To solve the question, we need to analyze both the assertion and the reason provided.
### Step-by-Step Solution:
1. **Understanding the Assertion:**
- The assertion states that the pH of hydrochloric acid (HCl) solution is less than that of acetic acid (CH₃COOH) solution of the same concentration.
- HCl is a strong acid, which means it completely dissociates in solution to produce H⁺ ions. For example, a 1 M solution of HCl will produce 1 M of H⁺ ions.
- Acetic acid, on the other hand, is a weak acid and does not completely dissociate. For a 1 M solution of acetic acid, only a fraction (α, the degree of ionization) will dissociate to produce H⁺ ions. Therefore, the concentration of H⁺ ions in acetic acid will be less than 1 M.
2. **Calculating pH:**
- For HCl: If the concentration is C, then [H⁺] = C. The pH can be calculated using the formula:
\[
\text{pH} = -\log[H⁺] = -\log(C)
\]
- For acetic acid: If the concentration is C, the concentration of H⁺ ions will be Cα, where α < 1. Thus, the pH is:
\[
\text{pH} = -\log(Cα)
\]
- Since α < 1, it follows that Cα < C, leading to a higher pH value for acetic acid compared to hydrochloric acid.
3. **Conclusion on Assertion:**
- Since HCl produces more H⁺ ions than acetic acid at the same concentration, the pH of HCl is indeed less than that of acetic acid. Therefore, the assertion is **true**.
4. **Understanding the Reason:**
- The reason states that in equimolar solutions, the number of titrable protons present in hydrochloric acid is less than that present in acetic acid.
- This statement is incorrect because hydrochloric acid, being a strong acid, has one titrable proton that completely dissociates, while acetic acid, being a weak acid, has a lower degree of dissociation. Thus, the number of titrable protons in HCl is equal to that in acetic acid (both have one titrable proton), but the extent of dissociation differs.
5. **Conclusion on Reason:**
- Therefore, the reason is **false**.
### Final Conclusion:
- The assertion is **true** and the reason is **false**.
