Carbon monoxide is converted to carbon dioxide via the following reaction: CO(g) + H2O(g) ⇌ CO2(g) + H2(g) In one experiment, 0.45 mol of CO and 0.30 mol of H2O were placed in a 1.00-L reaction vessel. When equilibrium was reached only 0.19 mol of CO remained. What is the equilibrium constant, at this temperature, for this reaction?

Question

Carbon monoxide is converted to carbon dioxide via the following reaction: CO(g) + H2O(g) ⇌  CO2(g) + H2(g) In one experiment, 0.45 mol of CO and 0.30 mol of H2O were placed in a 1.00-L reaction vessel. When equilibrium was reached only 0.19 mol of CO remained. What is the equilibrium constant, at this temperature, for this reaction?

BlackTom AI · Accepted Answer

Equilibrium expression: Kc = [CO2][H2] / ([CO][H2O]).

1) Relevant knowledge points and concepts
- For the balanced reaction CO(g) + H2O(g) ⇌ CO2(g) + H2(g), the equilibrium constant in concentration form (Kc) uses molar concentrations (mol·L^-1).
- Initial moles in a 1.00 L vessel equal initial concentrations in M (mol·L^-1).
- Use an ICE (Initial–Change–Equilibrium) approach to find equilibrium concentrations, then plug into Kc.

2) Step-by-step reasoning (ICE table)
Initial concentrations (M): [CO]0 = 0.45, [H2O]0 = 0.30, [CO2]0 = 0, [H2]0 = 0.
At equilibrium [CO] = 0.19 (given). Change in [CO] = 0.19 − 0.45 = −0.26, so x = 0.26 moles converted.
Stoichiometry: for every 1 mol CO consumed, 1 mol H2O consumed and 1 mol each CO2 and H2 produced.

3) Intermediate concentration calculations
- [CO]eq = 0.19 M (given)
- [H2O]eq = 0.30 − 0.26 = 0.04 M
- [CO2]eq = 0 + 0.26 = 0.26 M
- [H2]eq = 0 + 0.26 = 0.26 M

4) Compute Kc and explanation why this is correct
Kc = [CO2][H2] / ([CO][H2O]) = (0.26 × 0.26) / (0.19 × 0.04).
Numerator = 0.26 × 0.26 = 0.0676.
Denominator = 0.19 × 0.04 = 0.0076.
Kc = 0.0676 / 0.0076 = 8.894736842 ≈ 8.89.
This value correctly follows from measured equilibrium concentrations and the equilibrium expression.

5) Why the other options are incorrect
- 4.47 would be about half of the correct value (likely from an arithmetic or stoichiometry error).
- 0.55, 0.63, and 1.0 are far from the value obtained using the correct equilibrium concentrations; they result from using wrong changes (incorrect x), using initial instead of equilibrium values, or misplacing products/reactants in the K expression.

6) Conclusion
Using the ICE method and the given equilibrium data yields Kc ≈ 8.89, which matches the provided correct answer.

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