# I am really confused about the relationship between Kp and Kc?? (1) Kp = Kc (2) Kp > Kc (3) Kp<Kc Please explain me very easy methods with basics. thanks a lot.

Dec 15, 2016

See below:

#### Explanation:

$\textsf{{K}_{p}}$ is the equilibrium constant expressed in partial pressures.

$\textsf{{K}_{c}}$ is the equilibrium constant expressed in concentrations.

For the general expression:

$\textsf{a A + b B r i g h t \le f t h a r p \infty n s c C + \mathrm{dD}}$

We get:

sf(K_p=(p_C^(c)xxp_D^(d))/(p_A^(a)xxp_B^(b)

and

$\textsf{{K}_{c} = \frac{{\left[C\right]}^{c} {\left[D\right]}^{d}}{{\left[A\right]}^{a} {\left[B\right]}^{b}}}$

The Ideal Gas expression gives us:

$\textsf{P V = n R T}$

$\therefore$$\textsf{P = \frac{n}{V} . R T}$

Since $\textsf{\frac{n}{V}}$ is the concentration we can say that:

$\textsf{P = \left[g a s\right] . R T}$

From this it can be shown that the relationship between $\textsf{{K}_{p}}$ and $\textsf{{K}_{c}}$ is given by:

$\textsf{{K}_{p} = {K}_{c} {\left(R T\right)}^{\Delta n}}$

Where $\textsf{\Delta n}$ is the number of moles of product molecules - the number of moles of reactant molecules as they appear in the equation.

I'll give 3 examples that show the possibilities that I think you are asking for:

(1)

$\textsf{{H}_{2} + {I}_{2} r i g h t \le f t h a r p \infty n s 2 H I}$

$\textsf{\Delta n = 2 - \left(1 + 1\right) = 0}$

$\therefore$$\textsf{{K}_{p} = {K}_{c} \cancel{{\left(R T\right)}^{0}} = {K}_{c}}$

Here you can see that $\textsf{{K}_{p}}$ and $\textsf{{K}_{c}}$ have the same numerical value and they are dimensionless quantities.

(2)

$\textsf{P C {l}_{5} r i g h t \le f t h a r p \infty n s P C {l}_{3} + C {l}_{2}}$

$\textsf{\Delta n = \left(1 + 1\right) - 1 = 1}$

$\therefore$$\textsf{{K}_{p} = {K}_{c} {\left(R T\right)}^{1} = {K}_{c} R T}$

(3)

$\textsf{2 S {O}_{2} + {O}_{2} r i g h t \le f t h a r p \infty n s 2 S {O}_{3}}$

$\textsf{\Delta n = 2 - \left(2 + 1\right) = - 1}$

$\therefore$$\textsf{{K}_{p} = {K}_{c} {\left(R T\right)}^{- 1} = {K}_{c} / \left(R T\right)}$

In (2) and (3) it is not valid to compare the relative magnitudes of $\textsf{{K}_{p}}$ and $\textsf{{K}_{c}}$ as the numbers now have different dimensions.

Its like saying 10 kg is bigger than 2 km.