STATEMENT-1: pH of `10^(-7)` M HCl is less than 7 at `25^(@)C.`
STATEMENT-2: At very low concentration of HCl, contribution of `H^(+)` from water is considerable.

Options

A. If both the statements are TRUE and STATEMENT-2 is the correct explanation of STATEMENT-1
B. If both the statements are TRUE AND STATEMENT-2 is NOT the correct explanation of STATEMENT-1
C. If STATEMENT-1 is TRUE and STATEMENT-2 is FALSE
D. If STATEMENT-1 is FALSE and STATEMENT-2 is TRUE

Answer

To solve the question, we need to analyze both statements provided and determine their validity.

### Step 1: Analyze Statement 1
**Statement 1:** pH of \(10^{-7}\) M HCl is less than 7 at \(25^\circ C\).

- **Understanding pH:** The pH scale ranges from 0 to 14, where a pH of 7 is considered neutral. A pH less than 7 indicates an acidic solution.
- **HCl as a Strong Acid:** Hydrochloric acid (HCl) is a strong acid, meaning it dissociates completely in solution. Therefore, a \(10^{-7}\) M solution of HCl would contribute \(10^{-7}\) M of \(H^+\) ions from HCl.
- **Contribution from Water:** At \(25^\circ C\), pure water also contributes \(10^{-7}\) M of \(H^+\) ions due to its self-ionization.
- **Total \(H^+\) Concentration:** In the case of \(10^{-7}\) M HCl, the total concentration of \(H^+\) ions in the solution would be:
\[ [H^+] = 10^{-7} \text{ M (from HCl)} + 10^{-7} \text{ M (from water)} = 2 \times 10^{-7} \text{ M} \]
- **Calculating pH:** The pH can be calculated using the formula:
\[ \text{pH} = -\log[H^+] \]
Substituting the total concentration:
\[ \text{pH} = -\log(2 \times 10^{-7}) \approx 6.7 \]
- **Conclusion for Statement 1:** Since \(6.7 < 7\), Statement 1 is **true**.

### Step 2: Analyze Statement 2
**Statement 2:** At very low concentration of HCl, the contribution of \(H^+\) from water is considerable.

- **Understanding Contributions:** At very low concentrations of strong acids like HCl, the contribution of \(H^+\) ions from the acid itself becomes comparable to that from water.
- **Low Concentration Impact:** For concentrations around \(10^{-7}\) M, the contribution from water (which is \(10^{-7}\) M) cannot be ignored as it is equal to the concentration of \(H^+\) from HCl.
- **Conclusion for Statement 2:** Since the contribution from water is significant at such low concentrations, Statement 2 is also **true**.

### Final Conclusion
Both statements are true, and Statement 2 provides a correct explanation for Statement 1. Therefore, the correct answer is that both statements are true, and Statement 2 is the correct explanation of Statement 1.