 Kp=Equilibrium constant in terms of partial pressure.
 Kc=Equilibrium constant in terms of concentration.
 Kx=Equilibrium constant in terms of mole fraction.

Kn=Equilibrium constant in terms of number of moles.

Kp and Kc are related as K_{P} = K_{C} (RT)^{∆n }………………………(eq 1)
Relationship between K_{P} and K_{n}
………………………(eq 2)
From ideal gas equation,PV=nRT
=>P=n(RT/V)
Where, n is the number of moles
So, P_{A} =n_{A}(RT/v), P_{B} = n_{B}(RT/V), P_{C} =n_{C}(RT/V) and P_{D} =n_{D}(RT/V)
Replacing equation 2 by the above value we get that,
[n_{C}(RT/V)]^{c }. [n_{D}(RT/V)]^{d }
K_{p }= ————————————
[n_{A}(RT/V)]^{a }. [n_{B}(RT/V)]^{b }
n_{C}^{c }. n_{D}^{d }
= > K_{p} = ————– . ( RT/V ) ^{(c + d) – (a + b)}
n_{A}^{a}. n_{B}^{b}
= > K_{p} = K_{n} . (RT/V) ^{∆n}
= > K_{p} = K_{n} . (P_{T}/n_{T}) ^{∆n }
∆n=number of gaseous moles of product – number of gaseous moles of reactant
Relation between Kp and Kx
So, P_{A = }x_{A . }P_{T}
P_{B = }x_{B . }P
P_{C = }x_{C . }P_{T}
P_{D = }x_{D . }P_{T}
Putting the values in whole equation:
Putting the values in whole equation:
( x_{C . }P_{T })^{c} . ( x_{D . }P_{T} )^{d}
K_{P }= ———————————
( x_{A . }P_{T} )^{a} . ( x_{B . }P_{T} )^{b}
x_{C}^{c}_{ . }x_{D}^{d}
_{ }= ————– _{ }P_{T}^{(c+d) – (a+b)}
x_{A}^{a}_{ . }x_{B}^{b}
= > K_{P }= K_{x }(P_{T}) ^{∆n }
Q.Check your understanding.
N_{2}O_{4}(g)=2NO_{2}(g) ,Calculate K_{c }_{and} K_{x }for the given reaction for which Kp=0.157
Nyc
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But when they all will be equal
When number of moles in both product side and reactant side are equal,i.e. when ∆n=0, all the equilibrium constants become equal.
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I want to know relation between Kc an Kx .
Between Kp ,Kc, and Kx which has dimension ?
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All have a dimensions
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