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

Hint: 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.