chem question?

Question

if Kc for 1/2 N2(g)+1/2 O2 (g)--> NO (g) is 1.3 *10^4

calculate Kc for N2(g) + O2---2NO (g)

we were debating whether it is the same or if you square it and my teacher isnt sure

Answer 1

You would square it because:

Using aA+bB-->cC+dD

The equation for the equalibrium constant (Kc) is:
Kc=[C]^c[D]^d
--------------
[A]^a[B]^b

1) [NO]
----------------------- = 1.3*10^4
[N2]^1/2 [O2]^1/2
to solve this you would want to eliminate the 1/2 exponents. So you would square both sides of the equation. This would give you:

[NO]^2
----------------------- = (1.3*10^4)^2 = 1.69*10^8
[N2] [O2]

Notice that if you were to write the Kc for the second equation you would get:

[NO]^2
-----------------------
[N2] [O2]

So the Kc of the second equation is the Kc of the first equation squared.