Kaplan MCAT General Chemistry Review

It is very important to remember that the rate of a reaction depends on the activation energy E_a, not the G. Spontaneous reactions may be fast or slow. Sometimes a reversible reaction may produce two products that differ both in their stability, as measured by the change in the Gibbs free energy associated with their production, and in their kinetics, as measured by their respective energies of activation. Sometimes the thermodynamically more stable product will have the slower kinetics due to higher activation energy. In this situation, we talk about kinetic versus thermodynamic reaction control. For a period of time after the reaction begins, the “dominant” product—that is, the major product—will be the one that is produced more quickly as a result of its lower energy of activation. The reaction can be said to be under kinetic control at this time. Given enough time, however, and assuming a reversible process, the dominant product will be the thermodynamically more stable product as a result of its lower free energy value. The reaction can then be said to be under thermodynamic control. Eventually, the reaction will reach its equilibrium, as defined by its K_eq expression.

A quick illustration may help to make this distinction clearer. Cats are famous for their ability to find the warmest spot in a house to take a nap. (Frankly, we find the word nap a bit lacking in its descriptive power as a reference to the 16+ hours per day that the typical house cat sleeps!) Imagine a cat wandering through a house on a sunny but cold winter day. She scurries up the staircase from the basement to the first floor and discovers a luscious patch of sunlight and basks in the warmth. She knows that there’s something even better up the next flight of stairs on the second floor: a roaring fire in the big brick fireplace. But she’s so tired and the sunlight is warm enough for now. So she lies down and sleeps for a little while. Eventually, though, the thought of all that crackling heat is too much to resist. So, she gets up, stretches, scurries up the second flight of stairs (Oh—so much energy to get up these stairs! she complains.) and nestles down in front of the fireplace. Sighing the sigh of pure contentment, she resolves never to leave this spot.

Standard Gibbs Free Energy

By now, it shouldn’t surprise you to learn that the free energy change of reactions can be measured under standard state conditions to yield the standard free energy, G°_rxn. For standard free energy determinations, the concentrations of any solutions in the reaction are 1 M. The standard free energy of formation of a compound, G°_f , is the free energy change that occurs when 1 mole of a compound in its standard state is produced from its respective elements in their standard states under standard state conditions. The standard free energy of formation for any element in its most stable form under standard state conditions (and therefore already in its standard state) is, by definition, zero. The standard free energy of a reaction, G°_rxn, is the free energy change that occurs when that reaction is carried out under standard state conditions; that is, when the reactants in their standard states are converted to the products in their standard states, at standard conditions of temperature (298 K) and pressure (1 atm). For example, under standard state conditions, conversion of carbon in the form of diamond to carbon in the form of graphite is spontaneous (because graphite is the standard state for carbon). However, the reaction rate is so slow that the conversion is never actually observed. You can imagine the distress caused to brides around the world if suddenly all those very expensive diamonds turned into the form of carbon used in pencils.

G°_rxn = Σ(G°_f of products) - Σ(G°_f of reactants)

MCAT Expertise

To make things easy for Test Day: Note the similarity of this equation to Hess’s law. Almost any state function could be substituted for G here.

Free Energy, K_eqandQ

We can derive the standard free energy change for a reaction from the equilibrium constant K_eq for this reaction:

G°_rxn = -RT ln K_eq

where K_eq is the equilibrium constant, R is the gas constant, and T is the temperature in K. This is a very valuable equation to know and understand for the MCAT, as it allows you to make not only quantitative evaluations of the free energy change of a reaction that goes from standard state concentrations of reactants to equilibrium concentrations of reactants and products, but also qualitative assessment of the spontaneity of the reaction. The greater the value of K_eq is, the more positive the value of its natural log. The more positive the natural log, the more negative the standard free energy change. The more negative the standard free energy change, the more spontaneous the reaction.