The Mass Action Expression

For any particular chemical system and temperature, the same equilibrium state is reached regardless of how the reaction is run.  That means that the ratio of product concentration to reactant concentration will always reach the same constant number, no matter where the reaction is started.  For example, the N2O4 -NOexperiment illustrated on the previous page might have started with a 50% mixture of each of the gases instead of starting with pure N2O4 gas but the equilibrium ratio, K, would still end up being the same.  To quantify this ratio at non-equilibrium conditions, the same ratio is used but is given the name Q, the mass action expression.

                                                                                
 
 

At equilibrium,   Q = K.  K, the equilibrium constant is only used to describe equilibrium states.  Q can be used to evaluate the progress of a reaction towards equilibrium at any time whether or not the system is in equilibrium. During non-equilibrium conditions, the value of Q varies as the reaction proceeds. When the numerical value of Q remains constant the system has reached equilibrium.  The form of Q and K are both  based directly on the balanced equation for the reaction, so they change if the equation is reversed or multiplied by  some factor.  For example, the Q for the reverse reaction is simply 1 / Qforward rxn.  Pure liquids or solids do not appear in Q or K because their concentration remain constant (100%),  Q and K can be expressed in terms of partial pressures for gases.  The gas law equation is then used to convert between gas phase and the more general form for K:

                                                                                Kpressure = K(RT) delta n

where delta n is the sum of the coefficents of the gaseous products minus the sum of the coefficients of the gaseous reactants, R is the universal gas constant. , and T is temperature in K.

Experimental data collected for this system for four different runs is shown in the table below.  Only the equilibrium ratios are constant indicating that Q = K.
 
The equation for the N2O4 -NO2  system is: 

The equilbrium constant expression is:

The mass action expression is:


 
[Initial]         [Equilibrium]     RATIO 
[N2O4] [NO2] [N2O4] [NO2] [NO2]2/[N2O4]
0.10000 0.00000 0.0491 0.1018 0.211
0.00000 0.10000 0.0185 0.0627 0.212
0.05000 0.05000 0.0332 0.0837 0.211
0.07500 0.02500 0.0411 0.0930 0.210


N2O5(g) NO2(g) + O2(g)
Quick Quiz: What is the exponent for the mass action expression for the above reaction ?

2
1
8
4


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