`50ml N//10 NaOH` solution is mixed with `50 ml N//20 HCl` solution. The resulting solution will
`(a)` Turns phenolphthalein solution pink`" " (b)` Turns blue litmus red
`(c )` Turns methyl orange red `" "(d) [H^(+)] & [OH^(-)]`

Options

A. only `(a)` is correct
B. `(a) & (b)` are correct
C. `(a) & (d)` are correct
D. all are correct

Explanation

To solve the problem, we need to determine the pH of the resulting solution when 50 ml of N/10 NaOH is mixed with 50 ml of N/20 HCl. We will follow these steps:

### Step 1: Calculate the moles of NaOH and HCl

1. **For NaOH:**
- Concentration = N/10 = 0.1 N
- Volume = 50 ml = 0.050 L
- Moles of NaOH = Concentration × Volume = 0.1 N × 0.050 L = 0.005 moles

2. **For HCl:**
- Concentration = N/20 = 0.05 N
- Volume = 50 ml = 0.050 L
- Moles of HCl = Concentration × Volume = 0.05 N × 0.050 L = 0.0025 moles

### Step 2: Determine the reaction between NaOH and HCl

The reaction between NaOH and HCl is:
\[ \text{NaOH} + \text{HCl} \rightarrow \text{NaCl} + \text{H}_2\text{O} \]

### Step 3: Calculate the remaining moles after neutralization

- Initially, we have:
- Moles of NaOH = 0.005 moles
- Moles of HCl = 0.0025 moles

- Since NaOH and HCl react in a 1:1 ratio, HCl will completely react with an equal amount of NaOH:
- Moles of NaOH remaining = 0.005 - 0.0025 = 0.0025 moles
- Moles of HCl remaining = 0.0025 - 0.0025 = 0 moles

### Step 4: Determine the nature of the resulting solution

Since there are remaining moles of NaOH (0.0025 moles) and no HCl left, the solution is basic in nature.

### Step 5: Calculate the concentration of OH⁻ ions

- Total volume of the solution = 50 ml + 50 ml = 100 ml = 0.1 L
- Concentration of OH⁻ ions = Moles of NaOH remaining / Total volume
\[ \text{Concentration of OH}^- = \frac{0.0025 \text{ moles}}{0.1 \text{ L}} = 0.025 \text{ M} \]

### Step 6: Determine the pH of the solution

- To find the pOH:
\[ \text{pOH} = -\log[OH^-] = -\log(0.025) \approx 1.60 \]

- To find the pH:
\[ \text{pH} = 14 - \text{pOH} = 14 - 1.60 \approx 12.40 \]

### Step 7: Analyze the options

(a) Turns phenolphthalein solution pink: **True** (because the solution is basic)

(b) Turns blue litmus red: **False** (because the solution is not acidic)

(c) Turns methyl orange red: **False** (because the solution is not acidic)

(d) [H⁺] & [OH⁻]: **False** (because there are no H⁺ ions left)

### Conclusion

The correct answer is **(a)** Turns phenolphthalein solution pink.

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