Help with a conceptual chemical equilibrium problem?

Question

K = 3.793

 

For the reaction 3A + C ? 2D

 

Calculate K for D ? (3/2)A + (1/2)C

 

Now, I believe the first thing is to invert K. Is that right? So would the first step be 1/3.793? What is the next step? The answer is apparently .5135, but I am not getting that. Even if I divide 3.793 in half then invert it is close to .5135 but not exact.

 

Please help if you can, I really need to get the actual concept! Thank you!  

 

Answer 1

Halving K is incorrect. You would need to take the square root of K and invert it. Suppose for a moment you don't invert it. If you write out the expressions for K for both situations, you will see why one is the square root of the other. Now let's do the calculation:

 

So that's 1/√3.793 = 0.5135