Free Energy: The Reason Why a Reaction Occurs

 

System, surroundings and the universe

The law of conservation of energy says the total energy of the universe is constant. This statement should bother people. Everyone has seen a bonfire or match burning. It sure looks like energy is going up in smoke. Why do people believe the first law works?

The secret is that the universe can be divided into two regions. The universe can be viewed to be made up of some user defined "system" and everything else outside the "system" which is identified as the "surroundings".

Universe = system + surroundings

This view should make sense when you think of the law of conservation of energy. The sum of the energy changes for the universe must total zero. This says that when the system gives off energy the surroundings gain energy. The two changes are equal in size but opposite in sign.

When we look at a bonfire as a "system" we can see that the bonfire gives off energy and the "surroundings" gain energy. The two changes are mirror images of one another.

The system can be as small as one atom or as big as a galaxy. The only restriction is that the two pieces system and surroundings must add up to equal the universe. These ideas are avoided by the text, but they should help explain why energy releasing events can happen. Energy simply gets transferred back and forth between system and surroundings.

Spontaneous and Nonspontaneous Processes

A spontaneous process is a naturally occurring process that once started will continue to happen without outside intervention. The concept includes all kinds of processes both mechanical and chemical. A ball rolling downhill is an example of a spontaneous mechanical process. The evaporation of water is an example of a spontaneous physical change. A burning match is an example of a spontaneous chemical change.

A nonspontaneous process is an unnatural process that after it is started will NOT continue to happen without outside intervention. A nonspontaneous process only happens when outside action introduces energy to drive the process. The concept includes all kinds of processes both mechanical and chemical. A ball being rolled uphill is an example of a nonspontaneous mechanical process. Compressing a gas is an example of a nonspontaneous physical change. Production of carbohydrates by plants is an example of a nonspontaneous chemical change, photosynthesis needs light energy.

Entropy, S, is a measure of chaos. High values for entropy, S, match high amounts of disorder. A physical law called the third law of thermodynamics says the entropy of the universe is increasing. This means that the entropy of the universe increases for every change that occurs. This is not a conservation law. delta S universe = delta S system + delta S surroundings > 0 This is clearly a break from conservation laws. This idea is very difficult to accept. The fact is that whenever something (a system) is organized there is an activity happening somewhere else (the surroundings) that produces more disorder. The two processes combine to yield an increase in entropy. ** If you expend energy to stack a pile of newspapers the stack is more organized but all the CO2 and metabolism products you produced as you worked are scattered willy nilly about the universe. The disorder you generated exceeds the order you made. This is nature's version of "heads I win, tails you lose".

  

The usefullness of entropy measurements may be difficult to understand. If you see a process that has an increase in entropy it will usually be spontaneous. Evaporation of a liquid is spontaneous and the particles are more disordered in the vapor than in the liquid. Fallen leaves spontaneously get spread about the neighborhood. They do not spontaneously gather in a clump. The leaves may get caught against a fence but, wind forces acted to put them there and entropy increased somewhere else because of the blowing wind. Hmm! No jokes about this being a lot of hot air.

Free Energy

An American physicist and chemist, J. Willard Gibbs, is responsible for the recognizing the mathematics behind the concept of energy changes, entropy and free energy. Gibbs is not famous in the way Einstein is but, he is as important to our understanding of the laws governing energy changes as Issac Newton and other notable scientists.

Gibbs proposed and proved the following equation delta G = delta H - T delta S The term "delta G" is defined as the change in "free energy" . This is the energy that can be used for a specific purpose and is available from a process. It is measured in calories or kilocalories. The term "delta H" is defined as the change in "enthalpy" . This is the energy change that accompanies a process. Typically this is a heat transfer. Enthalpy is measured in calories or kilocalories. The term "Tdelta S" is the energy used to produce the entropy effects that accompany the process. When wood burns the solid is converted to water vapor (a gas) and carbon dioxide another gas. The expansion and escape of the gases uses some of the energy producced in the burning. The calories used to spread the gas molecuels around is "lost" and not useable. Entropy has weird units of calories/degree Kelvin. The "T" is the temperature in Kelvin degrees.

Predicting whether or not a process is spontaneous.

Spontaneous processes have a negative free energy change, DG is negative or less than zero.

The system releases energy to its surroundings as the process occurs. This kind of change is an exergonic process, delta G = -. The size of the free energy change indicates the "driving force" behind the reaction. The bigger and more negative the DG the more likely the process. A reaction with a DG = -623,400 kcal has a better chance of happening than a reaction with a DG = -500 kcal. The reactants change into products, release the stored energy and gradually the system reaches a stable condition of equlibrium.

Nonspontaneous processes have a positive free energy change, deltaG is positive or greater than zero.

The system must take in energy from the surroundings for the process to occur. This is an endergonic process, deltaG = +. The reactants are forced to change by energy put into the system. Outside forces "drive" the reaction. If the system is given no additional energy the process will stop.

What happens when the value for delta G is zero? A system or process at equilibrium has delta G equal to zero, delta G = 0. The free energy change, delta G is neither positive nor negative.

A process (system) at equilibrium has a zero free energy change, delta G = zero.

Predictions and free energy change delta G calculations

 

The Gibbs free energy equation, DG=DH - TDS , is used to calculate the free energy change for a reaction or process. The quantities in the formula can be measured or calculated from thermodynamic data tables. You need to have the values or tables to do the calculation. Don't worry about where the numbers come from. People have spent their entire lifetime making measurements and tabulating the data. When a new compound is made one of the first things physical chemists do is attrmpt to measure the enthalpy, entropy and free energy values for the substance. I did that kind of thing as an undergraduate and even when I was a graduate student. You should be able to substitute into the Gibbs formula.

Example: What is the free energy change for the conversion of diamonds into graphite? Will diamonds spontaneously convert to diamonds? C(s,diamond) ----> C(s,graphite) delta G= - 693 calories The DH for the reaction is exothermic and -453. calories/mole. The DS for the reaction at 298 Kelvin is 0.804 calorie/degree kelvin. Substituting into the definition for free energy delta G=-453. calories - (298 K)(0.804 calories/K) delta G=-453. calories -240 calories = -693 calories The free energy change is a small negative number. The conversion of diamonds to graphite is spontaneous. Graphite is more stable than diamonds. That makes sense because the is more graphite lying about the universe than ther are diamonds. the more stable form of carbon, graphite, is more common. Diamonds are valuable because they are hard to find. They are rare. diamonds are not forever contrary to the advertising campaigns.

Summary

1. Spontaneous processes have a negative free energy change. The process once started will proceed without outside intervention. delta G= negative

2. Nonspontaneous pocesses have a positive free energy change. The process will only proceed if aided from the outside. delta G= positive

3. The free energy change for a process is equal in size to the free energy for the reverse process. The signs are opposite.

C(s,diamond) ----> C(s,graphite) DG= - 693 calories

C(s,graphite) ----> C(s,diamond) DG= + 693 calories

4. The free energy change for a process says nothing about the speed of a process. A spontaneous process need not happen quickly. (Rusting of iron is spontaneous and occurs gradually.)

Exercise: The reaction betweeen mercury and oxygen to form mercuric oxide is written below. 2 Hg(l) + O2(g) ----> 2 HgO(s) The DH for the reaction is -43,000 calories/mole and clearly exothermic. What is the sign for the entropy change? Is the reaction spontaneous? Justify your answer. Answer