# What is the law of mass action? What determines the direction of a chemical reaction in a formula equation?

Oct 29, 2014

The law of mass action states that any reversible chemical reaction will reach a state of dynamic equilibrium when the ratio of concentrations of products to reactants is equal to a specific constant for that reaction called the equilibrium constant.

Example:

$2 N {O}_{2} \leftrightarrow {N}_{2} {O}_{4}$

The equilibrium constant for this reaction, when concentrations are expressed in mol/L, is ${K}_{c} = \frac{\left[{N}_{2} {O}_{4}\right]}{{\left[N {O}_{2}\right]}^{2}} = 4.7$

If the equilibrium concentration of $N {O}_{2}$ is $0.04 M$, then we know that the equilibrium concentration of ${N}_{2} {O}_{4}$ must be $4.7 \times {\left(0.04\right)}^{2} = 0.0075 M$

However, if we double the equilibrium concentration of $N {O}_{2}$ to $0.08 M$, then the equilibrium concentration of ${N}_{2} {O}_{4}$ becomes $4.7 \times {\left(0.08\right)}^{2} = 0.03 M$, or 4 times the original concentration.

The direction of spontaneous chemical reaction depends on whether the experimental ration of concentrations is greater than or less than the equilibrium constant. For any particular system (not at equilibrium, we can define the ratio of concentrations (products divided by reactants) to be Q. In the example above $Q = \frac{\left[{N}_{2} {O}_{4}\right]}{{\left[N {O}_{2}\right]}^{2}}$ and will not be equal to 4.7 if the system is not at equilibrium.

If $Q < K$, the reaction will proceed in the forward direction until $Q = K$ (equilibrium). If $Q > K$ the reaction will proceed in the reverse direction until $Q = K$ (equilibrium). Thermodynamics guarantees that the system will proceed spontaneously in a direction that leads to equilibrium, but does not say how fast the system will go to get there.