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

Explanation

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

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

Now, let's calculate the mass percentage for each option step by step.

### Step 1: Calculate for Solution I
- **Mass of solute (sodium chloride)** = 10 g
- **Mass of solvent (water)** = 200 g
- **Total mass** = 10 g + 200 g = 210 g

\[ \text{Mass percentage} = \left( \frac{10}{210} \right) \times 100 = \frac{10 \times 100}{210} \approx 4.76\% \]

### Step 2: Calculate for Solution II
- **Mass of solute (sugar)** = 15 g
- **Mass of solvent (water)** = 160 g
- **Total mass** = 15 g + 160 g = 175 g

\[ \text{Mass percentage} = \left( \frac{15}{175} \right) \times 100 = \frac{15 \times 100}{175} \approx 8.57\% \]

### Step 3: Calculate for Solution III
- **Mass of solute (potassium permanganate)** = 60 g
- **Mass of solvent (water)** = 200 g
- **Total mass** = 60 g + 200 g = 260 g

\[ \text{Mass percentage} = \left( \frac{60}{260} \right) \times 100 = \frac{60 \times 100}{260} \approx 23.08\% \]

### Step 4: Calculate for Solution IV
- **Mass of solute (sodium carbonate)** = 20 g
- **Mass of solvent (water)** = 90 g
- **Total mass** = 20 g + 90 g = 110 g

\[ \text{Mass percentage} = \left( \frac{20}{110} \right) \times 100 = \frac{20 \times 100}{110} \approx 18.18\% \]

### 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), which has a mass percentage of approximately **23.08%**.

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