The equilibrium constant is given for one of the reactions below. Determine the value of the missing equilibrium constant. Show your work for full credits.

Question

BlackTom AI · Accepted Answer

To tackle this equilibrium problem, I first restate the given information and target transformation clearly.
The given equilibrium is 2 SO2(g) + O2(g) ⇌ 2 SO3(g) with Kc = 1.7 × 10^6.
We are asked for the equilibrium constant of the reaction SO3(g) ⇌ 1/2 O2(g) + SO2(g).
Now, analyze the relationships step by step:
1) Divide the original reaction by 2 to obtain SO2(g) + 1/2 O2(g) ⇌ SO3(g). When you divide a reaction by 2, the new Kc is the square root of the original Kc because Kc_original = ([SO3]^2)/([SO2]^2[O2]); taking the square root corresponds to the single-molecule production of SO3 in the half-reaction. Therefore, K_half = sqrt(1.7 × 10^6) ≈ 1.30 × 10^3.
2) Now consider the target reaction, which is the reverse of the half-reaction: SO3(g) ⇌ 1/2 O2(g) + SO2(g). Reversing a reaction inverts its equilibrium constant, so K_target = 1 / K_half.
3) Compute the reciprocal: 1 / (1.30 × 10^3) ≈ 7.7 × 10^-4.
Thus, {SO3(g) ⇌ 1/2 O2(g) + SO2(g)} has an equilibrium constant on the order of 7.7 × 10^-4.
If you want to verify the intermediate steps, you can also track the algebra directly from the original Kc by expressing Kc in terms of the species for the half-reaction and then applying the reversal rule to obtain the final value.
In summary, the sequence of operations—dividing the original equation by 2, taking the square root for the new Kc, and then inverting for the reverse direction—yields approximately 7.7 × 10^-4 as the equilibrium constant for the requested reaction.

The equilibrium constant is given for one of the reactions below. Determine the value of the missing equilibrium constant. Show your work for full credits.

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