CHEM 1050 Lecture Notes - Lecture 4: Gibbs Free Energy, Spontaneous Process, Joule

Model 1 – Spontaneous Processes Process Description Change in Enthalpy (∆H) Change in Entropy (∆S) Spontaneous? A Two pure → Homogeneous substances mixture ~ 0 Increasing Yes B Solute on Solute on one side of → both sides of membrane membrane ~ 0 Increasing Yes C Polypeptide → Individual chain amino acids Exothermic (negative) Increasing (positive) Yes D C3 H8 + 5O2 → 3CO2 + 4H2 O Exothermic Increasing Yes E 6CO2 + 6H2 O → C6 H12O6 + 6O2 Endothermic Decreasing No F Glucose → Starch Endothermic Decreasing No G Water → Ice Exothermic Decreasing Below 0 °C, yes Above 0 °C, no H Cold water (25 °C) → Hot water (60 °C) Endothermic Increasing Below 60 °C, no Above 60 °C, yes

Some of the processes in Model 1 are spontaneous—that is, they will occur without any additional work being done on the system. For example, a solute will diffuse across a membrane until the concentrations of both sides are equal. However, glucose will not spontaneously form from carbon dioxide and water in the atmosphere. The Second Law of Thermodynamics states that a process will be spontaneous when it results in an increase of total entropy in the universe. In other words, either the system or the surroundings must have an increase in entropy, or both. (Please note that the term “spontaneous” does not imply that the change will happen quickly. Rusting is spontaneous under the right conditions, but it can still occur very slowly.)

13. Predict the change in entropy of the surroundings for an endothermic reaction.

Q1. Which of the following processes are spontaneous and which are non spontaneous.
a) The combustion of natural gas
b) Extraction of Aluminum metal from its ore
c) A ball rolling down a hill
d) A bike going up a hill

Q2. Predict the entropy change (positive or negative) for the following processes/reactions
a) a lake freezing
b) weeding a garden
c) N2(g) + 2 H2(g) ? N2H4 (g)
d) Mg(s) + 2H2O(l) ? Mg(OH)2 (s) + H2(g)

Q3. The element Cesium (Cs) freezes at 28.4 C and its molar enthalpy of fusion ΔH_fusion = 2.09 kJ/mol.
a) When molten Cs solidifies to Cs (s) at its normal melting point, is the entropy change ΔS positive or negative?
b) Calculate the entropy change S when 15.0 g of Cs(l) solidifies at 28.4 C.

Q4. Using the values for standard molar entropies ΔS_f° from the appendix in your textbook, calculate ΔS° for the following reactions.
a) Be(OH)₂ (s) ? BeO (s) + H2O (g)
b) Mg(OH)2 (s) + 2 HCl (g) ? MgCl2 (s) + 2H2O (l)
c) 2CH4(g) ? C2H6 (g) + H2(g)

Q5. Using the data in the appendix of your textbook, calculate the Gibbs free energy change ΔG° for the following reactions. In each case, indicate whether the reaction is spontaneous or not
a) H2 (g) + Cl2(g) ? 2HCl (g)
b) 2 POCl3 (g) ? 2 PCl3 (g) + O2 (g)

Q6. Consider the reaction 2 NO2 (g)---N2O4 (g)
a) Using the data in the appendix in your text, calculate the standard Gibbs free energy change (ΔG°) for the reaction at 298K.
b) For the above reaction, calculate the value of Keq at 298K
c) For the same reaction, calculate G at 298 K when the partial pressures for NO₂ and N2O4 are 0.40 atm and 0.36 atm, respectively.

Q7. Consider the reaction I2 (g) + Cl2 (g)----2 ICl (g) Kp = 81.9 at 298 K
a) Calculate the standard free energy change (ΔG°)
b) What will be the Free energy change when the above reaction is at equilibrium
c) Calculate G for the reaction at 298 K when PICl = 2.55 atm, PI2=0.325 atm and PCl2 = 0.221 atm

Q8. Consider the decomposition of Lead carbonate PbCO3 (s) ? PbO(s) + CO2 (g)
a) Calculate the Gibbs free energy change (ΔG°) for the reaction at298 K.
b) Calculate G for the reaction at 400 K.
c) Write down the equilibrium expression and calculate the value of Keq at 298 K
d) Calculate the partial pressure of CO2 at 298 K. (Hint: Look at the equilibrium expression and the value of Keq at 298 K)

Q9. For the reaction: 2Al(s) + 3/2 O2(g) ? Al2O3(s), ΔH^o_rxn = -1617 kJ/mol and ΔH^o_rxn = -1577 kJ/mol. Use this data to calculate ΔS^o_rxn reaction at 298 K.

Q10. Calculate the ΔG^o for the following reaction using the data from your text:
2SO2(g) + O2(g) ? 2SO3(g)

Q11. Using the thermodynamic data available from the Appendix(?Go’s), calculate ΔG^o rxn and calculate the equilibrium constant(K) for the reaction at 25 oC:
CaCO3(s) ? CaO(s) + CO2(g)

Q12. What is the minimum temperature required for the spontaneous conversion of CCl4(l) to CCl4(g) when ΔH°(vap) is 57.3 kJ/mol andΔS°(vap) is 164 J/(mol K)? reaction: CCl4(l) ? CCl4(g)

Q13. Given the following
Fe2O3(s) + 3CO(g) . ? 2Fe(s) + 3CO2(g) ΔG° =  29.4 kJ
3Fe2O3(s) + CO(g) . ? 2Fe3O4(s) + CO2(g) ΔG° =  61.6 kJ
Calculate ΔG° for Fe(s) + Fe2O3(s) + CO2(g) ? Fe3O4(s) +CO(g)

Q14. Calculate ΔG° rxn for 2CO(g) + O2(g) ? 2CO2(g) and then calculate ΔG for the reaction at 298K; if the pressure of CO =20. atm,P O2 = 10. atm and P CO2= 0.50 atm. Will increasing the pressure of the reactants make the reaction more or less spontaneous? Explain using your calculations and Le Chatelier’s principle.

Q15. Write the reaction for photosynthesis (production ofC6H12O6(s) and oxygen from carbon dioxide and water as a gas).Calculate ?H, ? S, and ?G for the reaction at standard state. Is the reaction spontaneous?