A 50 ml of 20% (w/w) solution of density 1.2 g/ml is diluted until is strength becomes 6% (w/w) . Determine the mass of water added.

Options

A. 88 g
B. 120 g
C. 140 g
D. 180g

Answer

To solve the problem, we need to determine the mass of water added when a 50 ml solution of 20% (w/w) is diluted to a 6% (w/w) solution. We will follow these steps:

### Step 1: Calculate the mass of the initial solution
Given:
- Volume of the solution (V) = 50 ml
- Density of the solution (d) = 1.2 g/ml

Using the formula for mass:
\[ \text{Mass} = \text{Density} \times \text{Volume} \]
\[ \text{Mass}_{\text{initial}} = 1.2 \, \text{g/ml} \times 50 \, \text{ml} = 60 \, \text{g} \]

### Step 2: Calculate the final volume of the solution after dilution
We know that the concentration at the initial stage (C_initial) is 20% and at the final stage (C_final) is 6%. We can use the dilution equation:
\[ C_{\text{initial}} \times V_{\text{initial}} = C_{\text{final}} \times V_{\text{final}} \]
Substituting the known values:
\[ 20\% \times 50 \, \text{ml = 6\%} \times V_{\text{final}} \]
Converting percentages to decimals:
\[ \frac{20}{100} \times 50 = \frac{6}{100} \times V_{\text{final}} \]
\[ 10 = 0.06 \times V_{\text{final}} \]
Now solve for \( V_{\text{final}} \):
\[ V_{\text{final}} = \frac{10}{0.06} = 166.67 \, \text{ml} \]

### Step 3: Calculate the mass of the final solution
Using the same density for the final solution:
\[ \text{Mass}_{\text{final}} = \text{Density} \times V_{\text{final}} \]
\[ \text{Mass}_{\text{final}} = 1.2 \, \text{g/ml} \times 166.67 \, \text{ml} = 200 \, \text{g} \]

### Step 4: Calculate the mass of water added
The mass of water added can be calculated by subtracting the initial mass from the final mass:
\[ \text{Mass}_{\text{added}} = \text{Mass}_{\text{final}} - \text{Mass}_{\text{initial}} \]
\[ \text{Mass}_{\text{added}} = 200 \, \text{g} - 60 \, \text{g} = 140 \, \text{g} \]

### Final Answer
The mass of water added is **140 g**.

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