Calculate the amount of water by which 50 mL of a solution having concentration `20%` w/v and density 2 g/mL should be diluted to obtain a solution of concentration `7.5%` w/v:

Options

A. `133.33` mL
B. `33.33` mL
C. `83.33` mL
D. `50` mL

Answer

To solve the problem, we need to find out how much water is required to dilute a 50 mL solution of 20% w/v concentration to a final concentration of 7.5% w/v.

### Step-by-Step Solution:

**Step 1: Calculate the mass of solute in the original solution.**

The concentration of the solution is given as 20% w/v. This means there are 20 grams of solute in 100 mL of solution.

For 50 mL of this solution:

\[ \text{Mass of solute} = \left(\frac{20 \text{ g}}{100 \text{ mL}}\right) \times 50 \text{ mL} = 10 \text{ g} \]

**Step 2: Determine the final volume required for the diluted solution.**

We want to dilute this 10 g of solute to achieve a concentration of 7.5% w/v.

Using the formula for w/v concentration:

\[ \text{Concentration (w/v)} = \left(\frac{\text{mass of solute}}{\text{volume of solution}}\right) \times 100 \]

Rearranging this to find the volume of the solution:

\[ \text{Volume of solution} = \frac{\text{mass of solute}}{\text{Concentration (w/v)}} \times 100 \]

Substituting the values:

\[ \text{Volume of solution} = \frac{10 \text{ g}}{7.5\%} \times 100 = \frac{10}{0.075} = 133.33 \text{ mL} \]

**Step 3: Calculate the amount of water to be added.**

Now, we need to find out how much water to add to the original 50 mL solution to reach a final volume of 133.33 mL.

\[ \text{Amount of water to be added} = \text{Final volume} - \text{Initial volume} \]

\[ \text{Amount of water to be added} = 133.33 \text{ mL} - 50 \text{ mL} = 83.33 \text{ mL} \]

### Final Answer:
The amount of water that should be added to the solution is **83.33 mL**.

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