Question

$^{35}Cl$ and $^{37}Cl$ are the two isotopes of chlorine, in the ratio $3:1$ respectively. If the isotope ratio is reversed, the average atomic mass of chlorine will be:
A. 35.0u
B. 35.5u
C. 36.0u
D. 36.5u

Answer 1

Since, we know the ratio of $^{35}Cl$ to $^{37}Cl$ is given by $3:1$, and after reversing it becomes $1:3$. It means one $^{35}Cl$ is there for three $^{37}Cl$. Then, to find the average atomic mass, we will solve $\dfrac{{{p_1}{x_1} + {p_2}{x_2}}}{{{p_1} + {p_2}}}$ after putting the
value.

Complete step by step answer:
The ratio of $^{35}Cl$ to $^{37}Cl$ is given by $3:1$,
Therefore, if 4x atoms are present then,
$^{35}Cl = 3x\left( {75\% } \right)$
$^{37}Cl = x\left( {25\% } \right)$
Now, if the isotope ratio is reversed from $3:1$ to $1:3$
Then,
$^{35}Cl = x$
$^{37}Cl = 3x$
Now, for average atomic mass,
Average atomic mass $= \dfrac{{{p_1}{x_1} + {p_2}{x_2}}}{{{p_1} + {p_2}}} = \dfrac{{(35 \times 1) + (37 \times 3)}}{{3 + 1}} = \dfrac{{35 + 111}}{4} = \dfrac{{142}}{4} = 36.5u$
So, the average atomic mass of chlorine is given by 36.5u

Therefore, the correct answer is option (D).

Note: Isotopes of an element have the same number of protons, that is, the same atomic number (Z), but different a number of neutrons (N), that is, different mass number. The relative atomic mass of the chlorine atom is 35.5 but it has two principle stable isotopes which are $^{35}Cl$ and $^{37}Cl$. $^{35}Cl$ has a mass number of 35 and its natural abundance is about $75.76\%$ on earth while $^{37}Cl$ has a mass number of 37 and its natural abundance is about $24.24\%$. The percentage abundance in nature and atomic masses of both isotopes of chlorine can be used to calculate the atomic mass of chlorine. Thus, we can determine that $^{35}Cl$ must be the most common of the two isotopes, and so it is chlorine#39;s most common isotope.