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KP and Kc

Key Concepts

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

  • Kc is an equilibrium constant calculated using the molarities (concentration) of each 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)

  • 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)

Example : Calculating Equilibrium Partial Pressure

A container at 800oC was filled NOCl gas which decomposes to form NO gas and chlorine gas.
The equilibrium partial pressure of NOCl was 0.657atm, what was the partial pressure of NO gas?
KP = 1.8 x 10-2         for the reaction         NOCl(g) NO(g) + ½Cl2(g)
  1. Write the decomposition equation:
    NOCl(g) NO(g) + ½Cl2(g)

  2. Write the expression for KP
    KP = PNOP½Cl2

    PNOCl

  3. Write expressions for the equilibrium partial pressure of each species:
    PNOCl = 0.657atm
    PNO = xatm
    PCl2 = ½xatm

  4. Subsitute these values into the expression for KP
    1.8 x 10-2 = xx)½

    0.657

  5. Simplify the expression for KP and solve for x

    1.8 x 10-2 x 0.657= (½x3)½
    0.0118 = (½x3)½
    (0.0118)2 = ½x3
    1.4 x 10-4 = ½x3
    1.4 x 10-4 x 2 = x3
    2.8 x 10-4 = x3
    3√2.8 x 10-4 = x
    0.065 = x = PNO

  6. Check your answer by substituting the values back into the equation:

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

    KP = PNOP½Cl2

    PNOCl
    KP = 0.065(0.0325)½

    0.657
    KP = 1.8 x 10-2

Example : Converting Kc to KP

For the equilibrium:
2NOCl(g) 2NO(g) + Cl2(g)

Kc = 3.75 x 10-6 at 796oC.
Calculate KP for this reaction at this temperature.
  1. Write the expression to convert Kc to Kp:

    KP = Kc(RT)Δn

  2. Extract the relevant data from the question:

    KP = ?
    Kc = 3.75 x 10-6
    R = 0.0821 (Ideal Gas Constant)
    T = 796oC = 796 + 273 = 1069K
    Δn = (2 + 1) - 2 = 1

  3. Substitute the values into the equation:

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


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