What shall be the pH of a solution formed by mixing 10 mL of 0.1 M `H_2SO_4` and 10 mL of N/10 KOH ?

Options

A. 11.4
B. 8.64
C. 3
D. `7.00`

Answer

To find the pH of a solution formed by mixing 10 mL of 0.1 M H₂SO₄ and 10 mL of N/10 KOH, we can follow these steps:

### Step 1: Calculate the moles of H₂SO₄
- The concentration of H₂SO₄ is 0.1 M.
- Volume of H₂SO₄ = 10 mL = 0.01 L.
- Moles of H₂SO₄ = Concentration × Volume = 0.1 mol/L × 0.01 L = 0.001 moles.

### Step 2: Determine the moles of H⁺ ions from H₂SO₄
- H₂SO₄ dissociates to produce 2 H⁺ ions for every mole of H₂SO₄.
- Therefore, moles of H⁺ from H₂SO₄ = 2 × 0.001 = 0.002 moles.

### Step 3: Calculate the moles of KOH
- KOH is given as N/10, which is equivalent to 0.1 N.
- Since KOH is a strong base, its normality equals its molarity (n-factor for KOH = 1).
- Volume of KOH = 10 mL = 0.01 L.
- Moles of KOH = Normality × Volume = 0.1 mol/L × 0.01 L = 0.001 moles.

### Step 4: Determine the moles of OH⁻ ions from KOH
- KOH dissociates to produce 1 OH⁻ ion for every mole of KOH.
- Therefore, moles of OH⁻ from KOH = 0.001 moles.

### Step 5: Calculate the net moles of H⁺ and OH⁻ ions
- Initially, we have 0.002 moles of H⁺ and 0.001 moles of OH⁻.
- The reaction between H⁺ and OH⁻ will neutralize each other:
- H⁺ + OH⁻ → H₂O
- After neutralization, the remaining moles of H⁺ = 0.002 - 0.001 = 0.001 moles.

### Step 6: Calculate the total volume of the solution
- Total volume = Volume of H₂SO₄ + Volume of KOH = 10 mL + 10 mL = 20 mL = 0.02 L.

### Step 7: Calculate the concentration of H⁺ ions in the final solution
- Concentration of H⁺ = Moles of H⁺ / Total volume = 0.001 moles / 0.02 L = 0.05 M.

### Step 8: Calculate the pH of the solution
- pH = -log[H⁺]
- pH = -log(0.05) = 1.301.

### Final Answer
The pH of the solution formed by mixing 10 mL of 0.1 M H₂SO₄ and 10 mL of N/10 KOH is approximately **1.301**.