To determine the equilibrium constant [tex]\( K \)[/tex] and whether the reaction favors the reactants, products, or neither, we follow these steps:
1. Write the Balanced Chemical Equation:
[tex]\[
O_2(g) + 2 SO_2(g) \rightleftarrows 2 SO_3(g)
\][/tex]
2. Write the Expression for the Equilibrium Constant ([tex]\( K \)[/tex]):
For the general equilibrium reaction [tex]\( aA + bB \rightleftarrows cC + dD \)[/tex], the equilibrium constant expression is:
[tex]\[
K = \frac{[C]^c [D]^d}{[A]^a [B]^b}
\][/tex]
For our specific reaction, the expression is:
[tex]\[
K = \frac{[SO_3]^2}{[O_2] \cdot [SO_2]^2}
\][/tex]
3. Substitute the Given Equilibrium Concentrations:
Given:
[tex]\[
[O_2] = 1.3 \, \text{M}, \quad [SO_2] = 0.46 \, \text{M}, \quad [SO_3] = 8.5 \, \text{M}
\][/tex]
Substituting these values into the equilibrium expression:
[tex]\[
K = \frac{(8.5)^2}{1.3 \cdot (0.46)^2}
\][/tex]
4. Calculate the Value of [tex]\( K \)[/tex]:
[tex]\[
K = \frac{72.25}{1.3 \cdot 0.2116}
\][/tex]
[tex]\[
K = \frac{72.25}{0.27508}
\][/tex]
[tex]\[
K \approx 262.65
\][/tex]
5. Determine Whether the Reaction Favors Reactants or Products:
- If [tex]\( K > 1 \)[/tex], the reaction favors the formation of products.
- If [tex]\( K < 1 \)[/tex], the reaction favors the formation of reactants.
In this case, [tex]\( K \approx 262.65 \)[/tex], which is much greater than 1, indicating that the reaction strongly favors the formation of products at this temperature.
Therefore, the correct answer is:
[tex]\[
\boxed{\text{C. } K=260; \text{ product favored}}
\][/tex]
