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To determine the correctness of the statements provided, we will analyze each statement one by one.
### Statement (a)
**Analysis of pH Calculation:**
1. **Calculate the equivalence of the strong acid (H2SO4):**
- The concentration of H2SO4 is 0.1 M and the volume is 400 mL.
- Since H2SO4 is a diprotic acid, it can donate 2 protons (H+).
- Therefore, the equivalence of H2SO4 is calculated as:
\[
\text{Equivalence of H}_2\text{SO}_4 = 0.1 \, \text{M} \times 2 \times 0.4 \, \text{L} = 0.08 \, \text{equivalents}
\]
2. **Calculate the equivalence of the strong base (NaOH):**
- The concentration of NaOH is 0.1 M and the volume is 400 mL.
- Therefore, the equivalence of NaOH is:
\[
\text{Equivalence of NaOH} = 0.1 \, \text{M} \times 0.4 \, \text{L} = 0.04 \, \text{equivalents}
\]
3. **Determine the net H+ concentration:**
- The net H+ concentration after neutralization is:
\[
[H^+] = \frac{(0.08 - 0.04) \, \text{equivalents}}{0.8 \, \text{L}} = \frac{0.04}{0.8} = 0.05 \, \text{M}
\]
4. **Calculate the pH:**
- The pH is calculated using the formula:
\[
pH = -\log[H^+] = -\log(0.05) \approx 1.3
\]
- Thus, statement (a) is correct.
### Statement (b)
**Ionic Product of Water:**
- The ionic product of water ($K_w$) is temperature dependent. As the temperature increases, the ionization of water increases, leading to a higher value of $K_w$. Therefore, statement (b) is correct.
### Statement (c)
**Degree of Dissociation of a Monobasic Acid:**
1. **Given:**
- $K_a = 10^{-5}$
- pH = 5
2. **Calculate the concentration of H+:**
- From the pH, we can find:
\[
[H^+] = 10^{-5} \, \text{M}
\]
3. **Using the formula for degree of dissociation ($\alpha$):**
- The formula for a weak acid is:
\[
K_a = \frac{c\alpha^2}{1 - \alpha}
\]
- Substituting the values:
\[
10^{-5} = \frac{10^{-5} \cdot \alpha^2}{1 - \alpha}
\]
- Rearranging gives:
\[
1 - \alpha = \alpha \Rightarrow \alpha = 0.5
\]
- Thus, the degree of dissociation is 50%, making statement (c) correct.
### Statement (d)
**Le Chatelier's Principle and Common-Ion Effect:**
- The common-ion effect is a specific application of Le Chatelier's principle, which states that if an external change is applied to a system at equilibrium, the system will adjust to counteract that change. Therefore, statement (d) is incorrect.
### Conclusion
The correct statements are (a), (b), and (c). Therefore, the correct answer is:
**(a), (b), and (c)**
