Solution of a monobasic acid has a pH=5. If one mL of it is diluted to 1 litre, what will be the pH of the resulting solution ?

Options

A. a.3.45
B. b.6.96
C. c.8.58
D. d.10.25

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the initial concentration of hydrogen ions
Given that the pH of the monobasic acid solution is 5, we can find the concentration of hydrogen ions \([H^+]\) using the formula:
\[ [H^+] = 10^{-\text{pH}} = 10^{-5} \, \text{mol/L} \]

### Step 2: Calculate the amount of hydrogen ions in 1 mL of the solution
We need to find the number of moles of hydrogen ions in 1 mL of the solution:
\[ \text{Moles of } H^+ = [H^+] \times \text{Volume in L} = 10^{-5} \, \text{mol/L} \times 0.001 \, \text{L} = 10^{-8} \, \text{mol} \]

### Step 3: Dilute the solution to 1 L
When we dilute this 1 mL solution to 1 L (1000 mL), the concentration of hydrogen ions will change. The new concentration can be calculated as follows:
\[ \text{New concentration of } H^+ = \frac{10^{-8} \, \text{mol}}{1 \, \text{L}} = 10^{-8} \, \text{mol/L} \]

### Step 4: Consider the contribution of hydrogen ions from water
Since we are diluting with water, we must also consider the contribution of hydrogen ions from pure water, which has a concentration of:
\[ [H^+]_{\text{water}} = 10^{-7} \, \text{mol/L} \]

### Step 5: Calculate the total concentration of hydrogen ions
Now we add the contributions from the diluted acid and the water:
\[ [H^+]_{\text{total}} = [H^+]_{\text{acid}} + [H^+]_{\text{water}} = 10^{-8} + 10^{-7} \]
To add these, we can express \(10^{-8}\) in terms of \(10^{-7}\):
\[ [H^+]_{\text{total}} = 10^{-8} + 10^{-7} = 10^{-7}(1 + 0.1) = 1.1 \times 10^{-7} \, \text{mol/L} \]

### Step 6: Calculate the new pH
Finally, we can find the new pH using the total concentration of hydrogen ions:
\[ \text{pH} = -\log([H^+]_{\text{total}}) = -\log(1.1 \times 10^{-7}) \]
Using logarithmic properties, this can be approximated as:
\[ \text{pH} \approx 6.96 \]

### Final Answer
The pH of the resulting solution after dilution is approximately **6.96**.

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