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 concentration of HCl is 0.5 M and the volume is 25 ml (which is 0.025 L).
\[ \text{Moles of HCl} = \text{Concentration} \times \text{Volume} = 0.5 \, \text{mol/L} \times 0.025 \, \text{L} = 0.0125 \, \text{mol} \]

### Step 2: Calculate the moles of NaOH
The concentration of NaOH is also 0.5 M and the volume is 10 ml (which is 0.010 L).
\[ \text{Moles of NaOH} = \text{Concentration} \times \text{Volume} = 0.5 \, \text{mol/L} \times 0.010 \, \text{L} = 0.005 \, \text{mol} \]

### Step 3: Determine the remaining moles of HCl after neutralization
Since HCl and NaOH react in a 1:1 ratio, we subtract the moles of NaOH from the moles of HCl.
\[ \text{Remaining moles of HCl} = 0.0125 \, \text{mol} - 0.005 \, \text{mol} = 0.0075 \, \text{mol} \]

### Step 4: Calculate the total volume of the solution
The total volume is the sum of the volumes of HCl, NaOH, and water.
\[ \text{Total volume} = 25 \, \text{ml} + 10 \, \text{ml} + 15 \, \text{ml} = 50 \, \text{ml} = 0.050 \, \text{L} \]

### Step 5: Calculate the concentration of H⁺ ions
The concentration of H⁺ ions in the solution can be calculated using the remaining moles of HCl and the total volume.
\[ [\text{H}^+] = \frac{\text{Remaining moles of HCl}}{\text{Total volume}} = \frac{0.0075 \, \text{mol}}{0.050 \, \text{L}} = 0.15 \, \text{M} \]

### Step 6: Calculate the pH
The pH is calculated using the formula:
\[ \text{pH} = -\log[\text{H}^+] = -\log(0.15) \]
Calculating this gives:
\[ \text{pH} \approx 0.82 \]

### Final Answer
The pH of the solution is approximately **0.82**.

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