This question is asking for the relationship between the degree of conversion ($\alpha$) of alcohol (B) and the equilibrium constant ($K_c$) for the synthesis reaction of compound (E). The goal is to determine the correct formula for $\alpha$.

Approach:

1. Degree of Conversion $\alpha$: It generally relates the amount of reactant converted into the product at equilibrium, dependent on the equilibrium constant $K_c$.

2. Derive the Formula: The correct formula for $\alpha$ must be consistent with the law of mass action and should match the equilibrium condition.

Analysis of Options:

The options provided are:

• $a. \alpha = \frac{\sqrt{K_c}}{2 + \sqrt{K_c}}$
• $b. \alpha = \frac{\sqrt{K_c}}{1 + 2\sqrt{K_c}}$
• $c. \alpha = \frac{\sqrt{K_c}}{1 + \sqrt{K_c}}$
• $d. \alpha = \frac{1 + \sqrt{K_c}}{\sqrt{K_c}}$

Using the standard formulation for equilibrium conversion, the dependence of $\alpha$ on $K_c$ typically involves terms for the forward and reverse reactions, balancing the equilibrium concentrations. From the structure of the formulas, you would simplify by assuming $\alpha$ varies inversely with $K_c$'s dependence on $\sqrt{}$ or $\sqrt{} + \text{constant terms}$.

The correct option should match the behavior of $\alpha$ with respect to increasing $K_c$.

Let me know if you'd like further clarification or need a detailed derivation to verify!

Related Questions:

1. What is the equilibrium constant and how is it derived for a synthesis reaction?
2. How does the degree of conversion vary with the magnitude of the equilibrium constant?
3. What assumptions are typically made in equilibrium calculations for chemical reactions?
4. Can $K_c$ be expressed in terms of partial pressures for gas-phase reactions?
5. How does temperature affect the equilibrium constant and the degree of conversion?

Tip: When solving equilibrium problems, carefully balance the reaction and apply the law of mass action for precise