Problems regarding Kc,Kp and rate of reaction In our chemistry textbook, the equilibrium constant $K_c$ is derived this way:

$$\ce{aA + bB &lt;=&gt; cC + dD}$$

in this reaction, rate of forward reaction is $k_\mathrm f= k_1[A]^a[B]^b$

rate of backward reaction is $k_\mathrm b = k_2[C]^c[D]^d$

in equilibrium, equalizing the two rates we get 
$$ K_c = \frac{k_1}{k_2}=\frac{[A]^a[B]^b}{[C]^c[D]^d}$$

Now, there is a problem... we know the $K_c$ depends on how we equalize the reaction... like we can write 
$$\ce{H2 + 0.5O2 -&gt; H2O}$$ or 
$$\ce{2H2 + O2 -&gt; 2H2O}$$, etc ways. But how the rate of reaction depends on the concentration? to what power?
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.