Sections 14.12 - 14.13: The Reaction Quotient (Q)

 

Consider the general gas phase reaction:

 

j A (g) + k B (g) D l C (g) + m D (g)

 

   

 

For a given system at a particular temperature, the values of Kc and KP are fixed.  When the reactants and products for a given reaction are mixed, it is useful to know whether the reaction system is at equilibrium.  If the system is not at equilibrium, then it is useful to know the direction in which the reaction must proceed for the system to reach equilibrium.  The reaction will occur in the direction favoring either the reactants or the products.

 

To determine the direction in which a reaction proceeds, one needs to determine the reaction quotient, Q.  Q can be expressed as Qc or QP in the same way as we expressed K as Kc or KP.  For the general gas phase reaction:

 

  

 

Recall that [ ] 0 is defined as the initial concentration, and (P) 0 is defined as the initial partial pressure. 

 

By comparing the numerical value of Q (Qc or QP) with K (Kc or KP), it is possible to decide the direction in which the reaction will proceed in order to achieve equilibrium.

 

Case 1:  If Qc < Kc or QP < KP

 

If Q < K, there is more reactant and less product in the initial conditions than at equilibrium.  Thus, the reaction will favor the formation of products (i.e. proceed to the right) so that Q increases and eventually becomes equal to K.

 

Case 2:  If Qc > Kc or QP > KP

 

If Q > K, there is less reactant and more product in the initial conditions than at equilibrium.  Thus, the reaction will favor the formation of reactants (i.e. proceed to the left) so that Q decreases and eventually becomes equal to K.

 

Note: If Q = K, the reaction system is already at equilibrium under initial conditions and there is no change.

 

 

Example:   For the synthesis of ammonia at 300°C,

 

N2 (g) + 3 H2 (g) D 2 NH3 (g)               Kc = 5.2 x 10-2

 

Predict the direction in which the reaction will proceed to reach equilibrium when the initial concentrations of NH3, N2 and H2 are 0.001 M, 0.0001 M, and 0.002 M, respectively.

 

First, calculate Qc.

 

 

[NH3] 0 = 0.001 M

[N2] 0 = 0.0001 M

[H2] 0 = 0.002 M

 

 

Thus, Qc > Kc

 

Q is greater than K.  Hence, there is more product and less reactant in the initial conditions than at equilibrium.  Thus, the reaction will proceed to the reactant side (i.e. to the left).