Chapter 14: Entropy & Free Energy

Question 1

Spontaneous process

Answer 1

A process that does occur under a specific set of conditions (e.g. T, P, [& concentration for solutions])

*Often, but not always, exothermic reactions

Question 2

Nonspontaneous process

Answer 2

A process that does not occur under a specific set of conditions

Question 3

Entropy

Answer 3

entropy = S

The measure of a system’s energy dispersal;
the greater the dispersal, the greater the entropy

Question 4

W = X^N

Answer 4

W = number of energetically equivalent different ways molecules in a system can be arranged

X = number of cells (“containers”)

N = number of moleucles

e.g. 2 cells & 4 molecules = 2⁴ = 16

Question 5

Quantitative definition of entropy

Answer 5

Based on W = X^N:

The most probable state is the one with the largest number of possible arrangements –> has the greatest entropy

Question 6

ΔU

Answer 6

Internal energy

ΔU = q + w
(heat + work)

**NOT ΔE** (taught wrong?)

Question 7

Standard entropy

Answer 7

S° = standard entropy

J/K • mol

The absolute entropy of a substance at 1 atm
*Temperature MUST be specified! NOT standard!
(Typically 25°C, however)

Entropies of substances are always positive, even for elements in standard states (UNLIKE standard enthalpy of formation ΔH_f°)

Question 8

Trends of standard entropy (4)

Answer 8

1. solid S° < liquid S° < gas S°
   gas phase of a substance always has highest standard entropy (disperses the most)
2. monatomic species (e.g. He (g), Ne (g))
   larger molar mass = greater S°
3. for 2 substances in same phase, with similar molar mass, the more complex substance has the greater S°
   e. g. F₂ versus O₃ (ozone is more complex)
4. an element that exists in 2+ allotropic forms
   form with more mobile atoms = form with greater S°
   e.g. graphite has greater S° than diamond

Question 9

Factors that influence entropy of system

Answer 9

1. Volume change
   As volume increases, space between translational energy levels decrease (causing more energy levels to become available, dispersing energy)
2. Temperature change
   As temperature increases, kinetic energy increases, causing more energy levels to be accessible
3. Molecular complexity
   The more complex a molecule is, the less restriction of motion there is (i.e. not only translational motion, but also rotational and vibrational)
4. Molar mass
   The larger the molar mass, the less the space is between energy levels, and the more energy levels within which the system’s energy can be dispersed
5. Phase change
   The more spaced out the molecules are, the more they can move, rearrange, and the greater the entropy

6. Chemical reaction
When product(s) have more gas molecules than reactant(s), the number of different arrangements (W) increases, and thus so does entropy

Question 10

Determining spontaneity based on ΔS_sys & ΔS_surr

Answer 10

ΔS_sys and -ΔS_surr –> spontaneous process

-ΔS_sys and ΔS_surr​ –> spontaneous process

ΔS_sys and ΔS_surr​ –> spontaneous process

*BOTH CANNOT BE NEGATIVE for spontaneous processes

Question 11

Relationship between ΔS_surr, -ΔH_sys, and T

Answer 11

ΔS_surr α -ΔH_sys α 1/T

i.e. ΔS_surr = -ΔH_sys / T

Question 12

Second law of thermodynamics

Answer 12

For a process to be spontaneous as written (in foward direction), ΔS_univ must be positive

ΔS_univ = ΔS_sys + ΔS_surr

System’s entropy can decrease so long as surrounding’s increase in entropy makes universe’s positive

Question 13

Equilibrium process

Answer 13

One that does not occur spontaneously in either the net forward nor reverse direction, but can be made to occur by the addition or removal of energy to a system at equilibrium

(e.g. melting of ice at 0°C, ice and water are in equilibrium with each other)

ΔS_univ = 0 = reaction is an equilibrium process

Question 14

Third law of thermodynamics

Answer 14

Entropy (S) of a perfect crystalline substance = 0 @ 0 K

As temperature increases, molecular motion increases, thus entropy increases

Entropy of any substance at any temperature above 0 K is greater than 0

*Impure/imperfect crystalline substance at 0 K has entropy (S) > 0

*This law enables us to determine experimentally the absolute entropies of substances

Question 15

[Gibbs] free energy (G)

Answer 15

free energy = energy available to do work

*state function*

ΔG = ΔH - TΔS

ΔG predicts spontaneity

Question 16

Determining spontaneity using ΔG when ΔG is <, >, or = 0

Answer 16

*At constant T & P*

ΔG < 0
SPONTANEOUS in forward direction
non-spontaneous in reverse

ΔG > 0
non-spontaneous in forward direction
spontaneous in reverse

ΔG = 0
system is at equilibrium

Question 17

Predicting the sign of ΔG using the signs of ΔH and ΔS

Answer 17

-ΔH and +ΔS = -ΔG
*ALWAYS SPONTANEOUS*
(Only enthalpy is negative.)

ΔH and -ΔS = +ΔG
*Always NONspontaneous*
(Only entropy is negative.)

• ΔH and -ΔS = -ΔG if TΔS < ΔH
• *(Both negative, low T = spontaneous.)**
• ΔH and -ΔS = +ΔG if TΔS > ΔH
• *(Both negative, high T = NONspontaneous.)**

+ΔH and +ΔS = -ΔG if TΔS > ΔH
(Both positive, high T = spontaneous.)
——
+ΔH and +ΔS = +ΔG if TΔS < ΔH
(Both positve, low T = NONspontaneous.)

Question 18

Standard free-energy change (ΔG°_rxn)

Answer 18

The free-energy change for a reaction when it occurs under standard-state conditions

i.e. when reactants in their standard states are converted to products in their standard states

Question 19

Standard states of pure substances and solutions for ΔG°_rxn

Answer 19

Gases: 1 atm pressure

Liquids: pure liquid

Solids: pure solid

Elements: most stable allotropic form at 1 atm & 25°C

Solutions: 1 molar concentration

Question 20

Standard free energy of formation (ΔG°_f)

Answer 20

Standard free energy of formation of a compound:

Free-energy change that occurs when 1 mole of the compound is synthesized from its constituent elements, each in its standard state

*Value changes with temperature