Kaplan MCAT General Chemistry Review

The law of mass action defines the position of equilibrium by stating that the ratio of the product of the concentrations of the products, each raised to their respective stoichiometric coefficients, to the product of the concentrations of the reactants, each raised to their respective stoichiometric coefficients, is constant. However, equilibrium is a state that is achieved only through time. Depending on the actual rates of the forward and reverse reactions, equilibrium might be achieved in minutes or years. What can we use as a kind of “timer” that tells us how far along in the process toward equilibrium the reaction has reached? We can take another measurement of concentrations called the reaction quotient, Q_c. At any point in time of a reaction, we can measure the concentrations of all the reactants and products and calculate the reaction quotient according to the following equation:

You should be struck by how similar this looks to the equation for K_eq. It’s the same form, but the information it provides is quite different. While the concentrations used for the law of mass action are equilibrium (constant) concentrations, when calculating a value of Q_c for a reaction, the concentrations of the reactants and products may not be constant. In fact, if Q_c changes over time because the concentrations of reaction species are changing, the reaction by definition is not at the equilibrium state. Thus, the utility of Q_c is not the value itself but rather the comparison that can be made of the calculated Q_c at any given moment in time of the reaction to the known K_eq for the reaction at a given temperature. For any reaction, if

• Q_c < K_eq, then the reaction has not yet reached equilibrium.

• Q_c > K_eq, then the reaction has exceeded equilibrium.

• Q_c = K_eq, then the reaction is in dynamic equilibrium.

Any reaction that has not yet reached the equilibrium state, as indicated by Q_c < K_eq , will continue spontaneously in the forward direction (that is, consuming reactants to form products) until the equilibrium ratio of reactants and products is reached. Any reaction in the equilibrium state will continue to react in the forward and reverse direction, but the reaction rates for the forward and reverse reactions will be equal and the concentrations of the reactants and products will be constant, such that Q_c = K_eq. Once a reaction is at equilibrium, any further “movement” either in the forward direction (resulting in an increase in products) or in the reverse direction (resulting in the re-formation of reactants) will be nonspontaneous. In Chapter 6, Thermochemistry, we’ll review methods of introducing changes in systems at equilibrium and discuss how those systems respond in terms of enthalpy, spontaneity, and entropy.

PROPERTIES OF THE LAW OF MASS ACTION

Remember the following characteristics of the law of mass action and the equilibrium constant expression:

• The concentrations of pure solids and pure liquids (the solvent, really) do not appear in the equilibrium constant expression, because for the purposes of the MCAT, their concentrations do not change in the course of the reaction. (Actually, the concentrations of any pure solids and/or pure liquids are included in the expression, but we assign them a value of 1 and “hide” the actual concentrations by incorporating them into the equilibrium constant.

• K_eq is characteristic of a particular reaction at a given temperature: The equilibrium constant is temperature dependent.

• Generally, the larger the value of K_eq, the farther to the right we’ll find the equilibrium and the more complete the reaction.

• If the equilibrium constant for a reaction written in one direction is K_eq, the equilibrium constant for the reaction written in reverse is 1/K_eq.

Le Châtelier’s Principle

We can think of few other examples of a scientist’s legacy being so tarnished by such rampant mispronunciation of her or his name. While we can all be thankful that the MCAT is not an oral examination with penalties for mispronunciation, let’s just clear it up once and for all: Henry Louis’s surname is pronounced . The principle that bears his name, and for which he is most famous, states that a system to which a “stress” is applied tends to shift so as to relieve the applied stress. No matter what the particular form the stress takes (e.g., change in concentration of one component or another, change in pressure, or change in temperature), the effect of the stress is to cause the reaction to move temporarily out of its equilibrium state, either because the concentrations or partial pressures of the system are no longer in the equilibrium ratio or because the equilibrium ratio has actually changed as a result of a change in the temperature of the system. The reaction then responds by reacting in whichever direction (that is, either forward or reverse) that results in a re-establishment of the equilibrium state.