the pH of a solution prepared by mixing 2M, 100 mL HCl and M, 200 mL NaOH at `25^(@)C` is

Options

A. 8
B. 7
C. 4
D. 5

Answer

To find the pH of the solution prepared by mixing 2M HCl and 1M NaOH, we can follow these steps:

### Step 1: Calculate the number of moles of HCl
We know that:
- Molarity (M) = Number of moles / Volume (L)

Given:
- Molarity of HCl = 2 M
- Volume of HCl = 100 mL = 0.1 L (since 1000 mL = 1 L)

Using the formula:
\[ \text{Number of moles of HCl} = \text{Molarity} \times \text{Volume} \]
\[ \text{Number of moles of HCl} = 2 \, \text{mol/L} \times 0.1 \, \text{L} = 0.2 \, \text{moles} \]

### Step 2: Calculate the number of moles of NaOH
Given:
- Molarity of NaOH = 1 M
- Volume of NaOH = 200 mL = 0.2 L

Using the same formula:
\[ \text{Number of moles of NaOH} = \text{Molarity} \times \text{Volume} \]
\[ \text{Number of moles of NaOH} = 1 \, \text{mol/L} \times 0.2 \, \text{L} = 0.2 \, \text{moles} \]

### Step 3: Determine the reaction between HCl and NaOH
The reaction between HCl and NaOH is a neutralization reaction:
\[ \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} \]

Since we have 0.2 moles of HCl and 0.2 moles of NaOH, they will completely react with each other:
- Moles of HCl remaining = 0.2 - 0.2 = 0
- Moles of NaOH remaining = 0.2 - 0.2 = 0

### Step 4: Determine the nature of the solution
After the reaction, we have formed 0.2 moles of NaCl and 0.2 moles of water. Since both the acid and base have completely neutralized each other, the resulting solution is neutral.

### Step 5: Calculate the pH of the solution
The pH of a neutral solution at 25°C is:
\[ \text{pH} = 7 \]

### Final Answer
The pH of the solution prepared by mixing 2M HCl and 1M NaOH at 25°C is **7**.

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