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  Relationship between Kp and Kc

Relationship between Kp and Kc:

Consider a common chemical equilibrium reaction, in which the reactants and products are in gaseous phases,
aA + bB + cC + ........ ↔ lL + mM + nN + .....
then,

186_kp & kc.jpg

Here,
p is the partial pressure of the respective gases. In terms of molar concentrations of reactants and products,
Kc = ([L]l[M]m[N]n…..)/([A]a[B]b[C]c…..)

For some gaseous component ‘i’ in a mixture, its partial pressure ‘pi’ is associated to its molar concentration ‘Ci’ as

Ci = pi/ RT since pi = (ni/V) RT

Here,
(ni/V) = Ci = number of moles of i per litre.
V = volume in litres.
Replacing, concentration in terms by partial pressures,

674_kp & kc 2.jpg

 

= Kp/(RT)Δng  and,
Kp = Kc (RT)Δng

Here,
Δng = total number of stoichiometric moles of gaseous products-total number of stoichiometric moles of gaseous reactants.

 

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