Find the pH of a solution prepared by mixing 25ml of a 0.5M solution of HCI,10ml of a 0.5M solution of NaOH and 15 ml of water :-

Options

A. 4
B. 3
C. 0. 82
D. 0. 10

Explanation

To find the pH of the solution prepared by mixing 25 mL of a 0.5 M solution of HCl, 10 mL of a 0.5 M solution of NaOH, and 15 mL of water, we can follow these steps:

### Step 1: Calculate the moles of HCl
The moles of HCl can be calculated using the formula:
\[ \text{Moles of HCl} = \text{Molarity} \times \text{Volume (in L)} \]
Given:
- Molarity of HCl = 0.5 M
- Volume of HCl = 25 mL = 0.025 L

Calculating:
\[ \text{Moles of HCl} = 0.5 \, \text{M} \times 0.025 \, \text{L} = 0.0125 \, \text{moles} \]

### Step 2: Calculate the moles of NaOH
Similarly, we can calculate the moles of NaOH:
\[ \text{Moles of NaOH} = \text{Molarity} \times \text{Volume (in L)} \]
Given:
- Molarity of NaOH = 0.5 M
- Volume of NaOH = 10 mL = 0.010 L

Calculating:
\[ \text{Moles of NaOH} = 0.5 \, \text{M} \times 0.010 \, \text{L} = 0.005 \, \text{moles} \]

### Step 3: Determine the remaining moles of HCl
Now, we need to find the remaining moles of HCl after the reaction with NaOH. The reaction between HCl and NaOH is a 1:1 reaction:
\[ \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} \]
Calculating the remaining moles of HCl:
\[ \text{Remaining moles of HCl} = \text{Initial moles of HCl} - \text{Moles of NaOH} \]
\[ \text{Remaining moles of HCl} = 0.0125 - 0.005 = 0.0075 \, \text{moles} \]

### Step 4: Calculate the total volume of the solution
Now, we calculate the total volume of the solution:
\[ \text{Total Volume} = \text{Volume of HCl} + \text{Volume of NaOH} + \text{Volume of water} \]
Given:
- Volume of HCl = 25 mL
- Volume of NaOH = 10 mL
- Volume of water = 15 mL

Calculating:
\[ \text{Total Volume} = 25 + 10 + 15 = 50 \, \text{mL} = 0.050 \, \text{L} \]

### Step 5: Calculate the concentration of H⁺ ions
The concentration of H⁺ ions in the solution can be calculated as follows:
\[ [\text{H}^+] = \frac{\text{Remaining moles of HCl}}{\text{Total Volume}} \]
Calculating:
\[ [\text{H}^+] = \frac{0.0075 \, \text{moles}}{0.050 \, \text{L}} = 0.15 \, \text{M} \]

### Step 6: Calculate the pH of the solution
The pH is calculated using the formula:
\[ \text{pH} = -\log[\text{H}^+] \]
Calculating:
\[ \text{pH} = -\log(0.15) \approx 0.8239 \]

### Final Answer
Thus, the pH of the solution is approximately:
\[ \text{pH} \approx 0.82 \]

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