Question

Arun has prepared $0.01\%$ (by mass) solution of sodium chloride in water. Which of the following correctly represents the composition of the solutions?

• A. $1.00\mathrm{g}\mathrm{of}\mathrm{NaCl}+100\mathrm{g}\mathrm{of}\mathrm{water}$
• B. $0.11\mathrm{g}\mathrm{of}\mathrm{NaCl}+100\mathrm{g}\mathrm{of}\mathrm{water}$
• C. $0.01\mathrm{g}\mathrm{of}\mathrm{NaCl}+99.99\mathrm{g}\mathrm{of}\mathrm{water}$
• D. $0.10\mathrm{g}\mathrm{of}\mathrm{NaCl}+99.90\mathrm{g}\mathrm{of}\mathrm{water}$

Answer 1

The correct option is C

$0.01\mathrm{g}\mathrm{of}\mathrm{NaCl}+99.99\mathrm{g}\mathrm{of}\mathrm{water}$

Explanation for the correct option:

(C) $0.01\mathrm{g}\mathrm{of}\mathrm{NaCl}+99.99\mathrm{g}\mathrm{of}\mathrm{water}$

1. $$\begin{gathered} \mathrm{Mass}\%=\frac{\mathrm{Mass}\mathrm{of}\mathrm{solute}}{\mathrm{Mass}\mathrm{of}\mathrm{solute}+\mathrm{Mass}\mathrm{of}\mathrm{solvent}}\times 100 \\ \mathrm{Mass}\%=\frac{0.01}{0.01+99.99}\times 100 \\ \mathrm{Mass}\%=\frac{0.01}{100}\times 100 \\ \mathrm{Mass}\%=0.01\% \end{gathered}$$
2. Therefore, this option (C) is correct.

Explanation for the incorrect options:

(A) $1.00\mathrm{g}\mathrm{of}\mathrm{NaCl}+100\mathrm{g}\mathrm{of}\mathrm{water}$

1. $$\begin{gathered} \mathrm{Mass}\%=\frac{\mathrm{Mass}\mathrm{of}\mathrm{solute}}{\mathrm{Mass}\mathrm{of}\mathrm{solute}+\mathrm{Mass}\mathrm{of}\mathrm{solvent}}\times 100 \\ \mathrm{Mass}\%=\frac{1.00}{1.00+100}\times 100 \\ \mathrm{Mass}\%=\frac{1.00}{101}\times 100 \\ \mathrm{Mass}\%=0.99\% \end{gathered}$$
2. Therefore, this option is incorrect.

(B) $0.11\mathrm{g}\mathrm{of}\mathrm{NaCl}+100\mathrm{g}\mathrm{of}\mathrm{water}$

1. $$\begin{gathered} \mathrm{Mass}\%=\frac{\mathrm{Mass}\mathrm{of}\mathrm{solute}}{\mathrm{Mass}\mathrm{of}\mathrm{solute}+\mathrm{Mass}\mathrm{of}\mathrm{solvent}}\times 100 \\ \mathrm{Mass}\%=\frac{0.11}{0.11+100}\times 100 \\ \mathrm{Mass}\%=\frac{0.11}{100.11}\times 100 \\ \mathrm{Mass}\%=0.1098\% \end{gathered}$$
2. Therefore, this option is incorrect.

(D) $0.10\mathrm{g}\mathrm{of}\mathrm{NaCl}+99.90\mathrm{g}\mathrm{of}\mathrm{water}$

1. $$\begin{gathered} \mathrm{Mass}\%=\frac{\mathrm{Mass}\mathrm{of}\mathrm{solute}}{\mathrm{Mass}\mathrm{of}\mathrm{solute}+\mathrm{Mass}\mathrm{of}\mathrm{solvent}}\times 100 \\ \mathrm{Mass}\%=\frac{0.10}{0.10+99.90}\times 100 \\ \mathrm{Mass}\%=\frac{0.10}{100}\times 100 \\ \mathrm{Mass}\%=0.1\% \end{gathered}$$
2. Therefore, this option is incorrect.

Hence, the correct option is (C) $0.01\mathrm{g}\mathrm{of}\mathrm{NaCl}+99.99\mathrm{g}\mathrm{of}\mathrm{water}$