Step 1: Understanding Heterogeneous Catalysis
- Heterogeneous catalysis occurs when the reactants and catalyst exist in different phases (e.g., solid catalyst with gaseous reactants).
- In contrast, homogeneous catalysis occurs when the catalyst and reactants are in the same phase.
Step 2: Identifying the Correct Option
- (A) Involves only gases, so it is homogeneous catalysis.
- (B) Involves only solids, not catalysis.
- (C) The reactants are gases, and the catalyst is solid (\( C (s) \)), which is a classic example of heterogeneous catalysis.
- (D) The catalyst and reactants are in the same phase (gaseous), making it homogeneous. 
Final Answer: The correct example of heterogeneous catalysis is option (C).
Observe the following reactions: 
\( AB(g) + 25 H_2O(l) \rightarrow AB(H_2S{O_4}) \quad \Delta H = x \, {kJ/mol}^{-1} \) 
\( AB(g) + 50 H_2O(l) \rightarrow AB(H_2SO_4) \quad \Delta H = y \, {kJ/mol}^{-1} \) 
The enthalpy of dilution, \( \Delta H_{dil} \) in kJ/mol\(^{-1}\), is:
If the roots of $\sqrt{\frac{1 - y}{y}} + \sqrt{\frac{y}{1 - y}} = \frac{5}{2}$ are $\alpha$ and $\beta$ ($\beta > \alpha$) and the equation $(\alpha + \beta)x^4 - 25\alpha \beta x^2 + (\gamma + \beta - \alpha) = 0$ has real roots, then a possible value of $y$ is: