100gm of an aq. solution of sugar contains 50% sugar by mass. How much water should be evaporated get 70% sugar solution by mass?

Explanation

To solve the problem, we need to determine how much water should be evaporated from a 100 g sugar solution that initially contains 50% sugar by mass in order to achieve a final solution that is 70% sugar by mass.

### Step-by-Step Solution:

1. **Determine the Initial Amount of Sugar and Water:**
- The solution is 100 g and contains 50% sugar by mass.
- Therefore, the mass of sugar = 50% of 100 g = 50 g.
- The mass of water = Total mass - Mass of sugar = 100 g - 50 g = 50 g.

2. **Determine the Final Condition:**
- We want a final solution that is 70% sugar by mass.
- Let the final mass of the solution be \( x \) grams.
- In this final solution, the mass of sugar should be 70% of \( x \), which means:
\[ \text{Mass of sugar} = 0.7x \]
- Since we are not changing the amount of sugar during evaporation, the mass of sugar remains 50 g.

3. **Set Up the Equation:**
- From the above, we can set up the equation:
\[ 0.7x = 50 \text{ g} \]
- Solving for \( x \):
\[ x = \frac{50}{0.7} \approx 71.43 \text{ g} \]

4. **Determine the Final Mass of Water:**
- The mass of water in the final solution can be calculated as:
\[ \text{Mass of water} = x - \text{Mass of sugar} = 71.43 \text{ g} - 50 \text{ g} \approx 21.43 \text{ g} \]

5. **Calculate the Amount of Water to Evaporate:**
- The initial mass of water was 50 g, and the final mass of water needed is approximately 21.43 g.
- Therefore, the amount of water to be evaporated is:
\[ \text{Water to evaporate} = \text{Initial mass of water} - \text{Final mass of water} = 50 \text{ g} - 21.43 \text{ g} \approx 28.57 \text{ g} \]

### Final Answer:
Approximately **28.57 g** of water should be evaporated to obtain a 70% sugar solution by mass.