Question

The average molar mass of chlorine is $35.5\mathrm{g}{\mathrm{mol}}^{-1}$. The ratio of ${}^{35}\mathrm{Cl}$ to ${}^{37}\mathrm{Cl}$ in naturally occurring chlorine is close to

• A. $1:1$
• B. $3:1$
• C. $2:1$
• D. $4:1$

Answer 1

The correct option is B

$3:1$

Step 1: Given data

The average molar mass of chlorine$=35.5\mathrm{g}$

Step 2: Calculating ratio

Let the ratio of ${}^{35}\mathrm{Cl}$ and ${}^{37}\mathrm{Cl}$ be $\mathrm{x}:1$

Applying the formula, Average molar mass$=\frac{{\mathrm{n}}_1{\mathrm{M}}_1+{\mathrm{n}}_2{\mathrm{M}}_2}{{\mathrm{n}}_1+{\mathrm{n}}_2}$

$35.5=\frac{\mathrm{x}\times 35+1\times 37}{\mathrm{x}+1}$

$35.5(\mathrm{x}+1)=35\mathrm{x}+37$

$35.5\mathrm{x}+35.5=35\mathrm{x}+37$

$\mathrm{x}=3$

Therefore, The ratio of ${}^{35}\mathrm{Cl}$ to ${}^{37}\mathrm{Cl}$ in naturally occurring chlorine is close to $3:1$