The `P^(H)` of HCI is 3. Then the `P^(H)` of NaOH solution having same molar concentration is

Options

A. 3
B. 6
C. 9
D. 11

Answer

To solve the problem, we need to find the pH of a NaOH solution that has the same molar concentration as the HCl solution with a pH of 3. Here’s a step-by-step solution:

### Step 1: Determine the concentration of H⁺ ions from the pH of HCl
The pH of HCl is given as 3. We can use the formula for pH to find the concentration of H⁺ ions:
\[ \text{pH} = -\log[H^+] \]
Rearranging this gives:
\[ [H^+] = 10^{-\text{pH}} \]
Substituting the pH value:
\[ [H^+] = 10^{-3} \, \text{M} \]

### Step 2: Determine the concentration of NaOH
Since the NaOH solution has the same molar concentration as the HCl solution, the concentration of NaOH is also:
\[ [\text{NaOH}] = 10^{-3} \, \text{M} \]

### Step 3: Determine the concentration of OH⁻ ions from NaOH
NaOH is a strong base and dissociates completely in solution:
\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]
Thus, the concentration of OH⁻ ions will also be:
\[ [OH^-] = 10^{-3} \, \text{M} \]

### Step 4: Calculate the pOH
Using the formula for pOH:
\[ \text{pOH} = -\log[OH^-] \]
Substituting the concentration of OH⁻:
\[ \text{pOH} = -\log(10^{-3}) = 3 \]

### Step 5: Calculate the pH from pOH
We know that:
\[ \text{pH} + \text{pOH} = 14 \]
Substituting the value of pOH:
\[ \text{pH} = 14 - \text{pOH} = 14 - 3 = 11 \]

### Final Answer:
The pH of the NaOH solution is **11**.

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