Chapter 17

THERMODYNAMICS

What is Thermodynamics?

Thermodynamics is the study of energy changes that accompany physical and chemical processes.

Word origin:

“Thermo”, from temperature, meaning heat

“Dynamics”, which means motion (under the action of forces)

What determines the direction of spontaneous chemical reactions?

Chemical thermodynamics answers the questions:

How much heat is evolved during a chemical reaction ("thermochemistry")?

Spontaneous Processes

A spontaneous process occurs by itself without any ongoing outside intervention

Reaction continues until equilibrium is reached

Examples: A cube of ice melting in water; a steel pipe rusting;

Spontaneous chemical reactions behave the same way

If a reaction is spontaneous in one direction, it is not spontaneous in the other

Spontaneity has nothing to do with rate/speed of reaction

C Diamond

Spontaneous; 1 atm, 25 0C

Spontaneity versus Speed/Rate

Spontaneous = Thermodynamically favorable; Large Keq)

C Graphite

Extremely slow = Kinetically unfavorable; Small rate)

Spontaneous ≠ Instantaneous (Fast)

Nonspontaneous; 1 atm, 25 0C

BUT…

Spontaneous Processes

If a reaction is spontaneous in one direction, it is not spontaneous in the other

Diamond to graphite: Spontaneous (but extremely slow) at room T

In the examples above energy is conserved (1st law). Yet one process occurs while the other does not.

Melting of ice cube at room T is spontaneous, but freezing of water at room T is not spontaneous.

Graphite to diamond: Nonspontaneous at room T (otherwise we’ll all be rich!)

Spontaneous Processes (Cont.)

Spontaneous processes may need a little “push” to get started

Example: Hydrogen and oxygen gases burn spontaneously only after being ignited by a spark

2H2 (g)   +    O2 (g) 2H2O(l)         

The reverse reaction is nonspontaneous (i.e. Water does not simply decompose into H2 and O2 gases)

Nonspontaneous reactions

Can we make nonspontaneous reactions happen?

Yes. It happens everyday. HOW?

By supplying energy

Examples:

Photosynthesis (CO2 (g) + H2O (l) = Carbohydrates) takes place upon absorption of solar energy

2H2O(l)          2H2 (g)   +    O2 (g)

The nonspontaneous reaction

happens if we pass electricity through water (electrolysis)

Factors Affecting Spontaneity

1. Changes in enthalpy (ΔH)

a) Exothermic reactions ( - ΔH) → tend to be thermodynamically favorable [ large Keq]

Example: All combustion reactions (such as the combustion of natural gas or methane) are spontaneous and exothermic.

b) Endothermic reactions ( + ΔH) → tend to be unfavorable

CH4 (g) + 2O2 (g) CO2 (g) + 2H2O (g) ΔHrxn0 = - 802 kJ

Methane

Spontaneous and

Exothermic (- ΔH)

Factors Affecting Spontaneity – Cont.

NOTE: Not all exothermic reactions are spontaneous

Examples of endothermic reactions that are spontaneous

Vaporization of water (+ΔH) at ordinary T and P

Dissolving of NaCl in water (+ΔH)

Thus, the sign of ΔH does not always predict spontaneous change

Q. What other factor affects direction of spontaneous reactions?

Factors Affecting Spontaneity – Cont.

2. Changes in entropy (ΔS) or degree of “disorder”

a) Increase in entropy ( + ΔS) or disorder → tend to be favorable [ large Keq]

Recall: Entropy (S) is a measure of the dispersal of energy as a function of temperature

b) Decrease in entropy ( - ΔS) or more order → tend to be unfavorable

Closely associated with randomness or disorder

The “Randomness” Factor

Randomness also predicts spontaneous processes

In general, nature tends to move spontaneously from a more ordered state to more random (less ordered) state .

http://www.lecb.ncifcrf.gov/~toms/molecularmachines.html

An example of a + ΔS

What? Are you expecting your room to become more ordered in time?

Change to more disordered (more random) state = Increase in entropy (+ ΔS)

Q. Which of the two images below has a + ΔS? Is spontaneous above 0 0C?

Image source: http://demo.physics.uiuc.edu/LectDemo/scripts/demo_descript.idc?DemoID=1114

MELTING

More disorder = higher entropy (+ ΔS)

Factors Affecting Spontaneity – Cont.

Spontaneous when T > 0 0C

Entropy (S) is a State Function

Recall that entropy is a state function:

ΔS = Sfinal - Sinitial

Depends only on the initial and final states of the system (Not on path taken from one state to another)

ΔSrxn = ∑ n x ΔSproducts - ∑ n x ΔSreactants

For a chemical reaction, entropy change is expressed as:

Most disordered

Most ordered

(Least disorder)

In general: ΔS gas > ΔS liquid > ΔS solid

Entropy (S) and Phase Changes

Exercise: Predict the sign of ΔS in each of the following processes.

Freezing

Vaporization

Condensation

- ΔS

+ ΔS (becomes more disordered)

- ΔS

Reactions that produce gas (+ ΔS) tend to be favorable

Entropy and the 2nd Law of Thermo.

Second law of thermodynamics: In a spontaneous process

there is a net increase in the entropy of the universe*

Layman’s term: All real processes occur spontaneously in the direction that increases disorder.

* Universe = System + Surrounding Thus,

ΔSuniverse = ΔSsystem + ΔSsurrounding

A process (or reaction) is spontaneous if ∆Suniverse is (+)

Entropy and the 2nd Law of Thermo. – Cont.

ΔSuniverse = ΔSsystem + ΔSsurrounding

Q. When is ∆Suniverse positive?

(+) ∆Suniverse when: ΔSsystem + ΔSsurrounding > 0

If this decreases, ∆Ssurr. must increase even more to offset the system’s decrease in entropy

Example: During growth of a child, food molecules (carbs, proteins, etc) are broken down into CO2, water and energy

Increases ∆Ssurrounding

But formation of body mass decreases ∆Ssystem

Exothermic ( -∆H)

Thus, ↓ ∆Ssystem is offset by ↑ ∆Ssurrounding = Still obeys 2nd law

Entropy and the 3rd Law of Thermo.

Third law of thermodynamics: The entropy of a pure

crystalline substance at 0 K is zero.

All motion/vibration at absolute zero has stopped Particles in highest order

Ssystem = 0 at T = 0 K

= System

Q. What happens to a system if we decrease the temperature

continuously?

Entropy will decrease (more order)

Recall: ∆S (g) > ∆S (l) > ∆S (s)

Entropy and 3rd Law - Cont.

It follows that as the temperature of a system increases, its

entropy also increases.

Thus, T (related to ∆H) and entropy (∆S) both influence spontaneous reactions

∆H can be measured using a calorimeter

How is ∆S measured?

Standard Molar Entropies, S0

Entropy (S) at standard conditions of 1 atm pressure and 25 0C temperature for one mole of a substance

Standard Molar Entropy, S0

Unit for S0: J/mol•K

Table 17.1: Standard molar entropies of substances

Elements and compounds have (+) S0

Aqueous ions may have (+) or (-) S0

ΔS0rxn = ∑ n x ΔS0

products - ∑ n x ΔS0reactants

NOTE: Be able to calculate ΔS0rxn from given S0 values

Gibbs Free Energy, G

At a constant temperature, the free energy change, ΔG, of a system is given by the Gibbs-Helmholtz equation:

So far you’ve learned that both ∆H and ∆S affect reaction spontaneity

Is there an equation that relates these two thermodynamic quantities?

ΔG = ΔH - TΔS

Free energy change

Enthalpy change

Kelvin T * Entropy

change

Standard Free Energy Change, ΔG0

The standard free energy change, ΔG0, applies to standards states as follows:

(1) 1 atm pressure for pure liquids and solids

ΔG0 = ΔH0 - TΔS0

(2) 1 atm partial pressure for gases

(3) 1 M concentration for solutions

Mathematically:

Importance of Free Energy Change:

The sign of ΔG0 determines reaction spontaneity

Importance of ΔG0

The sign of ΔG0 determines reaction spontaneity

(1) - ΔG0 = spontaneous reaction*

(2) + ΔG0 = nonspontaneous reaction

(3) ΔG0 = 0 for reactions at equilibrium (occurs in either direction)

*At a constant T and P, reactions go in the direction that lowers the free energy of the system.

ΔG0 and Spontaneous Reactions

Q. Just when is a reaction spontaneous by looking at ΔG0?

ΔG0 = ΔH0 - TΔS0

Source: Principles of General Chemistry by Silberberg, © 2007.

ΔG0 versus ΔG

ΔG0 vs. ΔG

ΔG0 = free energy of the system at standard conditions [Pgas = 1 atm; [ ] = 1 M for species in solution (aq)]

Fixed during a reaction under std. conditions

ΔG = free energy of the system at any given condition [i.e. at any point in the reaction]

Changes during a reaction

Importance of ΔG0

For a given chemical reaction aA + bB → cC + dD

the free energy of the reaction is given by the equation

∆G = ∆G0 + RT ln Q

Std. free energy

Gas constant Kelvin

temp.

Reaction quotient

Q =[C]c [D]d

[A]a [B]b

Importance of ΔG0 – Cont.

At equilibrium, reaction seem to have stopped (ratefwd = raterev.) and:

At equilibrium ∆G = 0 ; Q = Keq

∆G = ∆G0 + RT ln Q

Thus, 0 = ∆G0 + RT ln Keq

or at equilibrium ∆G0 = - RT ln Keq

= 0 = Keq

or Keq = e - (∆G0/RT)

Importance of this equation:

Allows us to calculate ∆G0 given Keq or Keq given ∆G0