Chemistry 112

For the reaction:

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

The equilibrium constant based on partial pressures is

From the ideal gas law:

PAeV = nART

nA is the number of moles of A

R 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 nA/V is just the molar concentration = [A]e

Substituting into the expression for Kp (for each gas phase component) gives

Collecting terms gives

The left part of the fraction is Kc, so

Kp = Kc × (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.

Kp = Kc × (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).



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