Chapter 19 cont. 19.3 and 19.4

http://ocw.mit.edu/resources/res-tll-004-stem-concept-videos-fall-2013/videos/

governing-rules/entropy/Microstates of Entropy

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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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 about an axis or rotation

about bonds.

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http://www.youtube.com/watch?v=3RqEIr8NtMI and disc from book: D:\Chapter_19\C_Media\molecular-motions\_molecular-motions.html

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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Entropy on the Molecular Scale• Each thermodynamic state has a specific number

of microstates, W, associated with it.• Entropy is

S = k ln Wwhere k is the Boltzmann constant, 1.38 1023 J/K.

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Entropy on the Molecular Scale• The change in entropy for a process, then,

isS = k ln Wfinal k ln Winitial

Wfinal

Winitial

S = k ln

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

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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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Entropy and Physical States• Entropy increases with the freedom of motion of

molecules.• Therefore,

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

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In which phase are water molecules least able to have rotational motion?

A. VaporB. LiquidC. Ice

Solutions

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

However, water becomes more organized. Why?

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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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What major factor leads to a decrease in entropy as the reaction shown takes place?

A. Increase in number of molecules during changeB. Decrease in number of molecules during changeC. Change in pressure of systemD. Change in internal energy of system

Third Law of Thermodynamics

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

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Why does the plot show vertical jumps at the melting and boiling points?

A. During melting or boiling at constant temperature entropydramatically increases because energy is removed from the

systemduring the change.

B. During melting or boiling at constant temperature entropy changessignificantly because more microstates exist for the final phasecompared to the initial phase.

C. During melting or boiling at constant temperature entropy changessignificantly because fewer microstates exist for the final phasecompared to the initial phase.

D. During melting or boiling at constant temperature entropy changessignificantly because no change in the number of microstatesoccurs during the phase change.

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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Standard Entropies

Larger and more complex molecules have greater entropies.

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What might you expect for the value of S° for butane, C4H10?

A. 270 J/mol-K to 300 J/mole-KB. 280 J/mol-K to 305 J/mole-KC. 310 J/mol-K to 315 J/mole-KD. 320 J/mol-K to 340 J/mole-K

Entropy Changes

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

S = nS(products) — mS(reactants)

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

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Entropy Changes in Surroundings

• Heat that flows into or out of the system changes the entropy of the surroundings.

• For an isothermal process:

Ssurr =qsys

T

• At constant pressure, qsys is simply H for the system.

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Entropy Change in the Universe

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

• Therefore,Suniverse = Ssystem + Ssurroundings

• For spontaneous processes

Suniverse > 0

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Entropy Change in the Universe• Since Ssurroundings =

and

qsystem = Hsystem

This becomes:Suniverse = Ssystem +

Multiplying both sides by T, we getTSuniverse = Hsystem TSsystem

Hsystem

T

qsystem

T

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Sample Exercise 19.5 Calculating ΔS° from Tabulated EntropiesCalculate the change in the standard entropy of the system, ΔS° , for the synthesis of ammonia from N2(g)and H2(g) at 298 K:

N2(g) + 3 H2(g) 2 NH3(g)

SolutionAnalyze We are asked to calculate the standard entropy change for the synthesis of NH3(g) from its constituent elements.

Plan We can make this calculation using Equation 19.8 and the standard molar entropy values in Table 19.1 and Appendix C.

Solve Using Equation 19.8, we have ΔS° = 2S°(NH3)–[S°(N2) + 3S°(H2)]

Substituting the appropriate values from Table 19.1 yieldsΔS° = (2 mol)(192.5 J/mol–K)–[(1 mol)(191.5 J/mol–K) + (3 mol)(130.6 J/mol–K)]

= –198.3 J/KCheck: The value for ΔS° is negative, in agreement with our qualitative prediction based on the decrease in the number of molecules of gas during the reaction.

Practice ExerciseUsing the standard molar entropies in Appendix C, calculate the standard entropy change, ΔS°, for the following reaction at 298 K:

Al2O3(s) + 3 H2(g) 2 Al(s) + 3 H2O(g)

Answer: 180.39 J/K

Plan today

Gibbs Free energy WS

Graph problems from WS

Problems from book

Reminder: Quest is a quiz grade, next text is Thursday after break!

WhiteboardGroup Problem

1 2,7

2 3,8

3 4,7

4 5,8

5 6,7

6 2,7

7 3,8

8 4,7