Answer:
The relative atomic mass of chlorine depends on the ratio between the abundance of these two naturally-occurring isotopes.
Explanation:
The relative atomic mass of an element is a weighted average of the atomic mass of its naturally-occurring isotopes. The relative abundance of each isotope gives its weight in this weighted average.
For these two naturally-occurring isotopes of chlorine:
- The relative atomic mass of [tex]^{35}{\rm Cl}[/tex] is approximately [tex]34.969[/tex] daltons. The relative abundance of this isotope in nature is approximately [tex]0.758[/tex].
- The relative atomic mass [tex]^{37}{\rm Cl}[/tex] is approximately [tex]36.966[/tex] daltons. The relative abundance of this isotope in nature is approximately [tex]0.242[/tex].
[tex]\begin{array}{|c|c|c|}\cline{1-3} \text{Isotope} & \text{Atomic Mass} & \text{Relative Abundance}\\ \cline{1-3} ^{35}{\rm Cl} & \approx 34.968\; \rm Da} & \approx 0.758 \\ \cline{1-3} ^{37}{\rm Cl} & \approx 36.966\; \rm Da & \approx 0.242 \\ \cline{1-3}\end{array}[/tex].
[tex]\begin{aligned}&\text{relative atomic mass of Cl} \\ &= \text{atomic mass of $^{35}{\rm Cl}$} \times \text{relative abundance of $^{35}{\rm Cl}$} \\&\quad + \text{atomic mass of $^{37}{\rm Cl}$} \times \text{relative abundance of $^{37}{\rm Cl}$} \\ &\approx 34.968\; \rm Da \times 0.758 + 36.966\; \rm Da \times 0.242 \\ &\approx 35.45\; \rm Da \end{aligned}[/tex].
The relative abundance of [tex]^{35}{\rm Cl}[/tex] is much higher than that of [tex]^{37}{\rm Cl}[/tex]. Consequently, the relative atomic mass of the element [tex]\rm Cl[/tex] is closer to the atomic mass of [tex]^{35}{\rm Cl}\![/tex] than that of [tex]^{37}{\rm Cl}\![/tex].
