K_P and K_c Chemistry Tutorial

Key Concepts

• K_P is an equilibrium constant calculated using the partial pressure of each gaseous reactant and product.
• K_c 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

  P_A = partial pressure of gas A (usually in atmospheres)
  P_B = partial pressure of gas B (usually in atmospheres)
  P_C = partial pressure of gas C (usually in atmospheres)
  P_D = 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 K_P and K_c is

  K_P = K_c(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?
K_P = 1.8 × 10^-2 for the reaction NOCl_(g) ⇋ NO_(g) + ½Cl_2(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) + ½Cl_2(g)
   (b) K_P = 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 K_P
   

   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 K_P and solve for P_(NO):

   1.8 × 10-2 =	x(½x)½
   	0.657

   Simplify the expression for K_P 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 = x^{3
   3}√2.8 × 10^-4 = x
   0.065 = x = P_NO

5. Is your answer plausible?

   Check your answer by substituting the values back into the equation:
   P_NOCl = 0.657 atm
   P_NO = 0.065 atm
   P_Cl2 = ½ × 0.065 = 0.0325 atm
   

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

   
   K_P = 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

Worked Example : Converting K_c to K_P

Question: For the equilibrium:

2NOCl_(g) ⇋ 2NO_(g) + Cl_2(g)

K_c = 3.75 × 10^-6 at 796°C.

Calculate K_P 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 K_P
   K_P = ?

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

   (a) 2NOCl_(g) ⇋ 2NO_(g) + Cl_2(g)
   (b) K_c = 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 K_c to K_p:
   K_P = K_c(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 K_P:

   K_P = K_c(RT)^Δn
   K_P = 3.75 × 10^-6(0.0821 × 1069)¹
   K_P = 3.29 × 10^-4

5. Is your answer plausible?

   Use your calculated value of K_P and the given value of K_c and temperature to find R.
   K_P = K_c(RT)^Δn
   K_P/K_c = (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:

   K_P = 3.29 × 10^-4