Entropy and Free Energy

1. Entropy and Free Energy Reaction Spontaneity

2. Free Energy • Many chemical and physical processes release energy that can be used to bring about other changes. • EXAMPLE: The burning of gasoline releases energy that can be used to move a car. • Free energy – energy available to do work. • Free energy isn’t used efficiently. • Only about 30% of the free energy released by burning gasoline is actually used to move the car. • The rest is lost to friction and waste heat. • Living things are among the most efficient users of free energy, and even they are seldom more efficient than 70%. • It is physically impossible for any process to be made 100% efficient.

3. Free Energy • Energy can be obtained from a chemical reaction only if the reaction actually occurs. • Just because a balanced chemical equation can be written doesn’t mean that a chemical rxn will occur. • EXAMPLE: CO2(g)  C(s) + O2(g) • This equation is balanced, however: • Carbon dioxide does not decompose into carbon and oxygen by itself. • In fact, the reverse reaction tends to happen: carbon will burn in the presence of O2(g) to form carbon dioxide.

4. Spontaneous Vs Non-Spontaneous Reactions • Spontaneous Rxn – occurs naturally and favors the formation of products. • Spontaneous Rxns release free energy. • Non-Spontaneous Rxn – Does not favor the formation of products. • A Non-Spontaneous Rxn absorbs free energy. • Consider the rxn H2CO3(aq)  CO2(g) + H2O(l) • In the forward direction the rxn is highly spontaneous. • If you start with pure H2CO3, most of it will break down to produce CO2 and H2O. • The reverse rxn CO2(g) + H2O(l)  H2CO3(aq) is non-spontaneous. • If you start with CO2 and H2O, hardly any H2CO3 will form.

5. Spontaneous Vs Non-Spontaneous Reactions H2CO3(aq)  CO2(g) + H2O(l) Amount Left in Container Amount Left in Container Amount Left in Container H2CO3(aq) CO2(g) H2O(l) H2CO3(aq) CO2(g) H2O(l) H2CO3(aq) CO2(g) H2O(l) Start with pure H2CO3 The reaction reaches equilibrium with a lot of CO2 and H2O and not much H2CO3 left in the container.  Start with CO2 and H2O

6. Spontaneous Reactions • A spontaneous rxn is not necessarily a fast reaction. • Some reactions proceed so slowly that they may appear non-spontaneous. • EXAMPLE: Sugar spontaneously combines with oxygen to produce CO2 and H2O: • C12H22O11(s) + 12 O2(g)  12 CO2(g) + 11 H2O(l) • A bowl of sugar on a table top at room temperature may take thousands of years to react with the oxygen in the air, but it is happening. • How could you speed the reaction up?

7. Non-Spontaneous Reactions • Some rxns that are non-spontaneous at one set of conditions may be spontaneous at other conditions. • Non-spontaneous rxns can be driven by the constant input of energy. • EXAMPLE: Photosynthesis can be summarized by one non-spontaneous rxn: • 6 CO2(g) + 6 H2O(l)  C6H12O6(s) + 6 O2(g) • This rxn does not happen without a constant supply of energy. • Where does the energy to drive photosynthesis come from?

8. Non-Spontaneous Reactions • A non-spontaneous reaction can be made to occur if it is coupled to a spontaneous rxn. • Coupled rxns are common in living organisms. • In living cells, the energy stored in glucose can be released by a series of spontaneous rxns. • Special molecules in cells capture and transfer free energy to non-spontaneous rxns. • EXAMPLE: The formation of proteins, a non-spontaneous rxn, is driven by free energy stored in ATP molecules.

9. Entropy • What do we know so far? • Spontaneous processes (ones that happen naturally) release free energy. • Free energy = energy available to do work. • What about ice melting? • If you place an ice cube on a kitchen counter at room temperature, does the ice cube melt spontaneously? • We know from experience that ice melts spontaneously in room-temperature air. • Is the melting of ice endothermic or exothermic? • Ice must absorb heat energy to melt, so it must be endothermic. • How can an endothermic process be spontaneous?

10. Entropy • We said that spontaneous processes must release free energy. • Ice melting absorbs energy, and yet it occurs spontaneously at room temperature. • There must be some other factor (besides heat movement) that determines whether free energy is being absorbed or released. • This factor is called entropy.

11. Entropy • Entropy (S) – a measure of the disorder of a system. • A system that is highly organized (high potential energy) has a low degree of entropy. • A system that is highly randomized and disordered has a high degree of entropy. • The entropy of the universe must always increase. • Entropy = time’s arrow • Over time, universal entropy increases. • It is possible to decrease entropy locally, but only if entropy increases elsewhere by a greater amount. • Work must be done on a system to decrease its entropy. • More on this in a moment…

12. Changes in Entropy • An increase in entropy (+S) favors a spontaneous chem. rxn. • A decrease in entropy (-S) favors a non-spontaneous rxn. • Four ways in which entropy can increase: • Entropy increases when: • solid  liquid or liquid  gas • substance is divided into parts (dissolved) • total number of product molecules > reactant molecules • temperature increases • All of these changes involve particles becoming more disorganized or random.

13. SolidLiquid or LiquidGas • For a given substance, the entropy of the gas is greater than the entropy of the liquid or the solid. Similarly, the entropy of the liquid is greater than that of the solid. Thus entropy increases in reactions in which solid reactants form liquid or gaseous products. Entropy also increases when liquid reactants form gaseous products.

14. Substance is Divided Into Parts • Entropy increases when a substance is divided into parts. For instance, entropy increases when a crystalline ionic compound, such as sodium chloride, dissolves in water. This is because the solute particles – sodium ions and chloride ions – are more separated in solution than they are in the crystal form.

15. Product Molecules > Reactant Molecules • Entropy tends to increase in chemical reactions in which the total number of product molecules is greater than the total number of reactant molecules.

16. Increasing Temperature • Entropy tends to increase when temperature increases. As the temperature increases, the molecules move faster and faster, which increases the disorder.

17. Entropy Changes • Does each change represent an increase or decrease in entropy? • An ice cube melts. • INCREASE • Water freezes. • DECREASE • A cube of sugar dissolves in water. • INCREASE • A solid precipitates out of solution. • DECREASE • A dish falls to the floor and shatters. • INCREASE • A protein is formed from amino acids. • DECREASE

19. Heat, Entropy, and Free Energy • In every chem. rxn, heat is either released or absorbed. • H is positive = heat absorbed • H is negative = heat released • In every chem. rxn, entropy either increases or decreases. • S is positive = entropy increases • S is negative = entropy decreases • The size and direction of enthalpy (H) and entropy (S) changes together determine whether a rxn is spontaneous.

20. Heat, Entropy, and Free Energy • Favorability of enthalpy changes: • - H = favorable • + H = unfavorable • Favorability of entropy changes: • + S = favorable • - S = unfavorable • - H and + S = rxn is always spontaneous • Favors products under any conditions. • + H and - S = rxn is never spontaneous • Never favors products under any conditions.

21. Conditional Spontaneity • - H and - S • Enthalpy change is favorable but entropy change is not. • Rxn will be spontaneous when temperatures are low enough that the enthalpy change can overcome the unfavorable entropy change. • Rxn is spontaneous at relatively low temperatures. • + H and + S • Enthalpy change is unfavorable but entropy change is favorable. • Rxn will be spontaneous when temperatures are high enough to overcome the unfavorable enthalpy change. • Rxn is spontaneous at relatively high temperatures.

22. Reaction Spontaneity • Why does ice melt? • It is an endothermic change, which is unfavorable (H > o). • However, it also increases entropy (S > 0). • Liquid water has greater entropy than solid ice. • The change should only be spontaneous at relatively high temperatures…and it is! • Ice melts when the temperature is greater than 0ºC!