Question

A solution contains 75 mg NaCl per mL. To what extent it must be diluted to give a solution of concentration 15 mg NaCl per mL of solution.

• A. 3 times
• B. 4 times
• C. 5 times
• D. 6 times

Answer 1

Answer: (C)

5 times

Answer 2

The principle of dilution states that the amount of solute remains constant when a solvent is added. Let $C_1$ be the initial concentration and $V_1$ be the initial volume. Let $C_2$ be the final concentration and $V_2$ be the final volume. The amount of solute in the initial solution is $C_1 \times V_1$. The amount of solute in the final solution is $C_2 \times V_2$. Since the amount of solute is conserved, $C_1 V_1 = C_2 V_2$. The extent of dilution is given by the ratio of the final volume to the initial volume, $\frac{V_2}{V_1}$. From the conservation equation, we can write: $\frac{V_2}{V_1} = \frac{C_1}{C_2}$ Given: Initial concentration, $C_1 = 75$ mg/mL Final concentration, $C_2 = 15$ mg/mL Substituting these values into the equation: $\frac{V_2}{V_1} = \frac{75 \text{ mg/mL}}{15 \text{ mg/mL}}$ $\frac{V_2}{V_1} = 5$ This means the final volume ($V_2$) must be 5 times the initial volume ($V_1$). Therefore, the solution must be diluted 5 times.