For the following reactions, equilibrium constants are given:
` S(s ) + O _ 2 (g) SO _ 2 (g ) , K _ 1 = 10 ^( 52 ) , 2 S ( s ) + 3O _ 2 ( g ) 2 SO _ 3 (g) , K _ 2 = 10 ^( 129) `
The equilibrium constant for the reaction, ` 2SO _ 2 (g ) + O _ 2 ( g ) 2 SO _ 3 (g) ` is

Options

A. ` 10 ^( 77) `
B. ` 10 ^( 154 ) `
C. ` 10 ^( 25 ) `
D. `10 ^( 181 ) `

Explanation

To find the equilibrium constant for the reaction \( 2SO_2 (g) + O_2 (g) \rightarrow 2SO_3 (g) \), we can use the given equilibrium constants \( K_1 \) and \( K_2 \) for the reactions:

1. \( S(s) + O_2(g) \rightarrow SO_2(g) \), with \( K_1 = 10^{52} \)
2. \( 2S(s) + 3O_2(g) \rightarrow 2SO_3(g) \), with \( K_2 = 10^{129} \)

### Step-by-Step Solution:

1. **Write the reactions and their equilibrium constants:**
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