The equilibrium constant, Kc, is only used with equilibrium concentrations at a given temperature. To determine the concentrations at any point during the reaction, the reaction quotient, Q, also called the Law of Mass Action is used. Consider the following general reaction.
\(\displaystyle Q_c\;=\;\frac{[C]^c[D]^d}{[A]^a[B]^b}\;\;\;or\;\;\;\;\; Q_p\;=\;\frac{P_C^cP_D^d}{P_A^aP_B^b}\)
If you know Kc at a given temperature, you can compare the values of Qc and Kc to determine if the reaction has reached equilibrium or in which direction the reaction is progressing to reach equilibrium. When comparing Qc and Kc, there are three cases.
Case 2. If Qc is greater than Kc, the reaction will proceed from right to left until Qc = Kc.
Case 3. If Qc is equal to Kc, the system is at equilibrium, and Qc = Kc.
The following reaction has Kc = 2.1 at 200 oC.
Which way will the reaction proceed if initial concentrations are: [COF2] = 0.40 M, [CO2] = 1.8 M, and [CF4] = 3.8 M? First, calculate Qc.
\(\displaystyle Q_c\;=\;\frac{[CO_2][CF_4]}{[COF_2]^2}\;=\;\frac{(1.8\times 3.8)}{(0.40)^2}\;=\;43\)
Qc > Kc and the reaction will proceed to the left until equilibrium is reached.
Exercises
Exercise 1. Calculate Qc for the following reaction if 0.040 mol of N2, 0.160 mol NH3, and 0.100 mol of H2 are placed into a 500 mL reaction vessel. What is Qp under these same conditions?
Exercise 2. Consider the following reaction.
3 O2 (g) ⇄ 2 O3 (g) Kc = 1.7 x 10-56 at 297oC
If [O2] = 0.145 M and [O3] = 2.45 M at 297oC, in which direction will the reaction proceed to reach equilibrium?
Exercise 3. The following reaction has Kp = 2.4 x 108.
H2 (g) + Br2 (g) ⇄ 2 HBr (g)
The following partial pressures were observed at some time during the reaction.
PHBr = 0.012 atm PH2 = 0.125 atm PBr2 = 0.198 atm
In which direction will the reaction proceed to equilibrium?
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