For the reaction:

aA(

g) + bB(g) + ...cC(g) + dD(g) + ...

The equilibrium constant based on partial pressures is

From the ideal gas law:

P

_{Ae}V = n_{A}RTn

_{A}is the number of moles of AR is the ideal gas constant = 0.0821 L•atm/mol•K

T the absolute temperature in K

P is the pressure in atm

V the system volume in L

Similar expressions can be written for each gas phase component.

Rearranging gives

but n_{A}/V is just the molar concentration = [A]_{e}

Substituting into the expression for K_{p} (for each gas phase component) gives

Collecting terms gives

The left part of the fraction is K_{c}, so

K

_{p}= K_{c}× (RT)^{(c+d+...)–(a+b+...)}

The exponent in RT is the sum of the stoichiometric coefficients for the reactants subtracted from the sum of the stoichiometric coefficients for the products, defined as n.

K

_{p}= K_{c}× (RT)^{n}

Because the derivation goes through the ideal gas law, the proper units for R in this case are L•atm/mol•K (i.e., R = 0.0821 L•atm/mol•K).