Equal volumes of solution of `pH=6and pH=8` are mixed. What will be the pH of resulting mixture?

Answer

To find the pH of the resulting mixture when equal volumes of solutions with pH 6 and pH 8 are mixed, we can follow these steps:

### Step 1: Understand the pH scale
The pH scale is a logarithmic scale used to specify the acidity or basicity of an aqueous solution. The pH is defined as:
\[ \text{pH} = -\log[H^+] \]
where \([H^+]\) is the concentration of hydrogen ions in the solution.

### Step 2: Identify the pH values
We have two solutions:
- Solution 1: pH = 6
- Solution 2: pH = 8

### Step 3: Convert pH to hydrogen ion concentration
Using the formula for pH, we can convert the pH values to hydrogen ion concentrations:
- For pH 6:
\[ [H^+]_1 = 10^{-6} \, \text{M} \]
- For pH 8:
\[ [H^+]_2 = 10^{-8} \, \text{M} \]

### Step 4: Calculate the average concentration of hydrogen ions
Since equal volumes of the two solutions are mixed, we can find the average concentration of hydrogen ions in the resulting mixture. The total concentration of hydrogen ions after mixing is:
\[ [H^+]_{\text{total}} = \frac{[H^+]_1 + [H^+]_2}{2} \]
Substituting the values:
\[ [H^+]_{\text{total}} = \frac{10^{-6} + 10^{-8}}{2} \]

### Step 5: Simplify the calculation
To simplify the calculation, we note that \(10^{-6}\) is much larger than \(10^{-8}\), so we can approximate:
\[ [H^+]_{\text{total}} \approx \frac{10^{-6}}{2} = 5 \times 10^{-7} \, \text{M} \]

### Step 6: Calculate the resulting pH
Now we can find the pH of the resulting mixture using the hydrogen ion concentration:
\[ \text{pH}_{\text{result}} = -\log[H^+]_{\text{total}} \]
Substituting the value:
\[ \text{pH}_{\text{result}} = -\log(5 \times 10^{-7}) \]
Using logarithmic properties:
\[ \text{pH}_{\text{result}} \approx 7 \]

### Final Answer:
The pH of the resulting mixture is approximately **7**.

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