 # KP and Kc Tutorial

## Key Concepts

• KP is an equilibrium constant calculated using the partial pressure of each gaseous reactant and product.
• Kc is an equilibrium constant calculated using the molarities (concentration in mol L-1 or M) of each gaseous reactant and product.
• For the gaseous reaction:

kA(g) + lB(g)mC(g) + nD(g)

 KP = PmCPnD PkAPlB
PA = partial pressure of gas A (usually in atmospheres)
PB = partial pressure of gas B (usually in atmospheres)
PC = partial pressure of gas C (usually in atmospheres)
PD = partial pressure of gas D (usually in atmospheres)

and

 Kc = [C]m[D]n [A]k[B]l
[A] = concentration of A in mol L-1
[B] = concentration of B in mol L-1
[C] = concentration of C in mol L-1
[D] = concentration of D in mol L-1

• The relationship between KP and Kc is

KP = Kc(RT)Δn

R = Ideal Gas Constant = 0.0821 (gas pressures in atm)
T = temperature in Kelvin
Δn = change in the number of moles of gas
= moles of products - moles of reactants
For the reaction above, Δn = (m + n) - (k + l)

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## Worked Example : Calculating Equilibrium Partial Pressure

Question: A container at 800°C was filled NOCl gas which decomposes to form NO gas and chlorine gas.
The equilibrium partial pressure of NOCl was 0.657 atm, what was the partial pressure of NO gas?
KP = 1.8 × 10-2 for the reaction NOCl(g) ⇋ NO(g) + ½Cl2(g)

Solution:
(Based on the StoPGoPS approach to problem solving in chemistry.)

1. What is the question asking you to do?

Calculate the partial pressure of NO gas.
P(NO(g)) = ? atm

2. What data (information) have you been given?

(a) NOCl(g) ⇋ NO(g) + ½Cl2(g)
(b) KP = 1.8 × 10-2
(c) P(NOCl(g)) = 0.657 atm

3. What is the relationship between what you know and what you need to find out?

Write the expression for KP

 KP = P(NO)P½(Cl2) P(NOCl)

Write expressions for the equilibrium partial pressure of each species based on the reaction stoichiometry (mole ratio):
P(NOCl) = 0.657 atm
P(NO) = x atm
P(Cl2) = ½x atm

4. Subsitute the values into the expression for KP and solve for P(NO):

 1.8 × 10-2 = x(½x)½ 0.657

Simplify the expression for KP and solve for x
1.8 × 10-2 × 0.657= (½x3)½
0.0118 = (½x3)½
(0.0118)2 = ½x3
1.4 × 10-4 = ½x3
1.4 × 10-4 × 2 = x3
2.8 × 10-4 = x3
3√2.8 × 10-4 = x
0.065 = x = PNO

PNOCl = 0.657 atm
PNO = 0.065 atm
PCl2 = ½ × 0.065 = 0.0325 atm

 KP = P(NO)P½(Cl2) P(NOCl) KP = 0.065(0.0325)½ 0.657

KP = 1.8 × 10-2 which is the same as the value we were given in the question so we are confident our answer is correct.

6. State your solution to the problem:

P(NO) = 0.065 atm

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## Worked Example : Converting Kc to KP

Question: For the equilibrium:

2NOCl(g) ⇋ 2NO(g) + Cl2(g)

Kc = 3.75 × 10-6 at 796°C.

Calculate KP for this reaction at this temperature.

Solution:
(Based on the StoPGoPS approach to problem solving in chemistry.)

1. What is the question asking you to do?

Calculate KP
KP = ?

2. What data (information) have you been given?

(a) 2NOCl(g) ⇋ 2NO(g) + Cl2(g)
(b) Kc = 3.75 × 10-6
(c) T = 796°C
Convert temperature in celsius to kelvin:
T = 796 + 273 = 1069 K

3. What is the relationship between what you know and what you need to find out?

Write the expression to convert Kc to Kp:
KP = Kc(RT)Δn

Use data sheet to find value for ideal gas constant, R,
R = 0.0821 (Ideal Gas Constant)

Use balanced chemical equation to calculate Δn :
Δn = (2 + 1) - 2 = 1

4. Substitute the values into the equation and solve for KP:

KP = Kc(RT)Δn
KP = 3.75 × 10-6(0.0821 × 1069)1
KP = 3.29 × 10-4

Use your calculated value of KP and the given value of Kc and temperature to find R.
KP = Kc(RT)Δn
KP/Kc = (RT)Δn
3.29 × 10-4/3.75 × 10-6 = (RT)1
87.73 = RT
87.73 = R(796 + 273)
87.73 = R × 1069
R = 87.73/1069 = 0.0821
Since this value of R is the same as that on the Data Sheet we are reasonably confident our answer is correct.

6. State your solution to the problem:

KP = 3.29 × 10-4

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