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)

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)

Example : Calculating Equilibrium Partial Pressure

A container at 800^{o}C 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?
K_{P} = 1.8 x 10^{-2} for the reaction NOCl_{(g)} NO_{(g)} + ½Cl_{2(g)}

Write the decomposition equation:

NOCl_{(g)} NO_{(g)} + ½Cl_{2(g)}

Write the expression for K_{P}

K_{P} =

P_{NO}P^{½}_{Cl2}

P_{NOCl}

Write expressions for the equilibrium partial pressure of each species:
P_{NOCl} = 0.657atm
P_{NO} = xatm
P_{Cl2} = ½xatm

Subsitute these values into the expression for K_{P}

1.8 x 10^{-2} =

x(½x)^{½}

0.657

Simplify the expression for K_{P} and solve for x

1.8 x 10^{-2} x 0.657= (½x^{3})^{½} 0.0118 = (½x^{3})^{½} (0.0118)^{2} = ½x^{3} 1.4 x 10^{-4} = ½x^{3} 1.4 x 10^{-4} x 2 = x^{3} 2.8 x 10^{-4} = x^{3} ^{3}√2.8 x 10^{-4} = x 0.065 = x = P_{NO}

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

P_{NOCl} = 0.657atm
P_{NO} = 0.065atm
P_{Cl2} = ½ x 0.065 = 0.0325atm

K_{P} =

P_{NO}P^{½}_{Cl2}

P_{NOCl}

K_{P} =

0.065(0.0325)^{½}

0.657

K_{P} = 1.8 x 10^{-2}

Example : Converting K_{c} to K_{P}

For the equilibrium:

2NOCl_{(g)} 2NO_{(g)} + Cl_{2(g)}

K_{c} = 3.75 x 10^{-6} at 796^{o}C.
Calculate K_{P} for this reaction at this temperature.

Write the expression to convert K_{c} to K_{p}:

K_{P} = K_{c}(RT)^{Δn}

Extract the relevant data from the question:

K_{P} = ?
K_{c} = 3.75 x 10^{-6} R = 0.0821 (Ideal Gas Constant)
T = 796^{o}C = 796 + 273 = 1069K
Δn = (2 + 1) - 2 = 1

Substitute the values into the equation:

K_{P} = K_{c}(RT)^{Δn} K_{P} = 3.75 x 10^{-6}(0.0821 x 1069)^{1} K_{P} = 3.29 x 10^{-4}