Question

question 23 of 32
the equilibrium concentrations for the reaction between so₂ and o₂ to form
so₃ at a certain temperature are given in the table below. determine the
equilibrium constant and whether the reaction favors reactants, products, or
neither at this temperature.

o₂(g) + 2so₂(g) ⇌ 2so₃(g)

o₂	so₂	so₃

a. ( k = 1.3 \times 10^4 ); reactant favored
b. ( k = 1.3 \times 10^{-3} ); reactant favored
c. ( k = 1.3 \times 10^{-3} ); product favored
d. ( k = 1.3 \times 10^4 ); product favored

Explanation:

Step1: Recall Equilibrium Constant Formula

For the reaction \( \text{O}_2(g) + 2\text{SO}_2(g)
ightleftharpoons 2\text{SO}_3(g) \), the equilibrium constant \( K \) is given by \( K=\frac{[\text{SO}_3]^2}{[\text{O}_2][\text{SO}_2]^2} \).

Step2: Substitute Concentrations

Given \( [\text{O}_2] = 0.024 \, M \), \( [\text{SO}_2] = 0.015 \, M \), \( [\text{SO}_3] = 0.26 \, M \). Substitute into the formula:
\[
K=\frac{(0.26)^2}{(0.024)(0.015)^2}
\]

Step3: Calculate Numerator and Denominator

• Numerator: \( (0.26)^2 = 0.0676 \)
• Denominator: \( (0.024)(0.015)^2 = 0.024 \times 0.000225 = 5.4 \times 10^{-6} \)

Step4: Compute K

\[
K=\frac{0.0676}{5.4 \times 10^{-6}} \approx 1.25 \times 10^4 \approx 1.3 \times 10^4
\]

Step5: Determine Reaction Favor

Since \( K > 1 \), the reaction favors the products (because a large \( K \) means products are more concentrated at equilibrium).

Answer:

D. \( K = 1.3 \times 10^4 \); product favored