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The problem on the screen shows two reactions used to manufacture hydrogen, and it asks for the overall equilibrium constant \( K \) in terms of the equilibrium constants \( K_1 \) and \( K_2 \) of the individual reactions.

Here are the reactions:

1. \( \text{CH}_4(g) + \text{H}_2\text{O}(g) \rightleftharpoons \text{CO}(g) + 3\text{H}_2(g) \) with equilibrium constant \( K_1 \)
2. \( \text{CO}(g) + \text{H}_2\text{O}(g) \rightleftharpoons \text{CO}_2(g) + \text{H}_2(g) \) with equilibrium constant \( K_2 \)

The overall reaction is:
\[ \text{CH}_4(g) + 2\text{H}_2\text{O}(g) \rightleftharpoons \text{CO}_2(g) + 4\text{H}_2(g) \]

To determine the overall equilibrium constant \( K \), you need to combine the two individual reactions.

### Steps:
- The first reaction contributes to the formation of CO and hydrogen gas.
- The second reaction converts CO into CO2 and generates more hydrogen.

When combining equilibrium constants for sequential reactions:
- Multiply the equilibrium constants of the individual steps. So, the overall equilibrium constant \( K \) is the product of \( K_1 \) and \( K_2 \):
\[
K = K_1 \times K_2
\]

This gives the overall equilibrium constant for the net reaction.

Would you like further explanation or have any questions about the process?

Here are five related questions to expand understanding:
1. How are equilibrium constants related to the Gibbs free energy of a reaction?
2. What happens to the equilibrium constant if one of the reactions is reversed?
3. How do temperature changes affect the equilibrium constant?
4. How can Le Chatelier's principle be applied to these reactions?
5. Can catalysts alter the equilibrium constant for a reaction?

**Tip:** When combining equilibrium constants from multiple reactions, ensure the direction of each reaction is consistent (i.e., if reversed, take the reciprocal of the constant).

Write an equation that gives the overall equilibrium constant K in terms of the equilibrium constants K1 and K2 for the reactions: CH4(g) + H2O(g) ⇌ CO(g) + 3H2(g) and CO(g) + H2O(g) ⇌ CO2(g) + H2(g).

Learn how to calculate the overall equilibrium constant for a sequence of reactions. Using the reactions of methane with steam and carbon monoxide with water, we show how to express the overall equilibrium constant in terms of K1 and K2.

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