Entropy

1. Entropy Section 16-2

2. Enthalpy • What is enthalpy? • What does a +ΔH mean in terms of the energy of reactants and energy of products? • What does a +ΔH mean in terms of energy production or consumption? • What is an exothermic reaction in terms of ΔH?

3. Spontaneous Rxn? • Spontaneous – proceeds without inputting energy • How is this similar to Exothermic (-ΔH)? • How is this different than Exothermic (-ΔH)?

4. Enthalpy & Reaction Tendency • Most reactions in nature are exothermic • Tendency in nature for a reaction to proceed in a direction that has less energy • Lower energy = More stability • Energy is inversely proportional to Stability

5. Page 2 • Melting is one example of a naturally occurring endothermic process. • An ice cube melts spontaneously at room temperature as energy is transferred from the warm air to the ice. • The well-ordered arrangement of water molecules in the ice crystal is lost, and the less-ordered liquid phase of higher energy content is formed. • A system that can go from one state to another without an enthalpy change does so with an increase in entropy.

6. Question • The decomposition of ammonium nitrate: • 2NH4NO3(s)  2N2(g) + 4H2O(l) + O2(g) Which side of the reaction has less order (simpler)? ***The arrangement of particles on the right-hand side of the equation is more random than the arrangement on the left side and hence is less ordered.

7. Entropy • There is a tendency in nature to proceed in a direction that increases the randomness of a system. • A random system is one that lacks a regular arrangement of its parts. • This tendency toward randomness is called entropy. • Entropy is a measure of chaos or disorder • Entropy,S, can be defined in a simple qualitative way as a measure of the degree of randomness of the particles, such as molecules, in a system.

8. Entropy Changes for some rxns

9. States of Matter • To understand the concept of entropy, consider the comparison between particles in solids, liquids, and gases. • In a solid, the particles are in fixed positions, and we can easily determine the locations of the particles. • In a liquid, the particles are very close together, but they can move around. Locating an individual particle is more difficult. The system is more random, and the entropy is higher.

10. Higher entropy? • So which has higher entropy, solids or liquids? • In a gas, the particles are moving rapidly and are far apart. Locating an individual particle is much more difficult, and the system is much more random. The entropy is even higher. • Rank the states of matter in terms of entropy.

11. Entropy Change • Absolute entropy, or standard molar entropy, of substances are recorded in tables and reported in units of kJ/(mol•K). • Entropy change, which can also be measured, is defined as the difference between the entropy of the products and the reactants. • An increase in entropy is represented by a positive value for ∆S, and a decrease in entropy is represented by a negative value for ∆S.

12. ΔG or Free Energy • Processes in nature are driven in two directions: toward least enthalpy and toward largest entropy. • As a way to predict which factor will dominate for a given system, a function has been defined to relate the enthalpy and entropy factors at a given temperature and pressure. • This combined enthalpy-entropy function is called the free energy,G, of the system; it is also called Gibbs free energy.

13. Spontaneous • Spontaneity is determined by the sign of ΔG • If ΔG is (-), then spontaneous rxn • Will proceed w/o energy input • If ΔG is (+), then NONspontaneous rxn • Will only proceed with energy input

14. Free Energy Equation • Only the change in free energy can be measured. It can be defined in terms of enthalpy and entropy. • At a constant pressure and temperature, the free-energy change, ∆G, of a system is defined as the difference between the change in enthalpy, ∆H, and the product of the Kelvin temperature and the entropy change, which is defined as T∆S: • ∆G0= ∆H0– T∆S0

15. ∆G0= ∆H0– T∆S0 • Use various combinations of signs of ΔH & ΔS, to determine: • Which combination guarantees a spont. Rxn? • Which combination guarantees a NONspont. Rxn? • Which combination depends on temperature to determine spontaneity?

17. Sample Problem • For the reaction NH4Cl(s)  NH3(g) + HCl(g), at 298.15 K, ∆H0= 176 kJ/mol and ∆S0= 0.285 kJ/(mol•K). Calculate ∆G0, and tell whether this reaction is spontaneous in the forward direction at 298.15 K.

18. Sample Problem Solution • Given:∆H0 = 176 kJ/mol at 298.15 K ∆S0 = 0.285 kJ/(mol•K) at 298.15 K • Unknown:∆G0 at 298.15 K • Solution:The value of ∆G0 can be calculated according to the following equation: • ∆G0= ∆H0– T∆S0 • ∆G0= 176 kJ/mol – 298 K [0.285 kJ/(mol•K)] • ∆G0= 176 kJ/mol – 84.9 kJ/mol • ∆G0= 91 kJ/mol

19. Which of the following two conditions will favor a spontaneous reaction? A. an increase in entropy and a decrease in enthalpy B. an increase in entropy and an increase in enthalpy C. a decrease in entropy and a decrease in enthalpy D. a decrease in entropy and an increase in enthalpy

20. Which of the following two conditions will favor a spontaneous reaction? A.an increase in entropy and a decrease in enthalpy B. an increase in entropy and an increase in enthalpy C. a decrease in entropy and a decrease in enthalpy D. a decrease in entropy and an increase in enthalpy

21. Which of the following processes has a negative ∆S? A. evaporating 1 mol of a liquid B. raising the temperature of 1 L of water from 295 K to 350 K C. freezing of 1 mol of a liquid D. None of the above.

22. Which of the following processes has a negative ∆S? A. evaporating 1 mol of a liquid B. raising the temperature of 1 L of water from 295 K to 350 K C.freezing of 1 mol of a liquid D. None of the above.

23. At a constant pressure, the following reaction is exothermic: 2NO2(g)  N2O4(g). Which of the following statements is true about the reaction (as written)? A. The reaction is always spontaneous. B. The reaction is spontaneous at low temperatures, but not at high temperatures. C. The reaction is spontaneous at high temperatures, but not at low temperatures. D. The reaction is never spontaneous.

24. At a constant pressure, the following reaction is exothermic: 2NO2(g)  N2O4(g). Which of the following statements is true about the reaction (as written)? A. The reaction is always spontaneous. B.The reaction is spontaneous at low temperatures, but not at high temperatures. C. The reaction is spontaneous at high temperatures, but not at low temperatures. D. The reaction is never spontaneous.

25. For certain molecules, enthalpies of formation can be determined from combustion data. Using the diagram below, calculate the enthalpy of formation of methane gas, CH4(g), and the enthalpies for two of the combustion reactions shown on the diagram below. C(s) + O2(g)  CO2(g) ∆H = –393.5 kJ H2(g) + O2(g)  H2O(l) ∆H = ? CH4(g) + 2O2(g)  CO2(g) + 2H2O(l) ∆H = ?

26. Answer • The formation reaction for CH4(g) is C(s) + 2H2(g)  CH4(g). • From the graph, ∆H for H2(g) + O2(g)  H2O(l) is [965.1 kJ  (393.5 kJ)]/2 = 285.8 kJ. • The ∆H for CH4(g) + 2O2(g)  CO2(g) + 2H2O(l) can be read directly from the graph and is 890.2 kJ. • The enthalpy of formation for CH4(g) is 965.1 kJ + 890.2 kJ = 74.9 kJ.