The equilibrium constant for reaction 1 is K. The equilibrium constant for reaction 2 is ________.

(1) SO2 (g) + (1/2) O2 (g)  ⇌
SO3 (g)
(2) 2SO3 (g)  ⇌
2SO2 (g) + O2 (g)

To find the equilibrium constant for reaction 2, let's analyze both reactions and their relationship.

### Given Reactions:
1. **Reaction 1:** 
   \[
   \text{SO}_2 (g) + \frac{1}{2} \text{O}_2 (g) \rightleftharpoons \text{SO}_3 (g)
   \]
   with equilibrium constant \( K_1 = K \).

2. **Reaction 2:**
   \[
   2\text{SO}_3 (g) \rightleftharpoons 2\text{SO}_2 (g) + \text{O}_2 (g)
   \]
   with equilibrium constant \( K_2 \) (which we need to determine).

### Analyzing the Relationship:
Reaction 2 is essentially the reverse of twice reaction 1. If we multiply reaction 1 by 2, we get:
\[
2\text{SO}_2 (g) + \text{O}_2 (g) \rightleftharpoons 2\text{SO}_3 (g)
\]
The equilibrium constant for this reaction would be \( K_1^2 \) because when a reaction is multiplied by a coefficient, the equilibrium constant is raised to the power of that coefficient.

Now, if we reverse this new reaction, we get reaction 2:
\[
2\text{SO}_3 (g) \rightleftharpoons 2\text{SO}_2 (g) + \text{O}_2 (g)
\]
When a reaction is reversed, the equilibrium constant becomes the reciprocal of the original equilibrium constant.

Thus:
\[
K_2 = \frac{1}{K_1^2} = \frac{1}{K^2}
\]

### Final Answer:
The equilibrium constant for reaction 2 is \( \frac{1}{K^2} \).

Would you like further details or have any questions?

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Here are some related questions you might find interesting:
1. What is the effect on the equilibrium constant if the temperature changes?
2. How does doubling the concentration of SO2 affect the equilibrium position?
3. Can you explain the significance of the equilibrium constant in chemical reactions?
4. How do catalysts affect the value of the equilibrium constant?
5. What happens to the equilibrium constant if the volume of the reaction container is changed?
6. How does the partial pressure of O2 affect the equilibrium constant in gas-phase reactions?
7. Can the equilibrium constant be negative?
8. How is the equilibrium constant expressed in terms of concentration for a reaction involving solids and liquids?

**Tip:** When analyzing equilibrium reactions, remember that reversing the reaction takes the reciprocal of the equilibrium constant, and scaling the reaction affects the constant exponentially.

Explore how to calculate the equilibrium constant for reaction 2 using the relationship between chemical reactions and equilibrium constants. Detailed step-by-step solution and analysis provided.

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