Relation between kp and kc - other detail
Here in this post, we will establish a relationship between kp and kc. And also derive it's formula. But before we go further let's know what is the meaning of kp and kc. What is its full form? From where this terms came? So let's start.
What is kp in chemistry?
Kp is a symbol by which a unit is represented in chemistry. Kp is an equilibrium constant of a partial pressure.
In chemistry, kp is used to represent the constant term of partial pressure.
What is kc in chemistry?
Kc is also a symbol by which a unit is represented in chemistry. Kc is an equilibrium constant in terms of concentration.
In chemistry, kc is used to represent the constant term of concentration.
Both kp and kc are a constant terms. These terms are used in a special type of a chemical equation.
The difference between kp and kc is only that kp is an equilibrium constant in terms of partial pressure but kc is an equilibrium constant in terms of concentration.
Relation between Kp and Kc in chemical equilibrium
The relation between kp and kc is the equilibrium constant in terms of partial pressure is always equal to the product of the equilibrium constant in terms of concentration (mole/litre), temperature and gas constant to the power n. that is given by,
Kp = Kc (RT)^Δn
Where n is the number of moles of gaseous product minus number of moles of gaseous reactant in balanced chemical equation. that is, n = (C + D) = (A + B).
Kp and Kc are the equilibrium constant expression involves the concentrations for Kp and partial pressure for Kp of the reactant and product.
The unit of K will depend upon the number of moles of reactsnt and products.
Unit of Equilibrium constant
- When total number of moles of product is equal to the total number of moles of reactant, K has no unit.
- When total number of moles of product is different than the total number of moles of reactant. in such a reaction k has unit. that is L/mol.
Derivation of the relation between kp and kc
Here is the derivation of the relation between kp and kc.
For the reaction,
a A + b B ⇌ c C + d D
Where, 'a' is a mole of reactant A,
'b' is a mole of reactant B,
'c' is a mole of reactant C,
'd' is a mole of reactant D.
the equilibrium constant for the reaction expressed in terms of the concentrations (mole/litre) may be expressed as:
Kc = [C]^c [D]^d/[A]^a [B]^b ------------ (1)
If the equilibrium involves gaseous species, then the concentrations may be expressed in terms of partial pressures of the gaseous substance. the equilibrium constant in terms of partial pressure is written by,
Kp = PC^c . PD^d / PA^a . PB^b ----------(2)
Where PA, PB, PC, and PD represent partial pressure of the substance A, B, C and D respectively. If gaseous are assumed to be ideal, then according to ideal gas equation,
pV = nRT
or,
p = n/v RT
where p is the pressure in Pa, n is the amount of the gas in mol, V is the volume in m3 and T is the temperature in Kelvin.
n/V = concentration, C
we can also write,
P = CRT or [gas] RT
Now,
Kp = ([C] RT )^c . ([D] RT)^d divided by ([A] RT)^a . ([B] RT)^b
= [C]^c [D]^d (RT) ^c+d divided by [A]^a [B]^b (RT)^ a+b
= [C]^c [D]^d / [A]^a [B]^b (RT)^(c+d) - (a+b)
= Kc (RT)^(c+d) - (a+b)
Kp = Kc (RT)^Δn
Some useful questions.
What is the formula of Kp?
the formula of Kp = PC^c . PD^d / PA^a . PB^b.
What is the formula of Kc?
the formula of Kc = [C]^c [D]^d/[A]^a [B]^b.
What is the difference between Kp and Kc?
Kp is equilibrium constant in terms of pressure but Kc is equilibrium constant in terms of concentration.