Which of the following solutions has the highest mass by mass percentage?
I. 10 g of sodium chloride in 200 g of water
II. 15 g of sugar in 160 g of water
III. 60 g of potassium permanganate in 200 g of water
IV. 20 g of sodium carbonate in 90 g of water

Options

A. I
B. II
C. III
D. IV

Answer

To find out which solution has the highest mass by mass percentage, we will calculate the mass percentage for each solution using the formula:

\[ \text{Mass by mass percentage} = \left( \frac{\text{mass of solute}}{\text{mass of solute} + \text{mass of solvent}} \right) \times 100 \]

Let's calculate the mass percentage for each of the given solutions step by step.

### Solution I: 10 g of sodium chloride in 200 g of water
1. **Mass of solute (sodium chloride)** = 10 g
2. **Mass of solvent (water)** = 200 g
3. **Total mass of solution** = 10 g + 200 g = 210 g
4. **Mass by mass percentage**:
\[ \text{Percentage} = \left( \frac{10}{210} \right) \times 100 \approx 4.76\% \]

### Solution II: 15 g of sugar in 160 g of water
1. **Mass of solute (sugar)** = 15 g
2. **Mass of solvent (water)** = 160 g
3. **Total mass of solution** = 15 g + 160 g = 175 g
4. **Mass by mass percentage**:
\[ \text{Percentage} = \left( \frac{15}{175} \right) \times 100 \approx 8.57\% \]

### Solution III: 60 g of potassium permanganate in 200 g of water
1. **Mass of solute (potassium permanganate)** = 60 g
2. **Mass of solvent (water)** = 200 g
3. **Total mass of solution** = 60 g + 200 g = 260 g
4. **Mass by mass percentage**:
\[ \text{Percentage} = \left( \frac{60}{260} \right) \times 100 \approx 23.08\% \]

### Solution IV: 20 g of sodium carbonate in 90 g of water
1. **Mass of solute (sodium carbonate)** = 20 g
2. **Mass of solvent (water)** = 90 g
3. **Total mass of solution** = 20 g + 90 g = 110 g
4. **Mass by mass percentage**:
\[ \text{Percentage} = \left( \frac{20}{110} \right) \times 100 \approx 18.18\% \]

### Summary of Results:
- Solution I: 4.76%
- Solution II: 8.57%
- Solution III: 23.08%
- Solution IV: 18.18%

### Conclusion:
The solution with the highest mass by mass percentage is **Solution III: 60 g of potassium permanganate in 200 g of water**, with a mass percentage of approximately **23.08%**.

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