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General Chemistry

Chapter 17: Thermodynamics: Entropy, Free Energy, and Equilibrium

Lecture 1 of 4 $

Spontaneous Processes

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Entropy and the second law of Thermodynamics

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Energy Dispersal and Entropy

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Second Law of Thermodynamics

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Heat Transfer and Entropy Changes in the Surroundings

Spontaneous Processes Recall: We expressed this mathematically as ΔU= q + w where

ΔU = change in internal energy of system q = heat absorbed by system from the surroundings w = work done by the surroundings by the system

Our problem: How do we determine whether a process is favoured (spontaneous) or not? S

We can=t use ΔU

S

We can=t rely on ΔH 1

Before we go on, what is spontaneity?

A process said to occur without any outside intervention is said to be________________ . Some spontaneous features of spontaneous processes: *It might need outside intervention momentarily, for instance for initiation of process but not continuous.

1.

A spontaneous process occurs without any continuous outside intervention.

2.

A process said to be spontaneous in one direction is not spontaneous in the opposite direction.

3.

Spontaneity can be dependent upon the conditions in which the process occurs.

Example. How many of the following processes are spontaneous? (a) The melting of ice cubes at -5 C and 1 bar pressure. (b) Dissolution of sugar in a cup of hot water. (c) The reaction of nitrogen atoms to from N 2 molecules at 25 C and 1 bar. (d) Alignment of iron filings in a magnetic field.

*While continuous intervention will speed up the processes, they will occur otherwise too

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Entropy and the Second Law of Thermodynamics Back to our problem: how do we determine if a reaction is spontaneous or not?

After much study it has been concluded that all spontaneous processes have a common characteristic.

entropy The common characteristic is an increase in the property we call ________________ Consider the following three spontaneous processes: 1.

Ice melting at T > 0 C

(An endothermic process)

2.

Dissolution of NH4NO3

(An endothermic process)

From the above processes we conclude that entropy can be viewed as a measure of randomness or disorder.

More precisely, entropy is a measure of the number of arrangements (positions and/or energy levels referred to as microstates) that are available to a system in a given state (energy dispersal) Entropy can be related to probability. ANature spontaneously proceeds towards the states that have high probabilities of existing.” Entropy (S): A thermodynamic quantity that increases with the number of energetically equivalent ways to arrange the components of a system to achieve a particular state.

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Features of S: 1. S is a state function 2. Delta S = S(final) - S(initial) 3. A positive delta S indicates an increase in energy dispersal and vice versa. 4.

Units: J/ K

5. Entropy of reaction delta(r) S has units J/ K mol

Energy Dispersal and Entropy

Ludwig Boltzmann related entropy to the number of possible arrangements (microstates) of particles in a system:

S=k x lnW Where k is the Boltzmann constant and W is related to the number of different arrangements (microstates) possible... Consider four gaseous molecules in a two-bulbed container with a valve. What are the possible arrangements for the molecules after the valve is opened? 4:0, 2:2, 3:1, 1:3, 0:4 (microstates) and 16 different ways if molecules are individualised (macrostates)

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Question: why does a gas spontaneously expand to evenly fill a container?

Atomic/Molecular view of entropy An atom or molecule has a total amount of energy that can be dispersed in a variety of ways (translational, kinetic, rotational, electronic, vibrational etc). A given set of conditions (P,V, T) defines the total energy (or macrostate) of the atom/molecule. The different ways the energy can be dispersed leads to different microstates. There are only certain allowed arrangements because of the nature of quantum mechanics. These ideas can be extended to systems containing more than one particle.

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2 microstates 2:6 4:4

3 particles e.g. 1:1:10 *Increase in vol means increase in entropy 1:7 3:5 2:6 4:4

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The Second Law of Thermodynamics The total change entropy of the universe can be expressed in terms of the change in entropy in the system and surroundings, e.g

Delta S (universe) = Delta S (system) + Delta S (surroundings) Earlier we stated that all spontaneous processes result in an increase in entropy. This becomes the basis for the second law of thermodynamics:

the total entropy of a system and its surroundings always increases for a spontaneous process *For a spontaneous reaction Delta S (universe) = Delta S (system) + Delta S (surroundings) > 0

Heat Transfer and Entropy Changes in the Surroundings Question: What is the relationship between the enthalpy change in the system and the entropy change, ΔSsurr, in the surroundings?

For an exothermic reaction, if the temperature of the surroundings is increase the entropy increases Delta S (surr) is proportional to the enthalpy change in the system. Question: How is the magnitude of

r affected

by temperature?

Inversely proportional relationship

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To Summarize, ΔSsurr is proportional to the heat flow ΔSsurr is inversely proportional to the temperature

Delta S (surr) = negative Delta H-sys (Heat Flow at constant P)/ Temperature - (K) Example. At 298 K, the formation of ammonia has a negative ΔS

N2 (g) + 3 H2 (g) ⇌ 2 NH3 (g)

o sys

ΔSsys = -197 J/K

Calculate ΔSuniv and state whether the reaction occurs spontaneously at this temperature.

Delta S-univ = delta S-sys + delta S-surr delta S-surr = -delta H-sys / T *Using values for enthalpy of formation from tb N, H = 0 (because elements), NH3 = -91.8 Kj/ mol Thus, -91.8 / 298 (*units converted) = 308 J/ K mol delta S-surr = -197 + 308 = 111 J/ K mol Hence, the reaction is spontaneous because the value is positive

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