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The problem in your image relates to calculating the overall equilibrium constant \( K \) for the combined reactions given their individual equilibrium constants \( K_1 \) and \( K_2 \).

The reactions provided are:

1. \( 2C(s) + O_2(g) \rightleftharpoons 2CO(g) \)  with equilibrium constant \( K_1 \),
2. \( \text{Fe}_2O_3(s) + 3CO(g) \rightleftharpoons 2Fe(s) + 3CO_2(g) \)  with equilibrium constant \( K_2 \).

The net reaction is:

\[ 2 \text{Fe}_2O_3(s) + 6C(s) + 3O_2(g) \rightleftharpoons 4Fe(s) + 6CO_2(g) \]

To find the overall equilibrium constant \( K \), we need to combine the constants \( K_1 \) and \( K_2 \). Since the second reaction involves 3 moles of CO, we will need to cube the equilibrium constant \( K_1 \) to account for that.

Here’s how the combination works:

- The first reaction is doubled (because we need 6 moles of CO), so the new equilibrium constant becomes \( K_1^3 \) (since the equilibrium constant is raised to the power of the stoichiometric coefficient).
- The second reaction remains unchanged, with equilibrium constant \( K_2 \).

Now, we multiply the equilibrium constants to get the overall equilibrium constant:

\[
K = K_1^3 \times K_2
\]

So, the final expression for \( K \) is:

\[
K = K_1^3 \times K_2
\]

Would you like more details on how this combination works or have any further questions?

Here are 5 related questions to further expand your understanding:
1. What is the physical significance of equilibrium constants in chemical reactions?
2. How do changes in reaction conditions affect the equilibrium constant?
3. Why is it necessary to cube \( K_1 \) in this reaction, and what does it represent?
4. Can equilibrium constants be used to predict the direction of a reaction?
5. How are equilibrium constants related to Gibbs free energy in a reaction?

**Tip:** Remember, when combining equilibrium constants from sequential reactions, the overall constant is the product of the individual constants, adjusting for any changes in the stoichiometry.

Write an equation that gives the overall equilibrium constant K in terms of the equilibrium constants K1 and K2 for the given reactions in the image.

Learn how to calculate the overall equilibrium constant K for a series of chemical reactions using individual constants K1 and K2. This solution covers the key concepts of equilibrium constants, stoichiometry, and the law of mass action. Suitable for high school chemistry students in Grades 11-12.

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