic masses of the isotopes of elements is termed as average atomic mass.

$\text{Average}\text{atomic}\text{mass}\text{=}\text{(}\text{mass}\text{of}\text{isotope×relative}\text{abundance)}$

The isotopes of chlorine are Cl $-35$ and Cl $-37$ and their abundance in nature is $75\%$ and $25\%$ for each respectively.

$\text{Average}\text{atomic}\text{mass}\text{=}(0.75\times 35)+(0.25\times 37)$

$=35.5u$

The isotopes of sulfur are S $-32$, S $-33$ , S $-34$ , S $-36$ and their abundance in nature are $95\%,0.76\%,4.22\%,0.014\%$ respectively.

$\text{average}\text{atomic}\text{mass =}\text{(0}\text{.95}\times \text{31}\text{.97}\text{+}\text{0}\text{.0076}\times \text{32}\text{.97+}\text{0}\text{.042}\times \text{35}\text{.96)}$

$\text{=}\text{32}\text{.06}\text{u}$

So, the calculated value of average atomic mass of chlorine $=35.5u$ that is not a whole number. While the sulfur’s average atomic mass $\text{=}\text{32}\text{.06}\text{u}$ that is close to the whole.

Hence, sulfur has an isotope with a very high abundance whereas, Chlorine has more than one isotope with a large percent abundance.

Conclusion

From the above calculation the atomic mass of the chlorine is not a whole number. It comes with fraction, but atomic mass of sulfur is just close to the whole number.