Q: A reaction has $$\Delta H = 111.4 kJ $$and $$\Delta S = 20.8 J/K. $$Calculate $$\Delta G at$$ $$T = 298 K. Is $$the reaction spontaneous at this temperature?

$$\Delta G = 111.4\ \text{kJ} - (298\ \text{K})(0.0208\ \text{kJ/K}) = 105.2\ \text{kJ}$$; The reaction is nonspontaneous.

Q: For the reaction $$\text{N}_2(g) + 3\text{H}_2(g) \rightarrow 2\text{NH}_3(g)$$, $$\Delta H = -92.6 kJ $$and $$\Delta S = -198.3 J/K. At $$what temperature does the reaction change from spontaneous to nonspontaneous?

$$T = \frac{\Delta H}{\Delta S} = \frac{-92.6\ \text{kJ}}{-0.1983\ \text{kJ/K}} = 467\ \text{K}$$

Q: Calculate $$\Delta G$$ for the reaction $$\text{P}_4(s) + 5\text{O}_2(g) \rightarrow \text{P}_4\text{O}_{10}(s) at 25$$°C, given $$\Delta H = -2984 kJ $$and $$\Delta S = -220 J/K.$$

$$\Delta G = -2984\ \text{kJ} - (298\ \text{K})(-0.220\ \text{kJ/K}) = -2930.4\ \text{kJ}$$

Q: For the reaction $$2\text{A}(g) + 8\text{B}(l) \rightarrow 3\text{AB}_3(g) + 8\text{C}(l)$$, $$\Delta H = 112.7 kJ $$and $$\Delta S = 78.9 J/K. At $$what temperature will the reaction become spontaneous?

$$T = \frac{\Delta H}{\Delta S} = \frac{112.7\ \text{kJ}}{0.0789\ \text{kJ/K}} = 1429\ \text{K}$$

Question 1

Which of the following correctly describes the Gibbs Free Energy formula and its components?

Accepted Answer

The formula is $$\Delta G = \Delta H - T\Delta S$$, where $$\Delta H is $$enthalpy, $$T is $$temperature in Kelvin, and $$\Delta S is $$entropy.

Question 2

A reaction has $$\Delta H = 111.4 kJ $$and $$\Delta S = 20.8 J/K. $$Calculate $$\Delta G at$$ $$T = 298 K. Is $$the reaction spontaneous at this temperature?

Accepted Answer

$$\Delta G = 111.4\ 	ext{kJ} - (298\ 	ext{K})(0.0208\ 	ext{kJ/K}) = 105.2\ 	ext{kJ}$$; The reaction is nonspontaneous.

Question 3

Given $$\Delta H \u003e 0$$ and $$\Delta S \u003e 0$$ for a reaction, under what temperature conditions will the reaction be spontaneous?

Accepted Answer

At high temperatures only.

Question 4

For the reaction $$	ext{N}_2(g) + 3	ext{H}_2(g) ightarrow 2	ext{NH}_3(g)$$, $$\Delta H = -92.6 kJ $$and $$\Delta S = -198.3 J/K. At $$what temperature does the reaction change from spontaneous to nonspontaneous?

Accepted Answer

$$T = \frac{\Delta H}{\Delta S} = \frac{-92.6\ 	ext{kJ}}{-0.1983\ 	ext{kJ/K}} = 467\ 	ext{K}$$

Question 5

Which statement best describes the spontaneity of a reaction when $$\Delta G \u003c 0$$?

Accepted Answer

The reaction is spontaneous as written.

Question 6

Calculate $$\Delta G$$ for the reaction $$	ext{P}_4(s) + 5	ext{O}_2(g) ightarrow 	ext{P}_4	ext{O}_{10}(s) at 25$$°C, given $$\Delta H = -2984 kJ $$and $$\Delta S = -220 J/K.$$

Accepted Answer

$$\Delta G = -2984\ 	ext{kJ} - (298\ 	ext{K})(-0.220\ 	ext{kJ/K}) = -2930.4\ 	ext{kJ}$$

Question 7

For the reaction $$2	ext{A}(g) + 8	ext{B}(l) ightarrow 3	ext{AB}_3(g) + 8	ext{C}(l)$$, $$\Delta H = 112.7 kJ $$and $$\Delta S = 78.9 J/K. At $$what temperature will the reaction become spontaneous?

Accepted Answer

$$T = \frac{\Delta H}{\Delta S} = \frac{112.7\ 	ext{kJ}}{0.0789\ 	ext{kJ/K}} = 1429\ 	ext{K}$$

Question 8

Nickel has $$\Delta H_{fus} = 370.4 kJ/$$mol and $$\Delta S_{fus} = 112.3 J/$$mol·K. Will nickel boil at 2700°C and 1 atm?

Accepted Answer

No, because $$T_{boil} = \frac{\Delta H_{fus}}{\Delta S_{fus}} = 3297\ 	ext{K}$$, which is higher than 2973 K.

Question 9

Which of the following is true about the standard Gibbs Free Energy of formation ($$\Delta G_f^\circ) $$for elements in their standard state?

Accepted Answer

$$\Delta G_f^\circ is $$always zero for elements in their standard state.

Question 10

Calculate $$\Delta G^\circ_{rxn}$$ for the reaction $$	ext{Fe}_2	ext{O}_3(s) + 3	ext{H}_2(g) ightarrow 2	ext{Fe}(s) + 3	ext{H}_2	ext{O}(l) at 25$$°C, given $$\Delta G_f^\circ$$ values: $$	ext{Fe}_2	ext{O}_3(s) = -740.0 kJ/$$mol, $$	ext{H}_2(g) = 0$$, $$	ext{Fe}(s) = 0$$, $$	ext{H}_2	ext{O}(l) = -237.2 kJ/$$mol.

Accepted Answer

$$\Delta G^\circ_{rxn} = [2(0) + 3(-237.2)] - [-740.0 + 3(0)] = -711.6 + 740.0 = 28.4\ 	ext{kJ}$$

Question 11

Which of the following reactions will always be spontaneous at all temperatures?

Accepted Answer

$$\Delta H  0$$

Question 12

If $$\Delta G$$ for a reaction is positive, what does this indicate about the reaction under those conditions?

Accepted Answer

The reaction is nonspontaneous as written.

Question 13

For the reaction $$	ext{HNO}_3(g) + 	ext{NH}_3(g) ightarrow 	ext{NH}_4	ext{NO}_3(s)$$, given $$\Delta G_f^\circ$$ values: $$	ext{HNO}_3(g) = -78.9 kJ/$$mol, $$	ext{NH}_3(g) = -16.4 kJ/$$mol, $$	ext{NH}_4	ext{NO}_3(s) = -183.5 kJ/$$mol, calculate $$\Delta G^\circ_{rxn}.$$

Accepted Answer

$$\Delta G^\circ_{rxn} = [-183.5] - [-78.9 + (-16.4)] = -183.5 + 95.3 = -88.2\ 	ext{kJ}$$

Question 14

Which of the following best explains why $$\Delta G is $$temperature dependent?

Accepted Answer

Because the $$T\Delta S$$ term in $$\Delta G = \Delta H - T\Delta S$$ means that entropy's contribution to free energy increases with temperature.

Question 15

A reaction has $$\Delta H = -50 kJ $$and $$\Delta S = -100 J/K. At $$what temperature does the reaction become nonspontaneous?

Accepted Answer

$$T = \frac{\Delta H}{\Delta S} = \frac{-50\ 	ext{kJ}}{-0.100\ 	ext{kJ/K}} = 500\ 	ext{K}$$

Question 16

Which of the following is a correct application of the Gibbs Free Energy of Reaction formula?

Accepted Answer

$$\Delta G^\circ_{rxn} = \sum \Delta G^\circ_f(	ext{products}) - \sum \Delta G^\circ_f(	ext{reactants})$$

Gibbs Free Energy Calculations and Spontaneity in Chemical Reactions

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