Entropy, Spontaneous and  Nonspontaneous Processes

Which of the following are spontaneous processes?

a) A grain of salt dissolves in water.

b) A rusty knife turns shiny.

c) Gas burning in a stove. 

d) A cup of sparkling water loses the CO₂. 

e) Water changing color after adding a food dye.

f) A wall of bricks is built.

Predict the sign of ΔS^o, if possible, for each of the following reactions.

a) 2K(s) + Cl₂(g) → 2KCl(s)

b) 2NO(g) + O₂(g) → 2NO₂(g)

c) CO(g) + H₂O(g) → CH₃OH(g)

d) N₂(g) + 2O₂(g) → 2NO₂(g)

e) 4NH₃(g) + 5O₂(g) → 4NO(g) + 6H₂O(g)

f) 2C₂H₂(g) + 3O₂(g) → 4CO(g) + 2H₂O(g)

g) C₂H₄(g) + 3O₂(g) → 2CO₂(g) + 2H₂O(l)

h) 2Al(s) + 3H₂O(l) → Al₂O₃(s)+ 3H₂(g)

ΔS for Phase Change

Determine the change in entropy, ΔS that occurs in the system when 1.00 mole of benzene (C₆H₆) melts at its melting point (5.5 °C). The heat of fusion for benzene is 9.92 kJ/mol.

Isopropanol (C₃H₈O) is used as rubbing alcohol. The heat of vaporization of isopropanol at its boiling point (82.5 ^oC) is 39.9 kJ/mol. What is the entropy change, ΔS when 1.30 mol C₃H₈O vaporizes at its boiling point?

Liquid nitrogen has many applications in chemical laboratories. Calculate the change in entropy, ΔS that occurs in the system when 8.60 mole of nitrogen condenses from a gas to a liquid at its boiling point (-196 °C). The heat of vaporization of nitrogen is 2.7928 kJ/mol.

What is the entropy change, ΔS when 45.0 g of diethyl ether (C₄H₁₀O) freezes at its melting point (-116.3 °C). The heat of fusion of the diethyl is 7.27 kJ/mol.

Chloroform, CHCl₃, is a common organic solvent once used as an anesthetic. Given that the heat of vaporization of chloroform is 29.24 kJ/mol, calculate the entropy change, ΔS of the system when 1.00 mol of CHCl₃ evaporates at its boiling point (61.2 °C). What is the entropy of the gaseous chloroform at this temperature if the standard entropy of chloroform is 295.6 J/(mol K).

Using the data in the attached Appendix, calculate the standard entropy changes, ΔS for the following reactions at 25°C:

a) 2KO₂(aq)+ 2H₂O(l) → 2KOH(aq) + O₂(g)+ H₂O₂(l)

b) C₂H₅OH(l) + 3O₂(g) → 2CO₂(g) + 3H₂O(g)

c) C₂H₄(g) + H₂(g) → C₂H₆(g)

d) C(s)_graphite + H₂O(g) → CO(g) + H₂(g)

e) 3NO₂(g) + H₂O(l) → 2HNO₃(aq) + NO(g)

f) 2H₂S(g) + 3O₂(g) → 2H₂O(l) + 2SO₂(g)

g) N₂O(g) + 3H₂(g) → N₂H₄(l) + H₂O(l)

h) 2C₃H₇OH(l) + 9O₂(g) → 6CO₂(g) + 8H₂O(l)

Given the ΔH°_rxn, calculate the ΔS_surr for each reaction at the same temperature.

a) ΔH°_rxn = -2560 kJ, T = 298 K

b) ΔH °_rxn = -454 kJ, T = 298 K

c) ΔH^o _rxn= 59 kJ, T = 250 K

d) ΔH^o _rxn= 148 kJ, T = 360 K

Determine whether each reaction is spontaneous or not by calculating the ΔS_univ based on the values of ΔH °_rxn, ΔS °_rxn, and T. Assume that all the components in the reaction are in their standard states.

a) ΔH °_rxn = +126 kJ; ΔS °_rxn = -231 J/K; T = 298 K

b) ΔH °_rxn = -5 kJ; ΔS °_rxn = +139 J/K; T = 298 K

Gibbs Free Energy, ΔG

Using the data for standard free energies of formations in the attached appendix, calculate the standard free energy of each reaction at 25 ^oC.

a) 2C₂H₆(g) + 7O₂(g) → 4CO₂(g) + 6H₂O(l)

b) 6Cl₂(g) + 2Fe₂O₃(s) → 4FeCl₃(s) + 3O₂(g)

c) 2CH₃OH(g) + H₂(g) → C₂H₆(g) + 2H₂O(g)

d) Fe₂O₃(s) + 3CO(g) → 2Fe(s) + 3CO₂(g)

Given the values of ΔH and ΔS, which of the following changes will be spontaneous at constant T and P?

a) ΔH = +35 kJ, ΔS = +10 J/K, T = 300. K

b) ΔH = +45 kJ, ΔS = +153 J/K, T = 312 K

c) ΔH = – 20. kJ, ΔS = +8.0 J/K, T = 298 K

d) ΔH = – 15 kJ, ΔS = -60. J/K, T = 250 K

At what temperatures will the following processes be spontaneous?

a) ΔH = +25.0 kJ, ΔS = +40.0 J/K

b) ΔH = -5.00 kJ, ΔS = -30.0 J/K

c) ΔH = -20.0 kJ, ΔS = +60.0 J/K

c) ΔH = +45.0 kJ, ΔS = -70.0 J/K

Given the data for the three combustion reactions below, calculate the free energy of the reaction producing methanol (CH₃OH) from carbon monoxide and hydrogen gas.

CO(g) + 2H₂(g) → CH₃OH(g), ΔG^o = ?

1) 2CO(g) + O₂(g) → 2CO₂(g), ΔG^o= -514 kJ

2) 2H₂(g) + O₂(g) → 2H₂O(g), ΔG^o = -458 kJ

3) 2CH₃OH(g) + 3O₂(g) → 2CO₂(g) + 4H₂O(g), ΔG^o = −1378 kJ

ΔG at Nonstandard Conditions, ΔG and Equilibrium Constant

Consider the evaporation of ethanol at 25.0 °C:

C₂H₅OH(l) → C₂H₅OH(g)

a) Determine the ΔG° at standard conditions when T = 25.0 °

b) Determine the ΔG at 25.0 °C when the pressure of ethanol is 0.845 atm.

Using data from the attached appendix (or the one from your textbook), calculate ΔG for the following reaction at 298 K and the given partial pressures:

2NOCl(g) ⇆ 2NO(g) + Cl₂(g)

P_NOCl = 1.00 x 10^-3 atm, P_NO = 2.00 x 10^-2 atm, PCl₂ = 1.00 x 10^-2 atm

Using the data from the attached appendix (or the one from your textbook), calculate ΔG for the reaction at 298 K and the following partial pressures:

4HCl(g) + O₂(g) ⇆ 2Cl₂(g) + 2H₂O(g)

P_HCl = 50.0 mmHg, P_O2 = 35.0 mmHg, P H₂O = 125 mmHg, P_Cl2 = 182 mmHg

Using the data from the attached appendix (or the one from your textbook), calculate the equilibrium constants at 25 °C for each reaction.

a) 2SO₃(g) ⇆ 2SO₂(g) + O₂(g)

b) NO(g) + O₃(g) ⇆ NO₂(g) + O₂(g)

Calculate the equilibrium constants for the reactions in the previous problem at 495 K.

a) 2SO₃(g) ⇆ 2SO₂(g) + O₂(g)

b) NO(g) + O₃(g) ⇆ NO₂(g) + O₂(g)

Using data from the attached appendix (or the one from your textbook), calculate the equilibrium constants at 295 °C for each reaction.

a) PCl₃(g) + Cl₂(g) ⇆ PCl₅(g)

b) N₂O₄(g) ⇆ 2NO₂(g)

Calculate K_P for the following reaction at 25°C:

H₂(g) + Br₂(g) ⇆ 2HBr(g) ΔG°= -106 kJ

Consider the dissociation reaction of Al(OH)₃ at 25 °C:

Al(OH)₃(s) ⇆ Al³⁺(aq) + 3OH^–(aq)

Calculate ΔG° for the reaction if K_sp = 2.0 x 10^-32

Use the data in the appendix to calculate the equilibrium constant for the dissociation of AgCl at 25°C.

AgCl(s) ⇆ Ag⁺(aq) + Cl^–(aq)

How does it compare to the textbook value of K_sp = 1.6 x 10^-10