What will be the pH when 0.01 mole of `HNO_3` is dissolved in V volume of water and `V rarr oo` ?

Options

A. 1
B. 2
C. 7
D. 0

Explanation

To solve the question of what the pH will be when 0.01 moles of HNO₃ is dissolved in an infinite volume of water, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Dissociation of HNO₃**:
HNO₃ (nitric acid) is a strong acid, which means it completely dissociates in water. The dissociation can be represented as:
\[ \text{HNO}_3 \rightarrow \text{H}^+ + \text{NO}_3^- \]
Therefore, for every mole of HNO₃ that dissolves, one mole of H⁺ ions is produced.

2. **Calculating the Concentration of H⁺ Ions**:
When 0.01 moles of HNO₃ is dissolved in an infinite volume of water (V → ∞), the concentration of H⁺ ions will approach zero because the volume is so large that the amount of solute becomes negligible. Mathematically, the concentration (C) of H⁺ ions can be expressed as:
\[ C = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]
As V approaches infinity, \( C \) approaches:
\[ C = \frac{0.01}{V} \rightarrow 0 \text{ (as } V \rightarrow \infty\text{)} \]

3. **Understanding pH Calculation**:
The pH of a solution is calculated using the formula:
\[ \text{pH} = -\log[H^+] \]
Where [H⁺] is the concentration of hydrogen ions in the solution.

4. **Determining the pH in Infinite Volume**:
Since the concentration of H⁺ ions approaches zero as the volume approaches infinity, we can substitute this into the pH formula:
\[ \text{pH} = -\log(0) \text{ (which is undefined, but we consider the neutral state)} \]
In pure water, the concentration of H⁺ ions is \( 1 \times 10^{-7} \) M, leading to a pH of 7.

5. **Conclusion**:
Therefore, when 0.01 moles of HNO₃ is dissolved in an infinite volume of water, the pH of the solution will approach 7, which is the neutral pH of water.

### Final Answer:
The pH will be 7.