23. Entropy and Gibbs Free Energy

Question 1

Define ‘entropy’.

Answer 1

A measure of the dispersal of energy (sys sur) at a specific temperature / the disorder/randomness of a system. Energetically, stability increases when disorder increases.

Question 2

What are the ‘surroundings’?

Answer 2

• Air around test tube
• Test tube itself
• Solvent
• Anything dipping into the test tube.

Question 3

What are spontaneous changes?

Answer 3

Changes that continue to occur naturally. They may be slow or in need of an input of energy to begin.

Question 4

How does diffusion occur?

Answer 4

Molecules move randomly in straight lines until they collide with like molecules, air molecules or container walls. They then switch direction. This is due to the laws of chance and probability. During a spontaneous process like diffusion, disorder increases and so does entropy.

Question 5

How many ways are there to arrange three molecules in two gas jars?

Answer 5

2 x 2 x 2. Each arrangement is equally likely (1/8), so the probability of a change in arrangement is higher than the probability of the arrangement remaining the same. More molecules = more arrangements.

Question 6

Define ‘standard molar entropy’.

Answer 6

The entropy of 1 mole of a substance in its STD state. Units: J/K/mol.
All values are positive.

Question 7

With what are standard molar entropy values compared?

Answer 7

A theoretically perfect crystal - 12g of a perfect diamond, cooled to the lowest temperature possible.

Question 8

State the third law of thermodynamics.

Answer 8

All perfect crystals have the same entropy at absolute zero.

Question 9

Name some generalisations about entropy values.

Answer 9

• Gases > liquids > solids (ex. CaCO3 and Hg)
• Complex substances > simple
• Softer substances > harder.

Question 10

How does temperature affect entropy?

Answer 10

As temperature increases, entropy increases. This is because particles vibrate/move more, so disorder increases.

Question 11

How does entropy change during melting?

Answer 11

Regularly arranged lattice of particles close together turns into an irregular arrangement of particles close together but sliding over each other. Disorder increases.

Question 12

How does entropy change during vaporisation?

Answer 12

Particles go from close together to far apart, able to move freely and rapidly. Disorder increases. More gas molecules = more ways of arranging.

Question 13

How does entropy change when an ionic solid dissolves?

Answer 13

The regular crystalline lattice breaks up, and the pure water becomes less ordered, as ions move between water molecules. Disorder increases.

Question 14

How does enthalpy affect the entropy of the surroundings?

Answer 14

EXO: Energy released to surroundings increases number of arrangements of energy (goes into rotating and translating the molecules), so entropy increase is likely.
ENDO: Energy absorbed from surroundings decreases number of arrangements.

Question 15

How do you calculate total entropy change?

Answer 15

Total = System + Surroundings

• Δ as S of R and P are different
• total increase in entropy means that the change is positive and the reaction is spontaneous.

Question 16

How do you calculate system entropy change?

Answer 16

System = Products - Reactants

• remember stoichiometry and states.

Question 17

How do you calculate surroundings entropy change?

Answer 17

Surroundings = -ΔHr/T

• enthalpy x1000, T in K
• large ΔH changes number of arrangements

Question 18

How does entropy work in equilibrium reactions?

Answer 18

Both reactants and products are present, so how can ΔS be positive both ways?

• As mixing proceeds, rate of increasing disorder decreases as more P formed.
• At EQM, the -> rate = the

Question 19

How is entropy change affected by temperature?

Answer 19

Above STD T, ΔS surroundings increases (assuming that ΔHr and S are not affected).
- The decomposition of ZnCO3 at 298K is not spontaneous, but it is at 550K.

A large increase in ΔS indicates completion, whereas a large decrease indicates that the reaction will not occur.

Question 20

Why are exothermic reactions feasible?

Answer 20

ΔS system is negative but the high ΔHr compensates for this as it causes -ΔHr/T to have a high positive value. Total ΔS will therefore be positive.

Question 21

Why are endothermic reactions not always spontaneous?

Answer 21

-ΔHr/T will be negative. If ΔS system is negative, total ΔS will be negative.
If ΔS system is highly positive, it could compensate for this and total ΔS will be positive.

Question 22

Define ‘standard molar Gibbs free energy of formation’.

Answer 22

Change in free energy when 1 mole of a compound is formed from its elements in their STD states. Units: kJ/mol

Question 23

What does Gibbs free energy indicate?

Answer 23

The likelihood of a reaction’s being spontaneous.

Question 24

Give two equations to find Gibbs free energy change.

Answer 24

ΔG = -TΔS total

ΔG = ΔHr - TΔS system

Question 25

How is the above equation derived from the entropy equation?

Answer 25

ΔS total = -ΔHr/T + ΔS system

• Multiply all terms by -T.
• Changes in entropy tend to be smaller than changes in enthalpy (J vs. kJ)
• When ΔG is 0, a state change may be occurring.

Question 26

How does Gibbs free energy predict spontaneity?

Answer 26

ΔS total must be positive, and T is always positive.
ΔG must be NEGATIVE.
When a spontaneous reaction occurs at constant temperature and pressure, G decreases.

Question 27

How does temperature change affect spontaneity in an exothermic reaction?

Answer 27

ASSUMPTION: ΔHr doesn’t change with T.

• ΔHr is negative.
• If ΔS sys is positive, the second term is negative.
• Spontaneous.
• If ΔS sys is negative, the second term is positive.
• Spontaneous at LOW TEMPERATURE.
• ΔHr is more likely to be higher negative than the second term is positive.

Question 28

How does temperature change affect spontaneity in an endothermic reaction?

Answer 28

• ΔHr is positive.
• If ΔS sys is negative, the second term is positive.
• Non-spontaneous.
• If ΔS sys is positive, the second term is negative.
• Spontaneous at HIGH TEMPERATURE.
• Second term is more likely to be higher negative than ΔHr is positive.

Question 29

Compare Gibbs free energy values of different states.

Answer 29

ΔGf of element is 0.

• Solid compounds have a high negative value.
• Gases and liquids can be positive or negative.
• State can affect ΔGf (eg. H2O (l) more negative than (g)).

Question 30

Define ‘standard Gibbs free energy change of reaction’.

Answer 30

Gibbs free energy change when the molar quantities of reactants shown in the stoichiometric equation react under STD conditions to form products in STD states.

Question 31

How would you construct a Hess cycle for ΔGr?

Answer 31

Reactants products.
- first arrow = ΔG1, second = ΔG2

ΔGr = ΔG2 - ΔG1
ΔGr = ΔG P - ΔG R

• Write balanced equation
• Construct cycle with elements at the bottom
• Arrows and correct directions
• Calculate ΔGr, take into account moles of R and P.

Question 32

How is ΔG related to work?

Answer 32

Part of the total enthalpy change required to do work.
ΔH = ΔG + TΔS
- ΔG = free energy for work (eg. driving charge in electrochemical cell)
- TΔS = energy unavailable to do work (involved in disorder of system).

Question 33

What do ΔGf and ΔGr represent?

Answer 33

f - stability of a compound wrt its elements (more negative = more stable)

r - feasibility of a reaction (more negative = more stable).

Question 34

How do you predict the direction of a reaction, using ΔGr values?

Answer 34

0 = EQM
Low negative = P predominate
Low positive = R predominate
High negative = completion
High positive = not feasible.