There are many situations in chemistry and biochemistry where we know the current state of a system and we want to know where things are going. Perhaps we are studying a enyzme-catalyzed metabolic reaction and we want to know which direction the reaction is heading. Perhaps we are studing a receptor/drug system and we want to know how many of the receptors will be occupied at a given drug concentration. Perhaps we are studying the distribution of a drug in the body and we want to know how much of the drug is in the brain at a given plasma concentration of the drug. All of these various problems can be thought of as a chemical equilibrium problem.
Let's begin by imagining a very simple reversible reaction of A turning into B.
aA ⇄ bB
Let's imagine that in the beginning, there is only A in the system at a concentration of [A]0 and B is at a concentration of 0. Over time, the A will be converted into B and B will be converted back to A until a balance or equilibrium is reached. If we start with only B in the system, the system would still approach the same equilibrium point over time. We can define a parameter called the equilibrium constant as follows.
$$K_{eq}=\frac{[B]_{eq}^b}{[A]_{eq}^a} $$
Here, [A]eq and [B]eq are the concentrations of A and B at equilibrium. For the more general case of multiple reactants, R, and multiple products, P, we can write a similar equation for the equilibrium constant.
$$K_{eq}=\frac{\prod\limits_i{[P]_{i,eq}^p}}{\prod\limits_i{[R]_{i,eq}^r}} $$
We can also define a related parameter, the mass action ratio, as follows.
$$Q(t)=\frac{\prod\limits_i{[P]_{i}^p}(t)}{\prod\limits_i{[R]_{i}^r}(t)} $$
Noe that the mass action ratio changes with time. The ratio of the mass action ratio to the equilibrium constant is called the disequilibrium ratio.
Updated on 230105