Solution (s) containing 40 gm NaOH is/are

Options

A. 50gm of 80% (w/w) NaOH
B. 50gm of 80% (w/v) NaOH `[d_("soln.") = 1.2 gm//m]`
C. 50 gm of 20M NaOH `[d_("soln.") = 1 gm//ml]`
D. 50 gm of 5 m NaOH

Answer

To determine which solutions contain 40 grams of NaOH, we will analyze each of the provided solutions step by step.

### Step 1: Analyze the first solution (50 grams of 80% weight by weight NaOH)

1. **Understanding weight by weight (w/w)**:
- 80% w/w means that there are 80 grams of NaOH in 100 grams of solution.

2. **Calculate the amount of NaOH in 50 grams of solution**:
\[ \text{Amount of NaOH} = \left(\frac{80 \text{ g NaOH}}{100 \text{ g solution}}\right) \times 50 \text{ g solution} = 40 \text{ g NaOH} \]

### Step 2: Analyze the second solution (50 grams of 80% weight by volume NaOH)

1. **Understanding weight by volume (w/v)**:
- 80% w/v means that there are 80 grams of NaOH in 100 mL of solution.
- The density of the solution is given as 1.2 g/mL.

2. **Calculate the mass of 100 mL of solution**:
\[ \text{Mass of solution} = \text{Volume} \times \text{Density} = 100 \text{ mL} \times 1.2 \text{ g/mL} = 120 \text{ g} \]

3. **Calculate the amount of NaOH in 50 grams of solution**:
\[ \text{Amount of NaOH} = \left(\frac{80 \text{ g NaOH}}{120 \text{ g solution}}\right) \times 50 \text{ g solution} = \frac{80 \times 50}{120} = \frac{4000}{120} \approx 33.33 \text{ g NaOH} \]
- This is not equal to 40 grams.

### Step 3: Analyze the third solution (50 grams of 20 molar NaOH)

1. **Understanding molarity**:
- Molarity (M) = moles of solute / volume of solution in liters.
- 20 M means there are 20 moles of NaOH in 1 liter (1000 mL) of solution.

2. **Calculate the volume of 50 grams of solution**:
- Given density = 1 g/mL, thus 50 grams = 50 mL.

3. **Calculate the moles of NaOH in 50 mL of solution**:
\[ \text{Moles of NaOH} = 20 \text{ moles/L} \times 0.050 \text{ L} = 1 \text{ mole} \]

4. **Calculate the mass of NaOH**:
\[ \text{Mass of NaOH} = \text{Moles} \times \text{Molar mass} = 1 \text{ mole} \times 40 \text{ g/mole} = 40 \text{ g NaOH} \]

### Step 4: Analyze the fourth solution (50 grams of 5 molal NaOH)

1. **Understanding molality**:
- 5 molal means 5 moles of NaOH per 1 kg of solvent.

2. **Calculate the mass of NaOH in 5 moles**:
\[ \text{Mass of NaOH} = 5 \text{ moles} \times 40 \text{ g/mole} = 200 \text{ g NaOH} \]

3. **Calculate the mass of solution**:
- The total mass of the solution is the mass of the solvent (1000 g) + mass of solute (200 g) = 1200 g.

4. **Calculate the amount of NaOH in 50 grams of solution**:
\[ \text{Amount of NaOH} = \left(\frac{200 \text{ g NaOH}}{1200 \text{ g solution}}\right) \times 50 \text{ g solution} = \frac{200 \times 50}{1200} \approx 8.33 \text{ g NaOH} \]
- This is not equal to 40 grams.

### Conclusion:
The solutions that contain 40 grams of NaOH are:
- The first solution (50 grams of 80% w/w NaOH).
- The third solution (50 grams of 20 molar NaOH).