Relationship between free energy change and reaction quotient.

Although you are not likely to be faced with a quantitative problem on the MCAT using these equations, there are no more important equations from physical science to understand for the exam. Imagine a standard free energy change, ΔG0 and see if you can predict the effect on equilibrium constant. Imagine different reaction quotients and see if you can predict the effect on the actual free energy change, ΔG, for different relative concentrations of product versus reagent. Learn to explain these formulas in plain English. This is a key step to understanding chemistry.

Let's discuss the meaning of free energy change, the equilibrium state, and develop our sense of Le Chatelier's principle. We are returning to these ideas again and again because if we can help you get an intuitive sense for this material it will be incredibly important for understanding things like bioenergetics later. Okay. Let's picture the simple case of gaseous reactants and products. Chemical equilibrium describes one of many possible states of our system. One possible state, which is not equilibrium, is for the system to be all Reagents A or the system to be all Products B. Equilibrium is somewhere in between, the system with some A and some B, favoring one or the other.

What is the equilibrium state? The equilibrium state is the combination of products and reagents that maximizes the multiplicity of states accessible (maximum system entropy) and heat loss (entropy in the universe). Another way to say exactly the same thing is that at the equilibrium state, heat flows are reversible. At equilibrium, whether heat flows from the system to the surroundings or surroundings to the system, each direction is equally likely. Free energy is a state function of the system that allows us to pin down equilibrium in terms of the system and the temperature of the surroundings. At equilibrium, the free energy change is zero. If a bit of A turns into B and heat flows one way, it is just as likely for a bit of B to turn into A and heat to flow the other way.

The composition of the system at equilibrium can be described with the equilibrium constant. We can predict the equilibrium constant from the Standard Free Energy Change, ΔG0. The Standard Free Energy Change is simply the free energy difference of equal concentrations of A and B. If you started out the system with an equal concentration of A and B, which way would it go? That's what the standard free energy change tells you. If the Standard Free Energy Change is negative, we know the reaction will spontaneously go forward in the direction of Products B. To say that Reagents A have more free energy than Products B is to say that, in a system of equal concentrations, when a bit of A turns into B, the entropy of the universe increases. Students get confused when they read this because the free energy equation, ΔG = ΔH - TΔS, only has entropy in one of the terms. However, if you divide both sides by -T (minus T), you can change the formula into something that actually makes sense: -ΔG/T = -ΔH/T + ΔS. This is the way we should all be learning this equation because it shows you the meaning of the free energy. This equation says that the entropy change of the universe, -ΔG/T, equals the entropy change to the surroundings due to heat flow, -ΔH/T, plus the entropy change to the system, ΔS. In other words, the free energy gives us a function of the system that predicts the effect of a reaction on the entropy of the universe. If a free energy change is negative, then that means when a bit of A turns into a bit of B, the entropy of the universe is increasing, i.e. the change is spontaneous.

But how do you describe the free energy change for all of the other possible states? The free energy of any state of the system can be expressed as a function of the reaction quotient, Q, basically the ratio of the concentration of products to reagents. If Q is 1, the free energy change equals the Standard Free Energy Change, ΔG0 (that's when the concentrations of A and B are equal). The free energy change is zero when Q equals k, the equilibrium constant.

If an equilibrium system is disturbed, the equilibrium between reactants and products will shift to restore equilibrium, as predicted by Le Chatelier's Principle. This happens because the disturbance has changed the relative free energy of products and reagents. Under the new conditions, the concentrations that before were described as a k, are now just another Q, and so spontaneous changes occur to get the system to the new k under the new conditions.

For gaseous reactants and products, changes in pressure will shift to favor the side with the lower total sum of stoichiometric coefficients because this side has the lower volume. At the higher pressure, the higher volume side has greater enthalpy. It has more heat to release because the stakes of pressure-volume work have increased now that the pressure is higher. Another common Le Chatelier's change is shifting to higher temperature, which tends push the reaction in the endothermic direction. At the higher temperature, the entropy changes due to heat flow become less significant in the balance, so the relative free energy of the higher enthalpy side goes down. Remember: Increasing pressure favors the lower volume side. Increasing temperature favors the endothermic direction.

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