Integrated SequencePhysics Chemistry Organic Biology

Web Resources

Chem1 Virtual Textbook - Free energy and equilibrium
Good tutorial on the thermodynamic basis of the equilibrium state.

Purdue University - Equilibrium Expressions
Good, clear comprehensive treatment covering the ins and outs of reaction quotients and equilibrium constants. Recommended.

Chem1 Virtual Textbook - Q and K: what's the difference?
Discussion of the crucial distinction between the reaction quotient, Q, and the equilibrium constant, K.

Chem1 Virtual Textbook - How to write equilibrium expessions
How to express reaction quotients and equilibrium constants for different types of reactions.

Chem1 Virtual Textbook - Measuring and calculating equilibrium constants
Problem solving techniques for equilibrium problems. Although the format of the MCAT is not conducive to quantitative problems with multiple steps, want to make sure you understand the problem-solving logic.



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Special points of emphasis

The Ideal Gas and Kinetic Theory

The First Law of Thermodynamics

Stoichiometry

Thermochemistry

Chemical Thermodynamics and the Equilibrium State

Picture the simple case of gaseous reactants and products. Let us discuss the meaning of free energy change, the equilibrium state, and develop our sense of Le Chatelier's principle.

Chemical equilibrium describes one of many possible states of the system. One possible state, which is almost never equilibrium, is for the system to be all Reagents A or the system to be all Products B. Equilibrium is usually somewhere in between, some combination of A and B, favoring one or the other.

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, the free energy of the products and reactants are equal. If a change at equilibrium releases heat to the surroundings, increasing entropy in the surroundings, it must be decreasing system entropy, and so it is just as likely for heat to flow in. Each direction is equally likely. The free energy change is zero. Heat is just as likely to flow one way as the other. If a bit of A turns into B, it is just as likely for a bit of B to turn into A.

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. 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? 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 temperature, you will make ΔH/T step forward, which is the entropy change due to heat flow. Whether or not ΔG is positive or negative is ultimately about entropy.

The free energy change describes whether a change decreases or increases 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 (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.

Increasing pressure favors the lower volume side. Increasing temperature favors the endothermic direction.




Work, Energy, and Power

Electricity

Intermolecular Forces

Thermochemistry

Chemical Thermodynamics and the Equilibrium State

Water

Solutions

The equilibrium state reached upon dissolving a weak electrolyte in water is described by a special kind of equilibrium constant, ksp, which is a function of the standard free energy change of reactants and products. The enthalpy change (heat flow), an important component of free energy change, very nearly equals the change in internal energy because system volume is very nearly constant (no pressure-volume work is involved). Furthermore, this internal energy change primarily depends on the change in the electrostatic potential energy at the molecular level between the system as solute and solvent as compared to final solution. Hess's Law gives us permission to conceptualize the internal energy change as the act of pulling solute and solvent particles apart, an internal energy increase, and letting them fall together into solution, a decrease in internal energy (this is not the true path, of course, but the overall internal energy change would be the same, having the same initial and final state).

In addition to the heat flow (internal energy change, electrostatic potential energy), that plays a roll in determining the difference between the undissolved and dissolved state is the difference in entropy. Despite the entropy of mixture, which might make you think that dissolving an electrolyte in water increases the entropy of the system, the solution process involving an electrolyte in water actually causes the entropy to decrease, because the water molecules become more ordered as they are constrained in the orderly geometry of hydration spheres. This occurs despite the entropy of mixture, which would dominate in the solution of an organic solute in an organic solvent, where there is very little constraint to molecular orientation. With a typical nonpolar solute in nonpolar solvent, the entropy definitely increases in the system over the course of the solution process, but when ions are dissolved in water, the system increases in its order.

Let us finish this discussion with the question. Why do salts dissolve at all? Almost all solution processes are endothermic (solubility increases with temperature, Le Chatelier's Principle). Furthermore, the solution of an electrolyte in an aqueous solution represents more order. Why then, when you place the salt in water, does it spontaneously dissolve, even if only sparingly? The answer is that our question is off base. When you have a salt ready to dissolve in pure water, you are not looking at a system with equal amounts of Reagents A and Products B. The answer is that your initial state is not the Standard State (quantifying the Standard State is a complicated problem for a nonhomogeneous process like this, i.e. having both solids and liquids). In the initial state of the solution process, you are starting with only Reagents A. Of course the direction the reaction takes toward equilibrium is toward the products, in other words, dissolving, even though a Standard State comparison of the solution process has positive free energy. The greater this positive free energy change, though, the less soluble the salt will be.




Work, Energy, and Power

Electricity

Intermolecular Forces

Thermochemistry

Chemical Thermodynamics and the Equilibrium State

Water

Acids and Bases

The difference between and strong and weak acid is a difference in the thermodynamics of protolysis. For example, trifluoroacetic acid is stronger than acetic acid, which, in turn, is stronger than ethanol. This series of weakening acidity tracks the decreasing capability of the conjugate base to stabilize the anion.

Likewise, hydrochloric acid is stronger than hydrofluoric acid. As with the example before, the difference comes down to the question of how the anion is able to minimize potential energy. The larger atomic radius of chlorine provides more 'room to spread out' for the negative charge, and so it can exist at lower energy.'These particular examples illustrate the rolls played by induction, resonance, and atomic radius in determining the internal energy change of a process and by extension (through enthalpy and free energy change) the position of equilibrium.

Don't forget though the internal energy change (and thus heat flow) is not the only factor, but that the entropy change can also be significant in acid-base activity. However, the entropy doesn't change much in cases where both the acid and base are charged, because no new hydration spheres are formed.




Work, Energy, and Power

Electricity

Periodic Properties

The Chemical Bond

Chemical Thermodynamics and the Equilibrium State

Oxidation-Reduction

Electrochemistry

Bioenergetics and Cellular Respiration

DC Current

The system of 'oxidation numbers' and 'reduction potentials', the oxidation-reduction system, is a shorthand method to account for the tendency of polar bonds to be stronger.

In the context of covalent bonding, the reduction potential of an element depends primarily on its electronegativity. The more electronegative an atom, the greater the internal energy decrease involved in bond formation as it pulls electrons towards itself. Electronegative elements love to gain electron control and form strong bonds.

A discussion of bond dissociation energies and standard chemical thermodynamics, like we are having here, is actually more conceptually transparent than the redox system, which is more convenient, though, from an accounting perspective, having oxidation numbers and the Nernst equation and useful stoichiometric congruence with electrical current in applied electrochemistry.

Somewhere along in the history of science education, though, these two systems of meaning seem to have detached from each other, and not too many students learn the underlying basis of the oxidation-reduction system. In biology, for example, there is constant reference to 'high energy electrons' when the understanding would benefit greatly from refering to these as 'electrons shared in weak bonds' that are on their way to strong bonds, such as the oxygen-hydrogen bonds of water at the end of oxidative metabolism.




Chemical Thermodynamics and the Equilibrium State

Bioenergetics and Cellular Respiration

Biological changes at the molecular level are governed by chemical thermodynamics. Coupling a reaction with the hydrolysis of ATP, for example, changing the equilibrium constant of the process by a factor of approximately 108. Coupling a thermodynamically unfavored process with one that is thermodynamically favored is a commonly encountered biochemical strategy.







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