Which of the following will have the largest `pH`?

Options

A. (a) `M//10 HCI`
B. (b) `M//100 HCI`
C. (c) `M//10NaOH`
D. (d) `M//100NaOH`

Explanation

To determine which of the given solutions has the largest pH, we need to analyze the pH values of the solutions provided. Here’s a step-by-step solution:

### Step 1: Understand the pH Scale
The pH scale ranges from 0 to 14:
- pH < 7 indicates an acidic solution.
- pH = 7 indicates a neutral solution.
- pH > 7 indicates a basic (alkaline) solution.

### Step 2: Identify the Solutions
We are given two solutions:
1. HCl (Hydrochloric acid)
2. NaOH (Sodium hydroxide)

### Step 3: Analyze HCl
HCl is a strong acid. Therefore, its pH will be less than 7. Since we are looking for the largest pH, we can eliminate HCl from consideration.

### Step 4: Analyze NaOH
NaOH is a strong base. We need to calculate its pH based on its concentration.

#### Case A: Concentration of NaOH = 10^-2 M
- **Calculate pOH**:
\[ \text{pOH} = -\log[\text{OH}^-] = -\log(10^{-2}) = 2 \]
- **Calculate pH**:
\[ \text{pH} = 14 - \text{pOH} = 14 - 2 = 12 \]

#### Case B: Concentration of NaOH = 0.1 M (1/10 M)
- **Calculate pOH**:
\[ \text{pOH} = -\log[\text{OH}^-] = -\log(10^{-1}) = 1 \]
- **Calculate pH**:
\[ \text{pH} = 14 - \text{pOH} = 14 - 1 = 13 \]

### Step 5: Compare pH Values
From the calculations:
- For 10^-2 M NaOH, pH = 12
- For 0.1 M NaOH, pH = 13

The largest pH value is 13 from the 0.1 M NaOH solution.

### Conclusion
The solution with the largest pH is the 0.1 M NaOH solution, which has a pH of 13.

### Final Answer
The correct answer is the 0.1 M NaOH solution.

---