pH values of HCl and NaOH solutions each of strength `(N)/(100)` will be respectively

Options

A. 2 and 3
B. 2 and 12
C. 12 and 2
D. 2 and 10

Explanation

To find the pH values of HCl and NaOH solutions, each with a strength of \( \frac{N}{100} \), we can follow these steps:

### Step 1: Understand the Normality
Normality (N) is a measure of concentration equivalent to molarity for acids and bases. For HCl, a strong acid, and NaOH, a strong base, we can assume that 1 N solution means 1 equivalent of H+ or OH- ions per liter.

### Step 2: Calculate the Concentration
Given that the strength is \( \frac{N}{100} \), we can express the concentration of HCl and NaOH in moles per liter:
- For HCl:
\[ \text{Concentration of HCl} = \frac{1}{100} \text{ N} = \frac{1}{100} \text{ mol/L} \]
- For NaOH:
\[ \text{Concentration of NaOH} = \frac{1}{100} \text{ N} = \frac{1}{100} \text{ mol/L} \]

### Step 3: Calculate pH of HCl
Since HCl is a strong acid, it completely dissociates in solution:
\[ \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \]
Thus, the concentration of \( \text{H}^+ \) ions is equal to the concentration of HCl:
\[ [\text{H}^+] = \frac{1}{100} \text{ mol/L} \]
Now, we can calculate the pH using the formula:
\[ \text{pH} = -\log[\text{H}^+] \]
Substituting the value:
\[ \text{pH} = -\log\left(\frac{1}{100}\right) = -\log(10^{-2}) = 2 \]

### Step 4: Calculate pOH of NaOH
For NaOH, which is a strong base, it also completely dissociates:
\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]
Thus, the concentration of \( \text{OH}^- \) ions is equal to the concentration of NaOH:
\[ [\text{OH}^-] = \frac{1}{100} \text{ mol/L} \]
Now, we can calculate the pOH:
\[ \text{pOH} = -\log[\text{OH}^-] \]
Substituting the value:
\[ \text{pOH} = -\log\left(\frac{1}{100}\right) = -\log(10^{-2}) = 2 \]

### Step 5: Calculate pH from pOH
Using the relationship between pH and pOH:
\[ \text{pH} + \text{pOH} = 14 \]
We can find the pH of the NaOH solution:
\[ \text{pH} = 14 - \text{pOH} = 14 - 2 = 12 \]

### Final Answer
Thus, the pH values of the HCl and NaOH solutions, each of strength \( \frac{N}{100} \), are:
- pH of HCl = 2
- pH of NaOH = 12