To 250.0 ml of `M//50H_(2)SO_(4),` 4.0 g of solid NaOH is added and the resulting solution is

Options

A. `12.0`
B. `11.25`
C. `11.95`
D. `12.95`

Answer

To solve the problem of determining the pH of the resulting solution after adding 4.0 g of NaOH to 250.0 mL of 1/50 M H₂SO₄, we will follow these steps:

### Step 1: Calculate the Normality of H₂SO₄
H₂SO₄ (sulfuric acid) is a diprotic acid, meaning it can donate two protons (H⁺ ions).

- **Molarity of H₂SO₄** = 1/50 M = 0.02 M
- **Normality (N)** = Molarity × Number of protons donated = 0.02 M × 2 = 0.04 N

### Step 2: Calculate the Number of Equivalents of H₂SO₄
To find the number of equivalents of H₂SO₄ in the solution:

- Volume of H₂SO₄ solution = 250 mL = 0.250 L
- **Equivalents of H₂SO₄** = Normality × Volume (in L) = 0.04 N × 0.250 L = 0.01 equivalents

### Step 3: Calculate the Number of Equivalents of NaOH
Next, we need to find out how many equivalents of NaOH are present in 4.0 g:

- Molecular weight of NaOH = 40 g/mol
- Moles of NaOH = Mass / Molecular weight = 4.0 g / 40 g/mol = 0.1 moles
- Since NaOH is a monoprotic base, the number of equivalents of NaOH is equal to the number of moles.

Thus, **Equivalents of NaOH** = 0.1 equivalents.

### Step 4: Determine the Reaction Between H₂SO₄ and NaOH
The reaction between H₂SO₄ and NaOH can be represented as:

\[ \text{H}_2\text{SO}_4 + 2 \text{NaOH} \rightarrow \text{Na}_2\text{SO}_4 + 2 \text{H}_2\text{O} \]

From the stoichiometry of the reaction:
- 1 equivalent of H₂SO₄ reacts with 2 equivalents of NaOH.

### Step 5: Calculate the Limiting Reactant
We have:
- 0.01 equivalents of H₂SO₄
- 0.1 equivalents of NaOH

Since 1 equivalent of H₂SO₄ requires 2 equivalents of NaOH, 0.01 equivalents of H₂SO₄ will require:
\[ 0.01 \times 2 = 0.02 \text{ equivalents of NaOH} \]

Since we have 0.1 equivalents of NaOH, H₂SO₄ is the limiting reactant.

### Step 6: Calculate Remaining NaOH
After the reaction, the remaining NaOH will be:
\[ \text{Remaining NaOH} = \text{Initial NaOH} - \text{NaOH used} \]
\[ \text{Remaining NaOH} = 0.1 - 0.02 = 0.08 \text{ equivalents} \]

### Step 7: Calculate the pOH of the Resulting Solution
The concentration of the remaining NaOH in the final solution can be calculated. The total volume of the solution after dilution to 1 L is 1 L.

Thus, the concentration of NaOH:
\[ \text{Concentration of NaOH} = \frac{0.08 \text{ equivalents}}{1 \text{ L}} = 0.08 \text{ N} \]

Now, calculate pOH:
\[ \text{pOH} = -\log(0.08) \approx 1.10 \]

### Step 8: Calculate the pH of the Solution
Using the relationship between pH and pOH:
\[ \text{pH} + \text{pOH} = 14 \]
\[ \text{pH} = 14 - 1.10 = 12.90 \]

### Final Answer
The pH of the resulting solution is approximately **12.90**.

---