If 0.4 gm NaOH is present in 1 litre solution, then its pH will be

Options

A. 2
B. 10
C. 11
D. 12

Explanation

To find the pH of a solution containing 0.4 grams of NaOH in 1 liter, we can follow these steps:

### Step 1: Calculate the number of moles of NaOH
To find the number of moles of NaOH, we use the formula:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

The molar mass of NaOH is approximately 40 g/mol.

Given:
- Mass of NaOH = 0.4 g
- Molar mass of NaOH = 40 g/mol

\[ \text{Number of moles of NaOH} = \frac{0.4 \, \text{g}}{40 \, \text{g/mol}} = 0.01 \, \text{mol} \]

### Step 2: Calculate the concentration of NaOH in the solution
Since the solution volume is 1 liter, the concentration (C) of NaOH can be calculated as:

\[ C = \frac{\text{Number of moles}}{\text{Volume (L)}} \]

\[ C = \frac{0.01 \, \text{mol}}{1 \, \text{L}} = 0.01 \, \text{M} \]

### Step 3: Determine the concentration of hydroxide ions (OH⁻)
Since NaOH is a strong base, it completely dissociates in water:

\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]

Thus, the concentration of hydroxide ions [OH⁻] is equal to the concentration of NaOH:

\[ [\text{OH}^-] = 0.01 \, \text{M} \]

### Step 4: Calculate the pOH of the solution
The pOH can be calculated using the formula:

\[ \text{pOH} = -\log[\text{OH}^-] \]

\[ \text{pOH} = -\log(0.01) = 2 \]

### Step 5: Calculate the pH of the solution
Using the relationship between pH and pOH:

\[ \text{pH} + \text{pOH} = 14 \]

We can find the pH:

\[ \text{pH} = 14 - \text{pOH} = 14 - 2 = 12 \]

Thus, the pH of the solution is **12**.

### Final Answer
The pH of the solution is **12**.

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