Step 1: Understanding the Given Reaction - The reaction provided is: \[ Xe(g) + 2F_2(g) \xrightarrow{873 K, 7 { bar}} XeF_4(s) \] - Here, 1 mole of Xenon reacts with 2 moles of Fluorine gas to form XeFsubscript{4}. 
Step 2: Analyzing the Ratio - The ratio of Xe to Fsubscript{2} in the equation is 1:2.
- However, in an extended fluorination process, more fluorine gas may be required to sustain and complete the reaction. 
Step 3: Applying Stoichiometry - From experimental data, the reaction sometimes requires 1:5 (Xe:Fsubscript{2}) under certain conditions.
- This is because excess fluorine helps drive the reaction forward.
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: