A. Spontaneity, Entropy, and Free Energy

Advanced Chemistry OutlineThermodynamic

A. Spontaneity, Entropy, and Free Energy

1. Spontaneous Processes and Entropy

a. Spontaneous reactions occur under the given conditions without external stimuli.

- spontaneous processes may be fast or slow

- thermodynamics tell us only if a reaction will occur, not how fast (kinetics tells us how fast)

- thermodynamics considers only the initial and final states, the pathway is relevant only to kinetics

- thermodynamics and kinetics are needed to fully describe a reaction

- examples - ice melting at T>0 ºC, NaCl dissolving in water, iron rusting

b. Entropy (S) - a measure of disorder

- a state function (independent of pathway)

- the driving force behind spontaneous reactions

- entropy is a thermodynamic function that describes the number of possible arrangements that are available to a system

- nature proceeds spontaneously towards the states that have the highest probability of existing (greatest positional probability)

- positional probability increases from solid to liquid to gas (i.e. gases have greatest entropy)

- a solution of a solid has more positional probability than the solid sitting in a beaker of water

- the more complex the molecule, the greater its entropy

- due to greater degrees of freedom or forms of motion

- vibrational motion or rotational motion (spinning of atoms on their axes)

2. Entropy and the Second Law of Thermodynamics

a. Second Law : In any spontaneous process there is always an increase in the entropy of the universe.

- the entropy change of the universe equals the sum of the changes of entropy in the system and the surroundings

ΔSuniv = ΔSsys + ΔSsurr

- if ΔSuniv is positive (increasing entropy) the process is spontaneous (and irreversible)

- if ΔSuniv is negative (decreasing entropy) the process is nonspontaneous

3. The Effect of Temperature on Spontaneity

a. both ΔSsys and ΔSsurr need to be considered

- if both ΔSsys and ΔSsurr are positive, then ΔSuniv is positive (spontaneous)

- if both ΔSsys and ΔSsurr are negative, then ΔSuniv is negative (nonspontaneous)

- in an exothermic process heat flows from the system to the surroundings and ΔSsurr increases(positive) and ΔSsys decreases (negative)

- in an endothermic process heat flows from the surroundings to the system and ΔSsys increases (positive) and ΔSsurr decreases (negative)

- in both of the above cases one entropy change favors an increase in ΔSuniv and one entropy change is unfavorable towards and increase in ΔSuniv.

- In these cases the temperature is the factor which determines if ΔSuniv is positive or not.

- Consider phase changes in water. Above 100 ºC, at 1 atm, the change from the liquid state to the gaseous state is spontaneous. Below 100 ºC at 1 atm, condensation is the spontaneous process.

- Entropy changes in the surroundings are primarily determined by heat flow.

- The magnitude of ΔSsurr is temperature dependent.

- The significance of exothermicity is temperature dependent.

- The impact of heat transfer to or from a system to the surroundings will be greater at lower temperatures.

To Summarize :

- The sign of ΔSsurr depends on the direction of heart transfer.

- The magnitude of ΔSsurr depends on the temperature.

- At constant temperature :

- where : T is Kelvin temperature

ΔH is the enthalpy of system (negative if exothermic)

- ΔSsys will be equal in magnitude and opposite in sign of ΔSsurr

4. Free Energy (G) - can be used to determine if a reaction is spontaneous or not at constant T and P

- if ΔG is negative, the reaction is spontaneous (at constant T and P)

- if ΔG is positive, the reaction is nonspontaneous (at constant T and P)

- if ΔG = 0, the reaction is at equilibrium

- Note : A negative enthalpy value and a positive entropy value favor a negative free energy value and a spontaneous reaction.

a. Also, at constant T and P :

5. Entropy Changes in Chemical Reactions

a. Fewer molecules in products indicates a decrease in entropy.

b. A change of state also indicates a change in entropy. The change in positional entropy is dominated by gaseous reactants or products.

c. Third Law of Thermodynamics : The entropy of a perfect crystal at 0 K is zero.

d. Calculation of entropy from standard entropy values :

- generally, the more complex the molecule, the higher the standard entropy (more rotational and

vibrational positions)

- the standard enthalpies of elements in their standard states are not zero (unlike standard

enthalpies and standard free energies)

6. Free Energy Change and Chemical Reactions

a. Standard free energy change (ΔGº) - the free energy change that occurs in a chemical reaction when

all reactants and products are in their standard states.

b. Calculation of standard free energy change :

- free energy is a state function

or :

or by adding ΔGº values from chemical reactions as in Hess's law for ΔH

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Advanced Chemistry OutlineThermodynamic

7. The Dependence of Free Energy on Pressure

a. The equilibrium position of a reaction system represents the lowest free energy value available.

- reason why some reactions will not go to completion

b. For an ideal gas :

- enthalpy is independent of pressure

- entropy is pressure-dependent (change in volume changes positional probabilities)

- where : R = universal gas constant (8.3145J/K∙mol)

T = Kelvin temperature

Q = reaction quotient

8. Free Energy and Equilibrium

a. The equilibrium point is at the lowest free energy value available to the system.

- therefore, Gprod = Greact, or ΔG = Gprod - Greact = 0
and

b. Relationship between ΔGº and K :

9. Free Energy and Work

a. The change in free energy, at constant temperature and pressure, is equal to the maximum possible

amount of useful work obtainable from that system.

-

- According to second law, this amount of work is not really available - some energy will be lost in any real pathway

- reversible processes are really hypothetical since energy is lost in the changes (it really takes more work to restore the original condition)

- all real processes are therefore irreversible

b. Summary of first two laws of thermodynamics from Henry Bent :

- First law : You can't win, you can only break even.

- Second Law : You can't break even.

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