Thermodynamics

Brown, LeMay Ch 19

AP Chemistry

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Review1st Law of Thermodynamics In any process, energy is neither created nor

destroyed. When a system changes from one state to another

(E = q + w), it1. Gains heat (+ q) or loses heat (- q) and/or2. Does work (- w) or has work done on it (+ w)

T and internal energy, E, are state functions (depend only on initial and final states of system and not path taken between them).

q and w are not state functions.

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Reversible reaction: can proceed forward and backward along same path (equilibrium is possible)

Ex: H2O freezing & melting at 0ºC

Irreversible reaction: cannot proceed forward and backward along same pathEx: ice melting at room temperature

Spontaneous reaction: an irreversible reaction that occurs without outside interventionEx: Gases expand to fill a container, ice melts at room temperature (even though endothermic), salts dissolve in water

19.1: Spontaneous Processes

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19.2: Molecules & Probability Spontaneity of a reaction is related to the number

of arrangements (microstates) a system can have.Ex: 2 gas molecules are placed in a two-chambered

container, yielding 4 possible microstates:

There is a ½ probability that one molecule will be in each chamber, and a ¼, or (1/2)2, probability that both will be in the right-side chamber.

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With 3 molecules:There is a ¾ probability that one molecule will be in one chamber and two in the other, and only a 1/8, or (1/2)3, probability that all 3 molecules will be in the right-side chamber.

All on left Evenly distributed All on right

Fre

qu

ency

6All on left Evenly distributed All on right

Fre

qu

ency

As the number of molecules increases to 100, a bell-shaped distribution of probable states, called a Gaussian distribution, is observed.

# molecules = 100

Carl Gauss(1777-1855)

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All on left Evenly distributed All on right

Fre

qu

ency

# molecules = 1023

Expanding this to 1 mole of molecules, there is only a (1/2)(6x10^23 probability that every molecule will be in the right-side chamber.

The Gaussian distribution is so narrow that we often forget that it is a distribution at all, thinking of the most probable state as a necessity.

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This demonstrates that: The most probable

arrangements are those in which the molecules are evenly distributed.

Processes in which the disorder of the system increases tend to occur spontaneously.

spontaneous non-spontaneous

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These probability distributions apply to the motion and energy of molecules, and thus can predict the most probable flow of heat.

We call a process spontaneous if it produces a more probable outcome, and non-spontaneous if it produces a less likely one.

spontaneous non-spontaneous

high K.E. low K.E.

evenly distributed K.E.

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EntropyEntropy (S): related to molecular randomness or disorder

Describes the number of arrangements (positions and energy levels) that are available to a system

S is a state function: S = Sfinal - Sinitial

+ S = more randomness

- S = less randomness

For a reversible process that occurs at constant T:

Units: J/KT

q S rev

system

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2nd Law of Thermodynamics The entropy of the universe increases in a

spontaneous process and remains unchanged in a reversible (equilibrium) process. S is not conserved; it is either increasing or constant

Reversible reaction:

SUNIVERSE = SSYS + SSURR = 0

or SSYS = - SSURR

Irreversible reaction:

SUNIV = SSYS + SSURR > 0

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Examples of spontaneous reactions: Gases expand to fill a container:

Ice melts at room temperature:

Salts dissolve in water:

Particles are more evenly distributed

Particles are no longer in an ordered crystal lattice

Ions are not locked in crystal lattice

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19.3: 3rd Law of Thermodynamics The entropy of a crystalline solid at 0 K is 0.

How to predict S: Ssolid < Sliquid < Sgas

Sfewer gas molecules < Smore gas molecules

Slow T < Shigh T

Ex: Predict the sign of S for the following:

1. CaCO3 (s) → CaO (s) + CO2 (g)

2. N2 (g) + 3 H2 (g) → 2 NH3 (g)

+, solid to gas

-, fewer moles produced

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19.4: Standard Molar Entropy, Sº Standard state (º): 298 K and 1 atm Units = J/mol·K Hºf of all elements = 0 J/mol

However, S° of all elements ≠ 0 J/mol·K

See Appendix C for list of values.

reactantsproducts Sm - Sn S • Where n and m are coefficients in the balanced chemical equation.

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19.5: Gibbs free energy, G Represents combination of two

forces that drive a reaction:H (enthalpy) and S (disorder)

Units: kJ/mol G = H - TS G° = H° - TS°

(absolute T)

reactantsfproductsf mG - Gn G Called “free energy” because G represents

maximum useful work that can be done by the system on its surroundings in a spontaneous reaction. (See p. 708 for more details.)

Josiah Willard Gibbs(1839-1903)

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Determining Spontaneity of a ReactionIf G is: Negative (the free energy of system decreases)

The reaction is spontaneous (proceeds in the forward direction)

Positive

Forward reaction is non-spontaneous; the reverse reaction is spontaneous

Zero The system is at equilibrium

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19.6: Free Energy & Temperature G depends on enthalpy, entropy, and temperature:

G = H - TSH S G and reaction outcome

- + Always (-); spontaneous at all T

2 O3 (g) → 3 O2 (g)

+ - Always +; non-spontaneous at all T

3 O2 (g) → 2 O3 (g)

- - Spontaneous at low T; non-spontaneous at high T

H2O (l) → H2O (s)

+ + Spontaneous only at high T ; non-spontaneous atlow T

H2O (s) → H2O (l)

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19.7: Free Energy & Equilibria The value of G determines where the system

stands with respect to equilibrium.

G = G° + RT ln Q

where R = 8.314 J/K•mol

or

G° = - RT ln Keq

or

RT

G-

eq e K

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19.7: Free Energy & Equilibria

G° Reaction outcome

Negative Spontaneous forward rxn, K > 1

Positive Non-spontaneous forward rxn, K < 1

Zero System is at equilibrium, K = 1