Given the following reaction: CO(NH₂)₂(g) + 3/2 O₂(g) → CO₂(g) + N₂(g) + 2 H₂O(l), ΔS° = +133.3 J/mol-K. Using the data below, calculate the ΔS°_f for urea.

Lead oxide can be reduced by carbon (graphite) to produce lead metal and carbon dioxide. Determine the temperature at which this reaction is spontaneous.

2 PbO(s) + C(s, graphite) → 2 Pb(s) + CO₂(g)

                            ΔH° (kJ/mol)           S° (J/mol•K)           ΔG° (kJ/mol)
PbO(s)                   –217.3                    68.70                  –187.9
C(s. graphite)         0                           5.69                        0
Pb(s)                       0                           68.85                      0
CO₂(g)                  –393.5                   213.6                    –394.4

One compound that is most often used as a biofuel additive for gasoline is ethanol (C₂H₅OH). Calculate the maximum amount of useful work that can be achieved by burning 1.00 mol of C₂H₅OH(g) under standard conditions.

                          ΔG° (kJ/mol)      
C₂H₅OH(g)        –168.5
O₂(g)                    0
CO₂(g)               –394.4
H₂O(l)                –237.13

(a) Predict the temperature at which the change in free energy for the conversion of Fe(s) to Fe(g) is zero. (b) The experimental melting point and boiling point of Fe are 1538°C and 2861°C, respectively. Which of the experimental values is closer to the values that you predicted?

                    ΔH° (kJ/mol)           S° (J/mol•K)
Fe(s)             0                             27.15
Fe(g)            415.5                       180.5

Calculate ΔH°, ΔS°, and ΔG° at 25.0°C for the following reaction: 2 Al(s) + 6 HCl(g) → 2 AlCl₃(s) + 3 H₂(g). Use the values given below:

                    ΔH° (kJ/mol)           S° (J/mol•K)
Al(s)             0                             28.32
AlCl₃(s)       –705.6                    109.3
HCl(g)         –92.30                    186.69
H₂(g)            0                             130.58

Ethanol can be prepared in several ways. It can be produced during alcohol fermentation (Reaction A). It is also produced commercially from ethylene (Reaction B). Calculate the ΔG°_rxn (kJ•mol^–1) of each reaction.

A. C₆H₁₂O₆(s) → 2 C₂H₅OH(l) + 2 CO₂(g)

B. C₂H₄(g) + H₂O(g) → C₂H₅OH(l)

Determine which method requires less energy under standard conditions.

Substance            ΔG°_f (kJ/mol)
C₆H₁₂O₆(s)           –910.4
C₂H₄(g)                   68.4
C₂H₅OH(l)           –174.8
H₂O(g)                 –228.6
CO₂(g)                 –394.4

Using the following reactions and their ΔG°_rxn values:

Cr₂O₃(s) + 3 CO(g) → 2Cr(s) + 3 CO₂(g)

Calculate the ΔG° (kJ) for the following reaction (express in one decimal place):

2 Cr(s) + 3/2 O₂(g) → Cr₂O₃(s),         ΔG°_rxn = –1058.1 kJ

CO(g) + 1/2 O₂(g) → CO₂(g),             ΔG°_rxn = –257.2 kJ