Relation Between Kp And Kc - A Complete Guide

Edited By Team Careers360 | Updated on Nov 12, 2024 09:42 PM IST

kp and kc are equilibrium constants in ideal gas mixture. K_P is the equilibrium constant taken with respect to atmospheric pressure and k_c is the equilibrium constant used to express the concentration of gaseous mixture in terms of molarity.

Let us consider an equilibrium state in a gaseous mixture of reactants A , B and products C ,D .

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The equation of the reaction be ,

aA + bB⇌cC+dD

In the above equation a, b, c and d are the mole numbers for A, B, C, and D respectively.

Therefore, the k_c can be written as

$k_c=\frac{[c]^d[D]^d}{[A]^a[B^b]}$

So, the k_p can be written as

$kp=\frac{[p_c]^c[p_o]^d}{[p_A]^a [p_B]^b}$

Here , p_A,p_B,p_C and p_D are the partial pressure of the gas A,B,C and D respectively.

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Example 1 :

2A+3B⇌4C+5D

$k_c=\frac{[C]^4[D]^5}{[A]^2[B]^3}$

Example 2 :

2A+3B⇌4C+5D

$k_p=\frac{[P_c]^4[p_D]^5}{[P_A]^2[P_B]^3}$

Here , p_A,p_B,p_C and p_D are the partial pressure of the gas A,B,C and D respectively.

From the equation of ideal gas ;

pV=nRT

Where , p = pressure ; V = volume ; n = no of moles ; R = gas constant ; T = temperature.

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How to find kp?

Derive the relation between kpand kc/Write kp kc relation/write the relation between kp and kc

Therefore,
pV=nRT

Or, $p=\frac{n}{V}RT.....(1)$

From the above equation we can say;

p_A=[A]RT

p_B=[B]RT

p_C=[C]RT

p_D=[D]RT

So, the

$k_p=\frac{[p_c]^c[p_D]^d}{[p_A]^a[p_B]^b}.......(2)$

$k_c=\frac{[c]^c[D]^d}{[A]^a[B]^b}.......(3)$

Substituting the values of, p_A,p_B,p_C and p_D in the equation (2)

$k_p=\frac{[c]^c [RT]^c[D]^d [RT]^d}{ [A]^a [RT]^a[B]^b[RT]^b}$

$k_p=\frac{[c]^c [D]^d[RT]^{(c+d)}} { [A]^a [B]^b[RT]^{(a+b)}}$

$k_p=\frac{[c]^c [D]^d[RT]^{(c+d){(a+b)})}} { [A]^a [B]^b$

$k_p=\frac{[c]^c[D]^d}{[A]^a[B]^b}[RT]^{\Delta n}.........(4)$

Here, (c+d) is the sum of the mole number of the products and (a+b) is the sum of the mole number of the reactants.

So, ∆n is the difference between the sum of the mole number of the products and the sum of the mole number of the reactants.

∆n=(c+d)-(a+b)

Substituting the value of equation (3) in equation (4):

Then the the relation between k_pand k_c is,

k_p=k_c[RT]^∆n

The above equation is the relation between k_p and k_c.

Special case, ∆n=0 then k_p=k_c ; it happens when there is no change in the mole numbers between the sum of the mole number of the products and the sum of the mole number of the reactants.

If , k_p=k_c[RT]^∆n then k_c=k_p[RT]^-∆n is the relation between k_c and k_p.

These are included in the relation between kp and kc pdf/relation between kp and kc class 11th chemistry.

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NCERT Physics Notes: