Analysis of a reaction mixture showed that it had the composition 0.43 mol/L N2, 0.541 mol/L H2, and 0.124 mol/L NH3 at 800 K, at which temperature Kc=0.278 for N2(g) + 3H2(g)<->2NH3(g).

Calculate the reaction quotient Qc

What's the problem Gabriella? You just act like the numbers quoted are equilibrium numbers (they aren't, of course) and what comes out is not the Kc but Qc

I got an answer of 0.226, now I need to know what the spontaneous direction of change is. It went from 0.278 to 0.226.

If Q<K then the reaction will flow from reactants to products. If Q>K then the reaction will flow from the products to the reactants. In this case K=.278 and your Q=.226 so Q<K. The reaction will flow from reactants to products.

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To calculate the reaction quotient (Qc), you need to use the provided composition of the reaction mixture and compare it to the equilibrium constant (Kc) expression for the given reaction.

The Kc expression for the reaction is as follows:
Kc = [NH3]^2 / ([N2] * [H2]^3)

Given that the composition of the reaction mixture is:
[N2] = 0.43 mol/L
[H2] = 0.541 mol/L
[NH3] = 0.124 mol/L

Substitute the values into the Kc expression:
Qc = [NH3]^2 / ([N2] * [H2]^3)
= (0.124 mol/L)^2 / (0.43 mol/L * (0.541 mol/L)^3)

Simplify and calculate the value:
Qc = 0.015344 mol^2 / (0.43 * 0.541^3 mol^5/L^4)
= 0.499 mol^2/L^4

Therefore, the reaction quotient Qc for the given reaction mixture is 0.499 mol^2/L^4.