Math Problem Statement

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).

Solution

The problem on the screen shows two reactions used to manufacture hydrogen, and it asks for the overall equilibrium constant KK in terms of the equilibrium constants K1K_1 and K2K_2 of the individual reactions.

Here are the reactions:

  1. CH4(g)+H2O(g)CO(g)+3H2(g)\text{CH}_4(g) + \text{H}_2\text{O}(g) \rightleftharpoons \text{CO}(g) + 3\text{H}_2(g) with equilibrium constant K1K_1
  2. CO(g)+H2O(g)CO2(g)+H2(g)\text{CO}(g) + \text{H}_2\text{O}(g) \rightleftharpoons \text{CO}_2(g) + \text{H}_2(g) with equilibrium constant K2K_2

The overall reaction is: CH4(g)+2H2O(g)CO2(g)+4H2(g)\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 KK, 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 KK is the product of K1K_1 and K2K_2: K=K1×K2K = 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).

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Math Problem Analysis

Mathematical Concepts

Chemical Equilibrium
Equilibrium Constants
Reaction Sequences

Formulas

K = K1 * K2
K = [Products]/[Reactants]

Theorems

Law of Mass Action
Equilibrium Constant Multiplication

Suitable Grade Level

High School (Grades 10-12), College Introductory Chemistry