The pH of a mixture of 100 ml 1M `H_2SO_4` and 200 ml 1 N NaOH at `25^@C` is

Options

A. More than 7
B. Less than 7
C. Equal to 7
D. Can't predict

Answer

To find the pH of a mixture of 100 ml of 1M H₂SO₄ and 200 ml of 1N NaOH at 25°C, we can follow these steps:

### Step 1: Calculate the moles of H₂SO₄
The formula to calculate moles is:
\[ \text{Moles} = \text{Molarity} \times \text{Volume (in liters)} \]
For H₂SO₄:
- Molarity = 1 M
- Volume = 100 ml = 0.1 L

Calculating moles:
\[ \text{Moles of H₂SO₄} = 1 \, \text{mol/L} \times 0.1 \, \text{L} = 0.1 \, \text{moles} \]

### Step 2: Determine the moles of H⁺ produced by H₂SO₄
H₂SO₄ is a strong acid that dissociates completely in water:
\[ \text{H₂SO₄} \rightarrow 2 \text{H}^+ + \text{SO₄}^{2-} \]
Thus, 1 mole of H₂SO₄ produces 2 moles of H⁺. Therefore:
\[ \text{Moles of H}^+ = 2 \times 0.1 = 0.2 \, \text{moles} \]

### Step 3: Calculate the moles of NaOH
For NaOH:
- Normality = 1 N (which is equal to molarity for NaOH since n-factor = 1)
- Volume = 200 ml = 0.2 L

Calculating moles:
\[ \text{Moles of NaOH} = 1 \, \text{mol/L} \times 0.2 \, \text{L} = 0.2 \, \text{moles} \]

### Step 4: Determine the moles of OH⁻ produced by NaOH
NaOH dissociates completely in water:
\[ \text{NaOH} \rightarrow \text{Na}^+ + \text{OH}^- \]
Thus, 1 mole of NaOH produces 1 mole of OH⁻. Therefore:
\[ \text{Moles of OH}^- = 0.2 \, \text{moles} \]

### Step 5: Compare moles of H⁺ and OH⁻
Now we compare the moles of H⁺ and OH⁻:
- Moles of H⁺ = 0.2
- Moles of OH⁻ = 0.2

Since the moles of H⁺ and OH⁻ are equal, they will neutralize each other.

### Step 6: Determine the pH of the solution
In a neutral solution, the pH is 7. Since the moles of H⁺ and OH⁻ are equal, the solution is neutral.

Thus, the pH of the mixture is:
\[ \text{pH} = 7 \]

### Final Answer:
The pH of the mixture is **7**.

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