If the equilibrium constants for the two reactions
2 HCl(g) H2(g) + Cl2(g)
and
I2(g) + Cl2(g) 2 ICl(g)
are denoted K1 and K2 respectively, then the equilibrium constant for the reaction
2 HCl(g) + I2(g) 2 ICl(g) + H2(g) equals

Question

If the equilibrium constants for the two reactions
2 HCl(g) H2(g) + Cl2(g)
and
I2(g) + Cl2(g)  2 ICl(g)
are denoted K1 and K2 respectively, then the equilibrium constant for the reaction
2 HCl(g) + I2(g)  2 ICl(g) + H2(g) equals

BlackTom AI · Accepted Answer

Let me restate the problem in my own words: we are given two equilibrium reactions with known equilibrium constants, K1 and K2, and we need the equilibrium constant for a third reaction that is obtained by combining the first two. The two given equilibria are:

1) 2 HCl(g) ⇌ H2(g) + Cl2(g) with K1 = [H2][Cl2] / [HCl]^2
2) I2(g) + Cl2(g) ⇌ 2 ICl(g) with K2 = [ICl]^2 / ([I2][Cl2])

The target reaction is:
2 HCl(g) + I2(g) ⇌ 2 ICl(g) + H2(g)

Step 1: Combine the first two reactions to see if they produce the target. If we take reaction 1 as written (2 HCl → H2 + Cl2) and add reaction 2 as written (I2 + Cl2 → 2 ICl), the sum is:
- Left side: 2 HCl + I2 + Cl2
- Right side: H2 + Cl2 + 2 ICl
Step 2: Cancel the species that appear on both sides. Cl2 appears on both sides, so it cancels, leaving:
2 HCl + I2 → H2 + 2 ICl
This is exactly the target reaction, just with the products listed in a different order. Therefore the overall equilibrium constant for the sum equals the product of the individual constants:
K(overall) = K1 × K2

Step 3: Interpret the options given. The only presented option is K1K2, which matches the product of the two equilibria constants as derived. If there were other options (e.g., K1, K2, 1/(K1K2), etc.), they would correspond to incorrect combinations of the individual equilibrium expressions or to mis-manipulated reactions. For example:
- If we had chosen K1 alone, that would only describe the first step and not account for the second reaction. 
- If we had chosen K2 alone, that would describe only the second step. 
- If we had used 1/K1 or 1/K2, that would correspond to using the reverse of one of the reactions, which is not what the given combination yields in this case.

Step 4: Conceptual check. When you add equilibria, the overall equilibrium constant is the product of the individual constants for the reactions that sum to the overall process, provided the species cancel appropriately and the stoichiometries line up to give the target reaction. Here that condition is satisfied, so the product K1 × K2 is the correct overall constant.

If the equilibrium constants for the two reactions 2 HCl(g) H2(g) + Cl2(g) and I2(g) + Cl2(g) 2 ICl(g) are denoted K1 and K2 respectively, then the equilibrium constant for the reaction 2 HCl(g) + I2(g) 2 ICl(g) + H2(g) equals

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