A solution can be expressed as 25% w/w as well as 20% w/v then mass of 20 ml of such solution is :

Options

A. 25 gm
B. 8 gm
C. 16 gm
D. 10 gm

Explanation

To solve the problem, we need to determine the mass of 20 ml of a solution that is 25% w/w and 20% w/v.

### Step-by-Step Solution:

1. **Understanding the Percentages**:
- **25% w/w** means there are 25 grams of solute in 100 grams of solution.
- **20% w/v** means there are 20 grams of solute in 100 ml of solution.

2. **Finding the Relationship Between w/w and w/v**:
- From the w/w percentage, we know that 25 grams of solute is present in 100 grams of solution.
- To find out how much solution corresponds to this amount of solute in terms of volume, we need to convert the weight of the solution to volume using the w/v percentage.

3. **Setting Up the Equation**:
- We can set up the equation using the information from the w/v percentage:
\[ \text{If } 20\% \text{ w/v means } 20 \text{ grams of solute in } 100 \text{ ml of solution, then for } 25 \text{ grams of solute, we can find the volume (x ml).} \]
- Using the formula:
\[ \frac{20 \text{ grams}}{100 \text{ ml}} = \frac{25 \text{ grams}}{x \text{ ml}} \]

4. **Solving for x**:
- Cross-multiplying gives:
\[ 20x = 25 \times 100 \]
- Simplifying:
\[ 20x = 2500 \implies x = \frac{2500}{20} = 125 \text{ ml} \]
- This means that 100 grams of solution corresponds to 125 ml.

5. **Finding Mass of 20 ml of Solution**:
- Now, we know that 125 ml of solution weighs 100 grams. We need to find the mass of 20 ml.
- Set up the proportion:
\[ \frac{100 \text{ grams}}{125 \text{ ml}} = \frac{y \text{ grams}}{20 \text{ ml}} \]
- Cross-multiplying gives:
\[ 100 \times 20 = 125y \]
- Simplifying:
\[ 2000 = 125y \implies y = \frac{2000}{125} = \frac{400}{25} = 16 \text{ grams} \]

### Final Answer:
The mass of 20 ml of the solution is **16 grams**.