Compare mass of pure NaOH in each of the aqueous solution
50 g of 40% (w/w) NaOH
50 ml of 50% (w/v) NaOH [`d_(soln)=1.2 g/(mL)`]

Options

A. `(ii)gt(i)`
B. `(i) gt(ii)`
C. `(i) =(ii)`
D. Mass in (i) is double than mass in (ii)

Answer

To compare the mass of pure NaOH in each of the given aqueous solutions, we will calculate the mass of pure NaOH in both cases.

### Step 1: Calculate the mass of pure NaOH in the first solution (50 g of 40% w/w NaOH)

1. **Understanding the percentage**: A 40% w/w solution means that there are 40 grams of NaOH in every 100 grams of solution.
2. **Calculate the mass of NaOH**:
\[ \text{Mass of NaOH} = \text{Total mass of solution} \times \left(\frac{\text{Percentage of NaOH}}{100}\right) \]
\[ \text{Mass of NaOH} = 50 \, \text{g} \times \left(\frac{40}{100}\right) = 20 \, \text{g} \]

### Step 2: Calculate the mass of pure NaOH in the second solution (50 ml of 50% w/v NaOH)

1. **Understanding the percentage**: A 50% w/v solution means that there are 50 grams of NaOH in every 100 ml of solution.
2. **Calculate the mass of NaOH**:
- First, we need to find the density of the solution to convert volume to mass. Given that the density \(d_{soln} = 1.2 \, \text{g/ml}\), we can find the mass of 50 ml of solution.
\[ \text{Mass of solution} = \text{Volume} \times \text{Density} = 50 \, \text{ml} \times 1.2 \, \text{g/ml} = 60 \, \text{g} \]
- Now, calculate the mass of NaOH:
\[ \text{Mass of NaOH} = \text{Mass of solution} \times \left(\frac{\text{Percentage of NaOH}}{100}\right) \]
\[ \text{Mass of NaOH} = 60 \, \text{g} \times \left(\frac{50}{100}\right) = 30 \, \text{g} \]

### Step 3: Compare the masses of pure NaOH in both solutions

- From the calculations:
- Mass of pure NaOH in the first solution = 20 g
- Mass of pure NaOH in the second solution = 30 g

### Conclusion

The mass of pure NaOH in the second solution (50 ml of 50% w/v NaOH) is greater than in the first solution (50 g of 40% w/w NaOH).

### Final Answer
The mass of pure NaOH in 50 ml of 50% (w/v) NaOH is greater than in 50 g of 40% (w/w) NaOH.

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