the equilibrium-constant expression for a reaction is

kc= [N2][H2O]2
----------
[NO]2[H2]
what is the equilibrium-constant expression when the equation for this reaction is halved and then reversed?

2NO + 2H2 --> N2 + 2H2O
NO + H2 ---> N + H2O
N + H2O --> NO + H
[NO][H]
------
[N][H2O]

Of course you realize you can't control the spacing on the board; therefore, you must time everything as a line format.

When taking 1/2 the equation, Kc becomes the sqrt Kc. When reversing, Kc becomes 1/Kc.

sorry new to typing in math or chem problems so i don't really understand the first part of your answer. but is [NO][H]over[N][H2O] right or did i mess up somewhere

If this is the equation,

2NO + 2H2 --> N2 + 2H2O

and H2O is a gas, then the Kc expression is
(N2)(H2O)^2/(NO)^2(H2)^2. I think you had (H2) and not (H2)^2

If we take half the equation, we don't split the way we write molecules. It would look this way.
1/2 NO + H2 ==>1/2 N2 + H2O

Then Kc = (N2)^1/2*(H2O)/(NO)^1/2*(H2) and the new Kc is sqrt the old Kc.

To find the equilibrium-constant expression for a reaction that has been halved and then reversed, we need to use a combination of the stoichiometry and the concept of equilibrium. Here are the steps to find the new equilibrium-constant expression:

Step 1: Halve the equation:

2NO + 2H2 --> N2 + 2H2O

The halved equation becomes:

NO + H2 ---> N + H2O

Step 2: Reverse the halved equation:

N + H2O --> NO + H

Step 3: Write the equilibrium-constant expression for the reversed equation:

[NO][H]
------
[N][H2O]

So, the equilibrium-constant expression for the reaction that has been halved and then reversed is:

[NO][H]
------
[N][H2O]