THC_Spontaneous Changes Lesson

Spontaneous Changes

Now that you have studied both enthalpy and entropy, we are ready to talk about factors that determine if a process is likely to occur spontaneously. Spontaneously means that the reaction occurs on its own. It does not imply anything about the time it takes to occur, however students often think that spontaneously means that it occurs immediately or very quickly. It does not! The rusting of a nail occurs spontaneously, although we would probably not call it fast! The term thermodynamically favored can be used instead of spontaneous for this reason.

So, what determines if a reaction is thermodynamically favored? If you think about it, you already know the answer. Think about the meaning of enthalpy. What does a positive ∆H mean? It means that that energy is required for the process. Another name for +∆H is endothermic . A negative ∆H means that energy is released (or exothermic ). It should make sense then that -∆H processes are thermodynamically favored.

-∆H favors spontaneous reactions

• Ice melting is an example of a spontaneous change, yet it is endothermic.  
• The ice absorbs heat energy from the surroundings in order to change phase from solid to liquid. 
• The evaporation of acetone in nail polish remover
• The chemical reactions that produce "cold packs" that are used for sports injuries
• Are all endothermic processes, and yet they occur spontaneously.

There must be another factor to consider! Entropy as plays a part in determining if a reaction is thermodynamically favored. Remember the 2^nd Law of Thermodynamics. Whenever a spontaneous event takes place in our universe, the total entropy of the universe increases. So, a reaction or process that increases entropy, +∆S, is thermodynamically favored.

Is this reaction likely to occur on its own?

• The freezing of water
• and the dissolution of sodium nitrate in water

-∆H and +∆S both indicate spontaneous changes. But what about processes that have +∆H and +∆S or -∆H and -∆S? How can we tell?

We need another quantity in order to determine the spontaneity in these situations!

Gibbs Free Energy

If a chemical or physical process is not driven by both entropy and enthalpy changes, then the Gibbs free energy change can be used to determine whether the process is thermodynamically favored. Gibbs free energy is calculated by comparing the quantities of entropy and enthalpy changes.  

In order for a process to occur spontaneously, at least one of these quantities must indicate that the process is thermodynamically favored. So, either ∆H must be negative or ∆S must be positive (or both). If the magnitude of a negative ∆H is large enough, the process can still be spontaneous even if ∆S is negative. If the magnitude of a positive ∆S is large enough, the process can still be spontaneous even if ∆H is positive. Also, recall that entropy was defined as the measure of energy dispersal of a system, as a function of temperature. So, temperature must be considered as well. This leads us to the equation for Gibbs free energy, ∆G.

If you plug in numbers for a process that is thermodynamically favored by both ∆H and ∆S, what do you get for ∆G?

∆G° = ∆H° - T∆S°

∆G° = (-) - (T)(+)

Don't forget here that T is measured in K, so it will always be a positive value.

∆G° = (-) - (+)(+)

∆G° = (-) - (+)

∆G° = (-)

This tells us that negative ∆G means spontaneous.

The following chart shows how different variations of enthalpy and entropy affect Gibbs free energy and spontaneity.

Now, let's see an example to calculate ΔG°. Remember that the ° symbol means standard conditions.

Remember Hess' Law? We can use it to calculate ΔG° for a given reaction. Look at this example to see how.

This problem can be solved another way as well. If you were not given those specific reactions to manipulate, you could use the standard free energy of formation, ∆G^o_f. ∆G^o _f of an element in its standard state is always zero. Notice that the equation looks just like the equations for ∆H^o_f and ∆S^o.

In summary, Gibbs free energy can be calculated three ways:

1. ΔG° = ΔH° - TΔS°
2. Using Hess's law
3. ΔG° = (sum of ΔG°_f products) - (sum of ΔG°_f of reactants)

It is important to mention that in some cases processes that are thermodynamically favored are not observed to occur. This is because of high activation energy. We will learn about activation energy in the module on kinetics.

Forcing Non-Spontaneous Processes to Occur

The application of external energy sources or the pairing of favorable with unfavorable reactions can be used to cause processes that are not thermodynamically favorable to become favorable.   For example, the recharging of a battery is not thermodynamically favorable, but can become so through the application of energy from an external source, in this case, an electrical current. Importantly, in biochemical systems, some reactions that oppose the thermodynamically favored direction are driven by coupled reactions. For example, many biochemical syntheses are coupled to the reaction in which ATP is converted to ADP + phosphate. Coupling means the process involves a series of reactions with common intermediates, such that the reactions add up to produce an overall reaction with a negative ∆G°.

Light may also be a source of energy for driving a process that in isolation is not thermodynamically favored. The overall conversion of carbon dioxide to glucose through photosynthesis is an example.  

$6CO_{2)(g)}+6H_2O_(l) \rightarrow C_6H_12O_{6(aq)} \Delta G^\circ=2880kJ/mol$

 Yet, we know that this reaction occurs naturally. It involves a multistep process that is initiated by the absorption of several photons in the range of 400-700 nm.

Remember to work on the module practice problems as you complete each section of content.

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