Chapter 16�Chemical Thermodynamics

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John D. Bookstaver

St. Charles Community College

Cottleville, MO

Chemical

Thermodynamics

First Law of Thermodynamics

• You will recall that energy cannot be created nor destroyed.
• Therefore, the total energy of the universe is a constant.
• Energy can, however, be converted from one form to another or transferred from a system to the surroundings or vice versa.

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Chemical

Thermodynamics

Spontaneous Processes

• Spontaneous processes are those that can proceed without any outside intervention.
• The gas in vessel B will spontaneously effuse into vessel A, but once the gas is in both vessels, it will not spontaneously return to vessel B.

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Chemical

Thermodynamics

Spontaneous Processes

Processes that are spontaneous in one direction are nonspontaneous in the reverse direction.

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Chemical

Thermodynamics

Spontaneous Processes

• Processes that are spontaneous at one temperature may be nonspontaneous at other temperatures.
• Above 0 C it is spontaneous for ice to melt.
• Below 0 C the reverse process is spontaneous.

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Chemical

Thermodynamics

Which process is NOT spontaneous at 25^oC?

1. the melting of an ice cube
2. the sublimation of dry ice
3. the boiling of liquid nitrogen
4. the freezing of ethyl alcohol

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Chemical

Thermodynamics

Reversible Processes

In a reversible process the system changes in such a way that the system and surroundings can be put back in their original states by exactly reversing the process.

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Chemical

Thermodynamics

Irreversible Processes

• Irreversible processes cannot be undone by exactly reversing the change to the system.
• Spontaneous processes are irreversible.

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Chemical

Thermodynamics

Entropy

• Entropy (S) is a term coined by Rudolph Clausius in the 19th century.
• Clausius was convinced of the significance of the ratio of heat delivered and the temperature at which it is delivered, .

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Chemical

Thermodynamics

Entropy

• Entropy can be thought of as a measure of the disorder of a system.
• It is related to the various modes of motion in molecules.

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Chemical

Thermodynamics

Entropy

• Like total energy, E, and enthalpy, H, entropy is a state function.
• Therefore,

S = S_final  S_initial

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Chemical

Thermodynamics

Entropy

For a process occurring at constant temperature (an isothermal process), the change in entropy is equal to the heat that would be transferred if the process were reversible divided by the temperature:

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Units = J/K

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Chemical

Thermodynamics

Second Law of Thermodynamics

The second law of thermodynamics states that the entropy of the universe increases for spontaneous processes, and the entropy of the universe does not change for reversible processes.

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Chemical

Thermodynamics

Second Law of Thermodynamics

In other words:

For reversible processes:

S_univ = S_system + S_surroundings = 0

For irreversible processes:

S_univ = S_system + S_surroundings > 0

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Chemical

Thermodynamics

Second Law of Thermodynamics

These last truths mean that as a result of all spontaneous processes the entropy of the universe increases.

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Chemical

Thermodynamics

Entropy on the Molecular Scale

• Ludwig Boltzmann described the concept of entropy on the molecular level.
• Temperature is a measure of the average kinetic energy of the molecules in a sample.

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Chemical

Thermodynamics

Entropy on the Molecular Scale

• Molecules exhibit several types of motion:
• Translational: Movement of the entire molecule from one place to another.
• Vibrational: Periodic motion of atoms within a molecule.
• Rotational: Rotation of the molecule on about an axis or rotation about  bonds.

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Chemical

Thermodynamics

Entropy on the Molecular Scale

• Boltzmann envisioned the motions of a sample of molecules at a particular instant in time.
• This would be akin to taking a snapshot of all the molecules.
• He referred to this sampling as a microstate of the thermodynamic system.

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Chemical

Thermodynamics

Entropy on the Molecular Scale

• Each thermodynamic state has a specific number of microstates, W, associated with it.
• Entropy is

S = k lnW

where k is the Boltzmann constant, 1.38  10^23 J/K.

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Chemical

Thermodynamics

Entropy on the Molecular Scale

• The change in entropy for a process, then, is

S = k lnW_final  k lnW_initial

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• Entropy increases with the number of microstates in the system.

Chemical

Thermodynamics

Entropy on the Molecular Scale

• The number of microstates and, therefore, the entropy tends to increase with increases in
• Temperature.
• Volume.
• The number of independently moving molecules.

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Chemical

Thermodynamics

Entropy and Physical States

• Entropy increases with the freedom of motion of molecules.
• Therefore,

S(g) > S(l) > S(s)

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Chemical

Thermodynamics

Solutions

Generally, when a solid is dissolved in a solvent, entropy increases.

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Chemical

Thermodynamics

Entropy Changes

• In general, entropy increases when
• Gases are formed from liquids and solids;
• Liquids or solutions are formed from solids;
• The number of gas molecules increases;
• The number of moles increases.

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Chemical

Thermodynamics

Entropy decreases when:

1. gases are formed from liquids.
2. liquids are formed from solids.
3. solids are formed from gases.
4. the number of gas molecules increases during a chemical reaction.

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Chemical

Thermodynamics

Predict the sign of DS, assume constant temperature

• H₂O_(l) → H₂O_(g)
• Ag⁺_(aq) + Cl^-_(aq) → AgCl_(s)
• 4Fe_(s) + 3O_2(g) → 2Fe₂O_3(s)
• N_2(g) + O_2(g) → 2NO_(g)

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Chemical

Thermodynamics

Third Law of Thermodynamics

The entropy of a pure crystalline substance at absolute zero is 0.

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Chemical

Thermodynamics

Standard Entropies

• These are molar entropy values of substances in their standard states.
• Standard entropies tend to increase with increasing molar mass.

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Chemical

Thermodynamics

Standard Entropies

Larger and more complex molecules have greater entropies.

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Chemical

Thermodynamics

Entropy Changes

Entropy changes for a reaction can be estimated in a manner analogous to that by which H is estimated:

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S = nS(products) — mS(reactants)

where n and m are the coefficients in the balanced chemical equation.

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Chemical

Thermodynamics

Example

• Calculate DS^o for the following reaction
• N₂(g) + 3H₂(g) → 2NH₃(g)

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Chemical

Thermodynamics

Entropy Changes in Surroundings

• Heat that flows into or out of the system changes the entropy of the surroundings.
• For an isothermal process:

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• At constant pressure, q_sys is simply H for the system.

Chemical

Thermodynamics

Example

• The normal freezing point of Hg is -38.9^oC, and its enthalpy of fusion is 2.29kJ/mol.
• What is the entropy change of the system when Hg freezes at its normal freezing point?
• What is the entropy change of the surroundings?

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Chemical

Thermodynamics

Entropy Change in the Universe

• The universe is composed of the system and the surroundings.
• Therefore,

S_universe = S_system + S_surroundings

• For spontaneous processes

S_universe > 0

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Chemical

Thermodynamics

Entropy Change in the Universe

• Since S_surroundings =

and q_system = H_system

This becomes:

S_universe = S_system +

Multiplying both sides by T, we get

TS_universe = H_system  TS_system

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Chemical

Thermodynamics

Gibbs Free Energy

• TDS_universe is defined as the Gibbs free energy, G.
• When S_universe is positive, G is negative.
• Therefore, when G is negative, a process is spontaneous.

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Chemical

Thermodynamics

Gibbs Free Energy

1. If DG is negative, the forward reaction is spontaneous.
2. If DG is 0, the system is at equilibrium.
3. If G is positive, the reaction is spontaneous in the reverse direction.

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Chemical

Thermodynamics

Standard Free Energy Changes

Analogous to standard enthalpies of formation are standard free energies of formation, G.

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_f

where n and m are the stoichiometric coefficients.

Chemical

Thermodynamics

Example

• Using data from the appendix, calculate DG^o for the reaction:

P₄(g) + 6Cl₂(g) → 4PCl₃(g)

• Calculate DG^o for the reverse reaction

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Chemical

Thermodynamics

Free Energy Changes

At temperatures other than 25°C,

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DG° = DH  TS

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How does G change with temperature?

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Chemical

Thermodynamics

Free Energy and Temperature

• There are two parts to the free energy equation:
• H— the enthalpy term
• TS — the entropy term
• The temperature dependence of free energy, then comes from the entropy term.

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Chemical

Thermodynamics

Free Energy and Temperature

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Chemical

Thermodynamics

Upon heating, limestone (CaCO₃) decomposes to CaO and CO₂. Speculate on the sign of DH and DS for this process.

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Chemical

Thermodynamics

Example

• For the following reaction at 298K, calculate:
• DH^o
• DS^o
• DG^o
• What would happen to DG if the temperature were raised to 773K?

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Chemical

Thermodynamics

Example

• Consider the reaction at 298K:

C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(l), DH = -2220 kJ

• Would you expect DG^o to be more negative or less negative than DH^o?
• Use the appendix to calculate DG^o.

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Chemical

Thermodynamics

Free Energy and Equilibrium

Under any conditions, standard or nonstandard, the free energy change can be found this way:

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G = G + RT lnQ

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(Under standard conditions, all concentrations are 1 M, so Q = 1 and lnQ = 0; the last term drops out.)

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Chemical

Thermodynamics

Free Energy and Equilibrium

• At equilibrium, Q = K, and G = 0.
• The equation becomes

0 = G + RT lnK

• Rearranging, this becomes

G = RT lnK

or,

K = e

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Chemical

Thermodynamics

Example

• Using the standard energies of formation, calculate the equilibrium constant for the following reaction at 25^oC:

N₂(g) + 3H₂(g) → 2NH₃(g)

• Is the constant K_p or K_c?
• Convert it to the other one?

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Chemical

Thermodynamics

Example

• Non-standard conditions
• Calculate DG at 298K of the same reaction for a mixture that contains 1.0atm of N₂, 3.0atm of H₂ and 0.50atm of NH₃.

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Chemical

Thermodynamics

Putting Things Together

• Consider the equilibria in which NaCl and AgCl dissolve in water at 298K.
• Why is NaCl considered soluble and AgCl is considered insoluble?
• i.e. solve for DG^o for both using standard energies

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Chemical

Thermodynamics

• Could also solve using standard enthalpies & entropies

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• The entropy terms are similar, which should make sense for these two salts
• The much lower heat of enthalpy for the solvation of NaCl makes it much more spontaneous to dissolve

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Chemical

Thermodynamics

• Calculate the solubility products (K_sp) for both salts
• Would you expect an increase in temperature to increase the solubility or decrease it?
• Why?

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Chemical

Thermodynamics

Putting Things Together

• Phase change at equilibrium
• The normal boiling point is the temperature at which a pure liquid is in equilibrium with its vapor at a pressure of 1 atm.
• Write the chemical equation that defines the normal boiling point of liquid carbon tetrachloride, CCl₄(l).
• What is the value of ΔG^o for the equilibrium in part (a)?
• Use thermodynamic data in the appendix to estimate the normal boiling point of CCl₄.

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Chemical

Thermodynamics