Two solutions, A and B, each of 100 L was made by dissolving 4g of NaOH and 9.8 g of H_(2) SO_(4)` in water, respectively. The pH of the resultant solution obtained from mixing 40 L of solution A and 10 L of solution B is_______.

Explanation

To solve the problem, we need to calculate the pH of the resultant solution obtained by mixing two solutions A and B. Here are the steps to arrive at the solution:

### Step 1: Calculate the number of moles of NaOH in Solution A
- Given mass of NaOH = 4 g
- Molar mass of NaOH = 23 (Na) + 16 (O) + 1 (H) = 40 g/mol
- Number of moles of NaOH = mass / molar mass = 4 g / 40 g/mol = 0.1 moles

### Step 2: Calculate the number of moles of H₂SO₄ in Solution B
- Given mass of H₂SO₄ = 9.8 g
- Molar mass of H₂SO₄ = 2(1) + 32 + 4(16) = 98 g/mol
- Number of moles of H₂SO₄ = mass / molar mass = 9.8 g / 98 g/mol = 0.1 moles

### Step 3: Calculate the molarity of NaOH in Solution A
- Volume of Solution A = 100 L
- Molarity of NaOH = moles / volume = 0.1 moles / 100 L = 0.001 M or 10⁻³ M

### Step 4: Calculate the molarity of H₂SO₄ in Solution B
- Volume of Solution B = 100 L
- Molarity of H₂SO₄ = moles / volume = 0.1 moles / 100 L = 0.001 M or 10⁻³ M

### Step 5: Calculate the number of moles of NaOH in 40 L of Solution A
- Moles of NaOH in 40 L = Molarity × Volume = 0.001 M × 40 L = 0.04 moles

### Step 6: Calculate the number of moles of H₂SO₄ in 10 L of Solution B
- Moles of H₂SO₄ in 10 L = Molarity × Volume = 0.001 M × 10 L = 0.01 moles

### Step 7: Determine the milliequivalents of NaOH and H₂SO₄
- NaOH is a strong base and provides 1 OH⁻ per mole.
- H₂SO₄ is a strong acid and provides 2 H⁺ per mole.
- Milliequivalents of NaOH = moles × basicity = 0.04 moles × 1 = 0.04 equivalents
- Milliequivalents of H₂SO₄ = moles × acidity = 0.01 moles × 2 = 0.02 equivalents

### Step 8: Calculate the remaining equivalents after the reaction
- NaOH reacts with H₂SO₄: 0.04 eq (NaOH) - 0.02 eq (H₂SO₄) = 0.02 eq of NaOH left unreacted.

### Step 9: Calculate the concentration of OH⁻ ions in the resultant solution
- Total volume after mixing = 40 L (A) + 10 L (B) = 50 L
- Molarity of OH⁻ = remaining equivalents / total volume = 0.02 eq / 50 L = 0.0004 M or 4 × 10⁻⁴ M

### Step 10: Calculate pOH from the concentration of OH⁻ ions
- pOH = -log[OH⁻] = -log(4 × 10⁻⁴) = 3.4 (using logarithmic properties)

### Step 11: Calculate pH from pOH
- pH = 14 - pOH = 14 - 3.4 = 10.6

### Final Answer
The pH of the resultant solution is **10.6**.

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