Consider the following reaction and calculate the equilibrium partial pressure of BrCl.:
Kp=1.11×10−4 at 150 K.
A reaction mixture initially contains a Br2 partial pressure of 780 torr and a Cl2 partial pressure of 730 torr at 150 K.
The equilibrium constant expression for this reaction is:
`K_p = (P_(BrCl))/((P_(Br_2))(P_(Cl_2))`
Initial partial pressures are:
BrCl = 0
Br2 = 780 torr
Cl2 = 730 torr
Equilibrium partial pressures, assuming the reactants each decreased by an amount x, are:
BrCl = 2x
Br2 = 780 torr -x
Cl2 = 730 torr -x
Kp = (2x)^2/(780-x)(730-x) = 1.110x10^(-4)
We will make the assumption that x is small enough to neglect subtracting it from the equilibrium pressures of the two reactants, leaving the equation:
(2x)^2 /(780)(730) = 1.110x10^-4
x = 3.97
The equilibrium partial pressure of BrCl is 2x, which is 2x3.97 = 7.94 torr
This value meets the 5% rule for neglecting x in an earlier step because it's less than 5% of 730 and 780. If it was more than 5% then it would be necessary to include the term (-x) and solve using the quadratic formula.