PRINCIPLES OF REACTIVITY: ENTROPY AND FREE ENERGY

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CHAPTER OVERVIEW

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This chapter examines factors that determine whether a reaction is spontaneous , product-favored , non-spontaneous , reactants favored.

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Review thermodynamic basics (next) 2

Thermodynamics

Thermodynamics is the science of heat (energy) transfer.

3 Heat energy is associated with molecular motions.

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CHEMICAL REACTIVITY

What drives chemical reactions? How do they occur?

The first is answered by THERMODYNAMICS the second by KINETICS .

and Have already seen a number of “driving forces” for reactions that are PRODUCT-FAVORED .

• • • • formation of a precipitate gas formation H 2 O formation (acid-base reaction) electron transfer in a battery

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CHEMICAL REACTIVITY

But ENERGY TRANSFER also allows us to predict reactivity.

In general, reactions that transfer energy to their surroundings are product-favored.

So, let us consider heat transfer in chemical processes.

19.1 SPONTANEOUS REACTIONS AND SPEED: THERMODYNAMICS VERSUS KINETICS 6

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A spontaneous or product-favored reaction is one in which most of the reactants can eventually be converted into products, given sufficient time. A non-spontaneous or reactant-favored reaction is one in which little of the reactants will be converted into products, regardless of the time allowed.

THERMODYNAMICS VERSUS KINETICS 7

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This can also be expressed in another way.

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Reactant-favored reactions are those in which the products will be converted to reactants, given sufficient time.

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Notice that the speed of the reaction is not an issue. Reaction speed is kinetics, Chapter 15. We are studying thermodynamics.

Entropy and Free Energy

How to predict if a reaction can occur, given enough time? THERMODYNAMICS 8 How to predict if a reaction can occur at a reasonable rate?

KINETICS

Thermodynamics

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Is the state of a chemical system such that a rearrangement of its atoms and molecules would decrease the energy of the system? If yes, system is favored to react — a product-favored system.

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Most product-favored reactions are exothermic.

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Thermodynamics

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Most product-favored reactions are exothermic.

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Often referred to as spontaneous reactions.

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Spontaneous does not imply anything about time for reaction to occur.

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Thermodynamics and Kinetics Diamond is thermodynamically favored to convert to graphite, but not kinetically favored.

Paper burns — a product favored reaction. Also kinetically favored once reaction begins.

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Product-Favored Reactions

In general, product favored reactions are exothermic .

Fe 2 O 3 (s) + 2 Al(s) ---> 2 Fe(s) + Al 2 O 3 (s) ΔH = - 848 kJ Thermite Reaction 12

Product-Favored Reactions

But many spontaneous reactions or processes are endothermic or even have Δ H = 0.

13 NH 4 NO 3 (s) + heat NH 4 NO 3 (aq)

14 19.2 DIRECTIONALITY OF REACTIONS: ENTROPY

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Spontaneous reactions occur because they generate a final state that is lower in energy, that is energy dispersed, and/or a final state that is more random or more disordered. The first condition is met by reactions that are exothermic.

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These reactions release heat to the universe resulting in more particles, molecules and/or atoms, having the energy that was originally concentrated on the reactants.

Entropy, S

One property common to product-favored processes is that the final state is more DISORDERED or RANDOM than the original.

SPONTANEITY IS RELATED TO AN INCREASE IN RANDOMNESS.

Reaction of K with water 15 The thermodynamic property related to randomness is ENTROPY, S .

Entropy: A Measure of Matter Dispersal or Disorder

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A perfect crystal at 0 Kelvin has no randomness or disorder. This statement is called the third law of thermodynamics. The thermodynamic function that represents the randomness of matter is called entropy and is given the symbol S. If energy is added to matter in such a way that there is essentially no temperature change we can calculate the change in entropy: Δ S = q/T 16

Entropy

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By adding up all these small changes from absolute zero to any temperature, T, the absolute entropy, S o of the substance at that temperature can be calculated.

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Appendix L has a list of these values for several pure substances at 298.15 K. The units on S o are e.u. or J/mole K. Table 20.1, page 917, is useful in identifying some general trends in entropy.

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Entropy For similar substances: •

S gas > S liquid > S solid

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S complex molecules S weak ionic bonds > S simple molecules > S strong ionic bonds

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S solution of solid or liquid > S solute + solvent

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*S solution of gas < S solute + solvent * volume of area is constricted for a gas when it is in a liquid note the less than symbol 18

19 The entropy of liquid water is greater than the entropy of solid water (ice) at 0 ° C.

Directionality of Reactions

How probable is it that reactant molecules will react? PROBABILITY suggests that a product-favored reaction will result in the dispersal of energy or of matter or both.

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Directionality of Reactions

Probability suggests that a product-favored reaction will result in the dispersal of energy or of matter or both.

Matter Dispersal 21

Directionality of Reactions

Probability suggests that a product favored reaction will result in the dispersal of energy or of matter or both.

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Energy Dispersal

Directionality of Reactions — Energy Dispersal

23 Exothermic reactions involve a release of stored chemical potential energy to the surroundings. The stored potential energy starts out in a few molecules but is finally dispersed over a great many molecules. The final state favored.

—with energy dispersed—is more probable and makes a reaction product-

Entropy, S

S (gases) > S (liquids) > S (solids) 24 S o (J/K•mol) H 2 O(liq) 69.91

H 2 O(gas) 188.8

Entropy, S

Entropy of a substance increases with temperature.

25 Molecular motions of heptane, C 7 H 16 Molecular motions of heptane at different temperatures.

Entropy, S

Increase in molecular complexity generally leads to increase in S.

S o (J/K•mol) CH 4 C 2 H 6 C 3 H 8 248.2

336.1 419.4

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Entropy, S

Entropies of ionic solids depend on coulombic attractions.

27 MgO NaF S o (J/K•mol) 26.9

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Entropy, S

Entropy usually increases when a pure liquid or solid dissolves in a solvent.

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Entropy Changes for Phase Changes 29 For a phase change, ΔS = q/T where q = heat transferred in phase change For H 2 O (liq) ---> H 2 O(g) Δ H = q = +40,700 J/mol

Entropy Changes for Phase Changes For a phase change, ΔS = q/T where q = heat transferred in phase change For H 2 O (liq) ---> H 2 O(g) ΔH = q = +40,700 J/mol 30

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S = q T = 40, 700 J/mol 373.15 K = + 109 J/K • mol

31 Entropy

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The entropy change for a change of state is calculated using the equation q/T, which becomes Δ H fus / T o for the fusion process.

See O.H. # 89 for graphical and equation information.

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The Δ H o vap for Al is 326 kJ/mole. The normal boiling point is 2467 o C. Calculate the entropy of vaporization, ΔS o vap , for Al. 119 e.u.

Entropy

Predict the sign of ΔS for each reaction below: X (g) ===> X (liq) X (s) ===> X (liq) + X (g) ===> X (aq) X (liq) ===> X (aq) + X (g) ===> X (s) 32

Calculating

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S for a Reaction

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S o =

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S o (products) -

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S o (reactants) Consider 2 H 2 (g) + O 2 (g) ---> 2 H 2 O(liq) Δ S o = 2 S o (H 2 O) - [2 S o (H 2 ) + S o (O 2 )] ΔS o Δ S o = 2 mol (69.9 J/K•mol) [2 mol (130.7 J/K•mol) + 1 mol (205.3 J/K•mol)] = -326.9 J/K Note that there is a decrease in S because 3 mol of gas give 2 mol of liquid.

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Figure 20.7

2 NO + O 2 2 NO 2 3 moles gas form 2 moles gas.

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S is negative.

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Entropy: Second Law of Thermodynamics

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The second law states that the entropy of the universe is increasing. For spontaneous, product-favored, reactions, ΔS o universe > 0 . This entropy change is calculated by considering the two terms that make up this entropy.

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Second Law of Thermodynamics

ΔS o universe = ΔS o surroundings + ΔS o system , where ΔS o surroundings = q surroundings / T = ΔH o system / T and Δ S o system = ΔS o (products) ΔS o (reactants), Equation 20.1.

Be sure to include the stoichiometric coefficient with each term.

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2nd Law of Thermodynamics

A reaction is spontaneous (product-favored) if ΔS for the universe is positive.

ΔS universe = ΔS system + ΔS surroundings ΔS universe > 0 for product-favored process First calculate entropy created by matter dispersal ( ΔS system ) Next, calculate entropy created by energy dispersal ( ΔS surround )

2nd Law of Thermodynamics

Dissolving NH 4 NO 3 water —an entropy driven process.

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2nd Law of Thermodynamics

2 H 2 (g) + O 2 (g) ---> 2 H 2 O(liq) Δ S o system = -326.9 J/K

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S o surroundings = q surroundings T = Δ H o rxn = Δ H o system = -571.7 kJ -

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H system T

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S o surroundings = - (-571.7 kJ)(1000 J/kJ) 298.15 K Δ S o surroundings = +1917 J/K 39

2nd Law of Thermodynamics

2 H 2 (g) + O 2 (g) ---> 2 H 2 O(liq) ΔS o system = -326.9 J/K ΔS o surroundings = +1917 J/K ΔS o universe = +1590. J/K The entropy of the universe is increasing, so the reaction is product-favored. Enthalpy driven.

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Second Law of Thermodynamics

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Table 19.2, page 804, shows how ΔH system and ΔS system can be used to predict the spontaneity of a reaction (product-favored).

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There are four possible cases which we will consider in another format using a new thermodynamic function G.

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