A solution of NaOH contain 0.04 gm of NaOH per litre. Its pH is

Options

A. 10
B. 9
C. 11
D. 12

Answer

To find the pH of a solution of NaOH that contains 0.04 g of NaOH per liter, we can follow these steps:

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

\[ \text{Moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

The molar mass of NaOH (sodium hydroxide) is approximately 40 g/mol. Given that we have 0.04 g of NaOH:

\[ \text{Moles of NaOH} = \frac{0.04 \, \text{g}}{40 \, \text{g/mol}} = 0.001 \, \text{mol} \]

### Step 2: Calculate the molarity of the NaOH solution
Since the solution is 1 liter, the molarity (M) is equal to the number of moles:

\[ \text{Molarity (M)} = \frac{\text{moles}}{\text{volume (L)}} = \frac{0.001 \, \text{mol}}{1 \, \text{L}} = 0.001 \, \text{M} \]

### Step 3: Calculate the concentration of hydroxide ions \([OH^-]\)
In a NaOH solution, NaOH completely dissociates into Na\(^+\) and OH\(^-\) ions. Therefore, the concentration of hydroxide ions is equal to the molarity of the NaOH solution:

\[ [OH^-] = 0.001 \, \text{M} \]

### Step 4: Calculate the pOH of the solution
We can calculate the pOH using the formula:

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

Substituting the concentration of hydroxide ions:

\[ \text{pOH} = -\log(0.001) = -\log(10^{-3}) = 3 \]

### 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:

\[ \text{pH} = 14 - \text{pOH} = 14 - 3 = 11 \]

### Conclusion
The pH of the NaOH solution is 11.