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Given the following equilibrium equations and their corresponding equilibrium constants:2 CO2 (g) + H2O (g) 2 O2 (g) + CH2CO (g) Kc = 6.1 x 10 8CH4 (g) + 2 O2 (g) CO2 (g) + 2 H2O (g) Kc = 1.2 x 1014Find Kc for the reaction: CH4 (g) + CO2 (g) CH2CO (g) + H2O (g)

Question

Given the following equilibrium equations and their corresponding equilibrium constants:2 CO2 (g) + H2O (g) 2 O2 (g) + CH2CO (g) Kc = 6.1 x 10 8CH4 (g) + 2 O2 (g) CO2 (g) + 2 H2O (g) Kc = 1.2 x 1014Find Kc for the reaction: CH4 (g) + CO2 (g) CH2CO (g) + H2O (g)

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Solution

To find the equilibrium constant (Kc) for the given reaction, we need to manipulate the given equations to match the target reaction and then multiply their equilibrium constants.

Given equations:

  1. 2 CO2 (g) + H2O (g) = 2 O2 (g) + CH2CO (g) Kc1 = 6.1 x 10^8

  2. CH4 (g) + 2 O2 (g) = CO2 (g) + 2 H2O (g) Kc2 = 1.2 x 10^14

Target equation:

CH4 (g) + CO2 (g) = CH2CO (g) + H2O (g)

Step 1: Reverse equation 1 and divide by 2:

CO2 (g) + 0.5 H2O (g) = O2 (g) + 0.5 CH2CO (g) Kc1' = 1/(6.1 x 10^8)^0.5 = 1.28 x 10^-4

Step 2: Divide equation 2 by 2:

0.5 CH4 (g) + O2 (g) = 0.5 CO2 (g) + H2O (g) Kc2' = (1.2 x 10^14)^0.5 = 3.46 x 10^7

Step 3: Add the modified equations 1 and 2:

CO2 (g) + 0.5 H2O (g) + 0.5 CH4 (g) + O2 (g) = O2 (g) + 0.5 CH2CO (g) + 0.5 CO2 (g) + H2O (g)

This simplifies to the target equation:

CH4 (g) + CO2 (g) = CH2CO (g) + H2O (g)

Step 4: Multiply the modified equilibrium constants:

Kc = Kc1' * Kc2' = 1.28 x 10^-4 * 3.46 x 10^7 = 4.43 x 10^3

So, the equilibrium constant for the target reaction is Kc = 4.43 x 10^3.

This problem has been solved

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