If confined at high temperature, ammonia and oxygen
quickly react and come to equilibrium with their products,
water vapor and nitrogen oxide. Write a balanced chemical
equation and an equilibrium expression for this system.

Question

If confined at high temperature, ammonia and oxygen
quickly react and come to equilibrium with their products,
water vapor and nitrogen oxide. Write a balanced chemical
equation and an equilibrium expression for this system.

accessdenied · Answer

So you know your reactants are ammonia and oxygen.  Your products are water vapor and nitrogen oxide.  You must determine their chemical formula first, then you have a skeletal equation:
     $ \rm Ammonia + Oxygen   \rightleftharpoons   Water \ vapor  + Nitrogen \ Oxide $
     $ \rm NH_3  +  O_2   \rightleftharpoons   H_2O + NO$      All gases
Now you can balance by modifying coefficients which requires a bit of work, or there exists a linear method as well if you didn't mind the Algebra but certain answers..

Then for your equilibrium expression, just use the definition with the newly derived formula
  $ \rm K_{c} = \dfrac{[C]^c [D]^d}{[A]^a [B]^b} $
Or you may use the partial pressures for gases, which has the same structure.

rock_mit182 · Answer

i see there are two way to solve this, great !, thanks you have been very helpfull like always in chemistry ! :)

accessdenied · Answer

Glad to help!  :)