To solve this problem, we need to determine the equilibrium constant ([tex]\(K\)[/tex]) for the given reaction:
[tex]\[O_2(g) + 2SO_2(g) \rightleftarrows 2SO_3(g)\][/tex]
The equilibrium expression for this reaction is given as:
[tex]\[ K = \frac{[SO_3]^2}{[O_2] \cdot [SO_2]^2} \][/tex]
Given the equilibrium concentrations from the table:
[tex]\[
[O_2] = 1.2 \, \text{M}
\][/tex]
[tex]\[
[SO_2] = 0.80 \, \text{M}
\][/tex]
[tex]\[
[SO_3] = 1.9 \, \text{M}
\][/tex]
We can substitute these values into the equilibrium expression to calculate [tex]\( K \)[/tex]:
[tex]\[
K = \frac{[SO_3]^2}{[O_2] \cdot [SO_2]^2}
\][/tex]
[tex]\[
K = \frac{(1.9)^2}{1.2 \cdot (0.80)^2}
\][/tex]
Calculating the squares and products in the denominator and numerator:
[tex]\[
(1.9)^2 = 3.61
\][/tex]
[tex]\[
(0.80)^2 = 0.64
\][/tex]
[tex]\[
1.2 \cdot 0.64 = 0.768
\][/tex]
Now, divide the results:
[tex]\[
K = \frac{3.61}{0.768} \approx 4.700520833333332
\][/tex]
Now that we have the value of [tex]\(K\)[/tex], we determine whether the reaction favors the reactants or the products by comparing the value of [tex]\(K\)[/tex] with 1.
- 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]\(K \approx 4.7\)[/tex], which is greater than 1, indicating that the reaction favors the formation of products.
Now, we review the answer choices:
A. [tex]\(K = 4.7\)[/tex]; product favored
B. [tex]\(K = 0.51\)[/tex]; product favored
C. [tex]\(K = 0.51\)[/tex]; reactant favored
D. [tex]\(K = 4.7\)[/tex]; reactant favored
Given our calculated [tex]\(K\)[/tex] value of approximately 4.7 and the understanding that this [tex]\(K\)[/tex] value indicates a product-favored reaction, the closest match in the provided choices would ideally be choice A. However, none of the given answer choices exactly match our findings in both [tex]\(K\)[/tex] value and description.
Thus, the final numerical result and determination is:
[tex]\[
K \approx 4.700520833333332, \quad \text{product favored}, \quad \text{None of the provided choices exactly match.}
\][/tex]
