Problems regarding Kc,Kp and rate of reaction
Well, there are two cases:


$a + b = c + d$; and
$a + b \neq c + d$


For case 2, it's fairly simple to tell how the equation was balanced because your $K_C$ will come in a different unit, but for case 1, because $K_C$ is dimensionless we depend on the convention that Chemical Reactions are balanced on the lowest whole number. So in the case of the example given, we would balance it as:

$$\ce{2H2 + O2 &lt;=&gt; H2O}$$

and $K_C$ would be defined on that basis.