Chapter 18: Free Energy & Thermodynamics

Question 1

What is a spontaneous process?

Answer 1

A process that occurs without ongoing outside intervention (such as the performance of work by some external force).

Question 2

How is entropy (S) defined?

Answer 2

Entropy is a thermodynamic function that increases with the number of energetically equivalent ways to arrange the components of a system to achieve a particular state.

Question 3

Which equation describes entropy mathematically?

Answer 3

S = k ln W

Question 4

In the mathematical entropy equation, what does k represent?

Answer 4

k is the Boltzmann constant (the gas constant divided by Avogadro’s number)

Question 5

In the mathematical entropy equation, what does W represent?

Answer 5

W is the number of energetically equivalent ways to arrange the components of the system. (the number of possible microstates that can result in a given macrostate)

Question 6

What defines the macrostate of a system?

Answer 6

A given set of conditions (P, V, and T) defines the macrostate (or state) of the system. The overall energy of a macrostate is constant as long as the conditions remain constant.

Question 7

What is the microstate of a system?

Answer 7

The exact internal energy distribution among the particles of a system at any one instant is a microstate.

Question 8

If system B has a larger W than system A, which has the greater entropy?

Answer 8

System B because it has more energetically equivalent ways to arrange the components of the system.

Question 9

How does the entropy of a macrostate change with the number of ways to arrange the components of the system?

Answer 9

The entropy of a macrostate of a system increases with the number of energetically equivalent ways to arrange the components of the system to achieve that particular macrostate.

Question 10

How is entropy related to the dispersal of energy?

Answer 10

A state in which a given amount of energy is more highly dispersed (or more highly randomized) has more entropy than a state in which the same energy is more highly concentrated.

Question 11

What is the second law of thermodynamics?

Answer 11

For any spontaneous process, the entropy of the universe increases (∆Suniverse > 0).

Question 12

How is spontaneity related to entropy?

Answer 12

Processes that increase the entropy of the universe–those that result in greater dispersal or randomization of energy–occur spontaneously. Processes that decrease the entropy of the universe do not occur spontaneously.

Question 13

Why can the change in entropy be calculated by subtracting the initial entropy from the final entropy?

Answer 13

Entropy, like enthalpy, is a state function–its value depends only on the state of the system, not on how the system arrived at that state.

Question 14

How does entropy determine the direction of chemical and physical change?

Answer 14

A chemical system proceeds in a direction that increases the entropy of the universe–it proceeds in a direction that has the largest number of energetically equivalent ways to arrange its components.

Question 15

For which phase transitions is ∆S > 0?

Answer 15

1. Solid -> liquid
2. Solid -> gas
3. Liquid -> gas

Question 16

How does an increase in the number of moles of gas affect the entropy of the system?

Answer 16

An increase in the number of moles of gas during a chemical reaction makes ∆S > 0.

Question 17

How is ∆S defined with relation to q and T? What criteria must be met for this equation to apply?

Answer 17

∆S = qrev / T
Must be a reversible process and T must be constant (the process is isothermal).

Question 18

What are the units of entropy?

Answer 18

J/K

Question 19

What is a reversible process?

Answer 19

A process that reverses direction upon an infinitesimally small change in some property. All reversible processes are in a constant state of equilibrium and represent highly idealized conditions.

Question 20

Why does the freezing of ice or the condensation of water increase the entropy of the surroundings?

Answer 20

Because both processes are exothermic: they give off heat to the surroundings. Because entropy is the dispersal or randomization of energy, the release of heat energy by the system disperses that energy into the surroundings, increasing the energy of the surroundings.

Question 21

How does an exothermic process affect the entropy of the surroundings?

Answer 21

It increases the entropy.

Question 22

How does an endothermic process affect the entropy of the surroundings?

Answer 22

It decreases the entropy.

Question 23

Why does the freezing of water become nonspontaneous above 0˚C?

Answer 23

Entropy represents the energy dispersed into a sample of matter per unit temperature–it has the units of joules per kelvin (J/K). The magnitude of the increase in entropy of the surroundings due to the dispersal of energy into the surroundings is temperature dependent.

Question 24

How is temperature related to entropy?

Answer 24

The greater the temperature, the smaller the increase in entropy for a given amount of energy dispersed into the surroundings. The higher the temperature, the lower the amount of entropy for a given amount of energy dispersed.

Question 25

What two things does the change in entropy of the surroundings depend on?

Answer 25

1. The amount of heat transferred into or out of the surroundings
2. The temperature of the surroundings.

Question 26

How is the magnitude of the change in entropy of the surroundings related to the magnitude of ∆Hsys?

Answer 26

The two values are proportional. ∆Ssurr = -∆Hsys/T (constant P and T)

Question 27

How is ∆G related to ∆Suniv?

Answer 27

∆G is proportional to the negative of ∆Suniv.

Question 28

How is Gibbs free energy related to spontaneity?

Answer 28

A decrease in Gibbs free energy (∆G < 0) corresponds to a spontaneous process.
An increase in Gibbs free energy (∆G > 0) corresponds to a nonspontaneous process.

Question 29

Describe the change in free energy when a reaction is exothermic and ∆Srxn is positive.

Answer 29

The change in free energy is negative at all temperatures and the reaction is spontaneous at all temperatures.

Question 30

Describe the change in free energy when a reaction is endothermic and ∆Srxn is negative.

Answer 30

The change in free energy is positive at all temperatures and the reaction is nonspontaneous at all temperatures.

Question 31

Describe the change in free energy when a reaction is exothermic and ∆Srxn is negative.

Answer 31

The sign of the change in free energy depends on temperature. The reaction is spontaneous at low T but nonspontaneous at high T.

Question 32

Describe the change in free energy when a reaction is endothermic and ∆Srxn is positive.

Answer 32

The sign of the change in free energy depends on T. The reaction is nonspontaneous at low T but spontaneous at high T.

Question 33

When does ∆G depend on T?

Answer 33

When ∆H and ∆S have opposite signs, the spontaneity of the reaction does not depend on T. When ∆H and ∆S have the same sign, the spontaneity does depend on T.

Question 34

What is the standard state for a gas?

Answer 34

The pure gas at a pressure of exactly 1 atm.

Question 35

What is the standard state for a liquid or solid?

Answer 35

The pure substance in its most stable form at a pressure of 1 atm and at the temperature of interest (often taken to be 25˚C).

Question 36

What is the standard state for a substance in solution?

Answer 36

The standard state for a substance in solution is a concentration of 1 M.

Question 37

How is the standard entropy change for a reaction defined (∆S˚rxn)?

Answer 37

The change in entropy for a process in which all reactants and products are in their standard states. Since entropy is a function of state, the standard change in entropy is the standard entropy of the products minus the standard entropy of the reactants.

Question 38

What is the third law of thermodynamics?

Answer 38

The entropy of a perfect crystal at absolute zero (0 K) is zero.

Question 39

Why is entropy zero at absolute zero?

Answer 39

A perfect crystal at a temperature of absolute zero has only one possible way (W = 1) to arrange its components. Based on Boltzmann’s definition of entropy, its entropy is zero.

Question 40

What does it mean to say entropy is an extensive property?

Answer 40

It depends on the amount of the substance.

Question 41

What is the relationship between molar mass and entropy?

Answer 41

Entropy increases with increasing molar mass.

Question 42

Why does entropy increase with increasing molar mass?

Answer 42

The energy states associated with the motion of heavy atoms are more closely spaced than those of lighter atoms. The more closely spaced energy states allow for greater dispersal of energy at a given T and therefore greater S.

Question 43

What are allotropes?

Answer 43

Some elements can exist in two or more forms with different structures–called allotropes–in the same state of matter.

Question 44

What is the relationship between entropy and molecular complexity?

Answer 44

Entropy generally increases with increasing molecular complexity.

Question 45

Why do molecules typically have greater S than atoms?

Answer 45

Molecules generally have more “places” to put energy than atoms. With atoms, the only form that energy can take is the translational motion of the atoms. With molecules, energy can take the form of translational motion, rotational motion, and (at high enough T) vibrational motion.

Question 46

How does the dissolution of a crystalline solid into solution affect its entropy?

Answer 46

This usually results in an increase in S.

Question 47

How do you calculate ∆S˚rxn?

Answer 47

Subtract the standard entropies of the reactants multiplied by their stoichiometric coefficients from the standard entropies of the products multiplied by their stoichiometric coefficients.

Question 48

When does Gibbs free energy (∆G) become the standard change in free energy (∆G˚rxn)?

Answer 48

When the reactants and products of a reaction are in their standard states.

Question 49

How is the free energy of formation (∆G˚f) defined?

Answer 49

The free energy of formation is the change in free energy when 1 mol of a compound in its standard state forms from its constituent elements in their standard states.

Question 50

What is the free energy of the formation of pure elements in their standard state?

Answer 50

Zero.

Question 51

How can a nonspontaneous process be made spontaneous?

Answer 51

It can be coupled to a process that is highly spontaneous.

Question 52

What does the change in free energy of a chemical reaction represent?

Answer 52

It represents the maximum amount of energy available, or free, to do work (if ∆G˚rxn is negative). It is the amount of energy that remains after accounting for the heat that must be lost to the surroundings.

Question 53

When the change in free energy is positive, what does ∆G˚rxn represent?

Answer 53

The minimum amount of energy required to make the reaction occur. However, ∆G˚rxn represents a theoretical, and making a real nonspontaneous reaction occur always requires more energy than the theoretical limit.

Question 54

Even though the free energy change for the evaporation of water is positive, why is it still spontaneous?

Answer 54

Under ordinary conditions the reactants and products are not in their standard states and ∆G˚rxn applies only when the reactants and product are in their standard states, sometimes called standard conditions.

Question 55

Give the equation for calculating the free energy change of a reaction under nonstandard conditions.

Answer 55

∆Grxn = ∆G˚rxn + RTlnQ

Question 56

If water is evaporating, what is the sign of ∆G?

Answer 56

Negative.

Question 57

If water is condensing, what is the sign of ∆G?

Answer 57

Positive.

Question 58

At equilibrium, what is ∆G?

Answer 58

0

Question 59

Under standard conditions, what does Q equal?

Answer 59

1

Question 60

Under standard conditions, does water evaporate or condense?

Answer 60

Water vapor condenses into liquid water.

Question 61

Give the equation that relates ∆G˚rxn to K.

Answer 61

∆G˚rxn = -RTlnK

Question 62

When K < 1, how are lnK and ∆G˚rxn affected?

Answer 62

lnK is negative and ∆G˚rxn is positive. Under standard conditions (when Q = 1), the reaction is spontaneous in the reverse direction.

Question 63

When K > 1, how are lnK and ∆G˚rxn affected?

Answer 63

lnK is positive and ∆G˚rxn is negative. Under standard conditions (when Q = 1), the reaction is spontaneous in the forward direction.

Question 64

When K = 1, how are lnK and ∆G˚rxn affected?

Answer 64

lnK is zero and ∆G˚rxn is zero. The reaction happens to be an equilibrium under standard conditions.