Q: Given the reaction: CH$$_4(g) + O$_2(g$$) $$\rightarrow CO$_2(g) + 2 H$_2O(g) + O$_3(g$$), calculate $$\Delta G_{rxn}^\circ at 25$$°C using the following values: $$\Delta G_f^\circ(CH$_4) = -50.5 kJ/$$mol, $$\Delta G_f^\circ(O$_2) = 0$$, $$\Delta G_f^\circ(CO$_2) = -394.4 kJ/$$mol, $$\Delta G_f^\circ(H$_2O) = -228.6 kJ/$$mol, $$\Delta G_f^\circ(O$_3) = 163.2 kJ/$$mol.

$$\Delta G_{rxn}^\circ = [-394.4 + 2 \times (-228.6) + 163.2] - [-50.5 + 0] = -738.9 kJ$$

Question 1

Which statement best describes the change in entropy ($$S) $$when water freezes (liquid to solid) at 0°C under standard atmospheric pressure?

Accepted Answer

Entropy of the system decreases because the molecules become more ordered.

Question 2

Which equation correctly defines Gibbs Free Energy ($$G) in $$terms of enthalpy ($$H) $$and entropy ($$S$$)?

Accepted Answer

$$G = H - TS$$

Question 3

According to the Third Law of Thermodynamics, what is the entropy of a perfect crystal at absolute zero?

Accepted Answer

It is zero.

Question 4

Order the following substances from least to most entropy: H$$_2O (l$$), H$$_2O (s$$), H$$_2O$_2 (l$$), C (s, diamond), D$$_2O (l).$$

Accepted Answer

C (s, diamond) \u003c H$$_2O (s$$) \u003c H$$_2O (l$$) \u003c D$$_2O (l$$) \u003c H$$_2O$_2 (l)$$

Question 5

Which of the following reactions is spontaneous at standard conditions based on the provided $$9G_{rxn}$$ values?

Accepted Answer

H$$_2O (g) + CO (g$$) $$\rightarrow H$_2 (g) + CO$_2 (g$$), $$\Delta G_{rxn}^\circ = -28.6 kJ$$

Question 6

Given the reaction: CH$$_4(g) + O$_2(g$$) $$\rightarrow CO$_2(g) + 2 H$_2O(g) + O$_3(g$$), calculate $$\Delta G_{rxn}^\circ at 25$$°C using the following values: $$\Delta G_f^\circ(CH$_4) = -50.5 kJ/$$mol, $$\Delta G_f^\circ(O$_2) = 0$$, $$\Delta G_f^\circ(CO$_2) = -394.4 kJ/$$mol, $$\Delta G_f^\circ(H$_2O) = -228.6 kJ/$$mol, $$\Delta G_f^\circ(O$_3) = 163.2 kJ/$$mol.

Accepted Answer

$$\Delta G_{rxn}^\circ = [-394.4 + 2 	imes (-228.6) + 163.2] - [-50.5 + 0] = -738.9 kJ$$

Question 7

For the reaction SO$$_2(g) + O$_2(g$$) $$\rightarrow SO$_3(g$$), calculate $$\Delta G_{rxn}^\circ at 25$$°C using the following data: $$\Delta H_f^\circ(SO$_2) = -296.8 kJ/$$mol, $$\Delta H_f^\circ(SO$_3) = -395.7 kJ/$$mol, $$S^\circ(SO$_2) = 248.2 J/$$mol·K, $$S^\circ(O$_2) = 205.2 J/$$mol·K, $$S^\circ(SO$_3) = 256.8 J/$$mol·K.

Accepted Answer

$$\Delta G_{rxn}^\circ = [-395.7] - [-296.8 + 0] - [256.8 - (248.2 + 205.2)] 	imes 298.15 / 1000 = -98.9 - (-196.6) = -98.9 kJ$

Question 8

Which equation relates the equilibrium constant ($$K) to $$the standard Gibbs free energy change ($$\Delta G^\circ$$)?

Accepted Answer

$$K = e$$^{-\frac{\Delta G^\circ}$${RT}}$$

Question 9

If $$\Delta G_{rxn}^\circ$$ for a reaction is positive, what can you conclude about the equilibrium constant ($$K) $$for the reaction?

Accepted Answer

$$K \u003c 1$$

Question 10

A reaction has $$\Delta H^\circ \u003e 0$$ and $$\Delta S^\circ \u003e 0. $$According to the plot of Gibbs free energy vs. temperature, at what temperature range will the reaction be spontaneous?

Accepted Answer

At high temperatures

Question 11

For the reaction 2NO(g) + O$$_2(g$$) $$\rightarrow 2NO$_2(g$$), $$\Delta G_{rxn}^\circ = -71.2 kJ at 298 K. If $$the partial pressures are $$P_{NO} = 0.100$$ atm, $$P_{O_2$} = 0.100$$ atm, $$P_{NO_2$} = 2.00$$ atm, is the reaction more or less spontaneous than under standard conditions?

Accepted Answer

More spontaneous because $$Q \u003c K$$

Question 12

Which statement is true regarding the spontaneity of a reaction when $$\Delta G = 0$$?

Accepted Answer

The reaction is at equilibrium and will not proceed in either direction.

Question 13

Which of the following best explains why water evaporates from clothes on a line even though $$\Delta G^\circ$$ for vaporization is positive?

Accepted Answer

Water vapor is not in its standard state, so $$\Delta G$$ can be negative under nonstandard conditions.

Question 14

Which equation allows you to calculate $$\Delta G_{rxn}$$ for a reaction under nonstandard conditions?

Accepted Answer

$$\Delta G_{rxn} = \Delta G_{rxn}^\circ + RT \ln Q$$

Question 15

If a reaction has $$K = 1$$, what is the value of $$\Delta G_{rxn}^\circ$$?

Accepted Answer

$$\Delta G_{rxn}^\circ = 0$$

Question 16

Which of the following is a correct real-world application of Gibbs Free Energy in predicting reaction spontaneity?

Accepted Answer

Combining CO and H$$_2O to $$produce H$$_2$$ and CO$$_2 is $$spontaneous under standard conditions.

Question 17

Which statement about the relationship between $$\Delta G^\circ$$, $$K$$, and temperature is correct?

Accepted Answer

$$\Delta G^\circ is $$constant for a given reaction, but $$K$$ changes with temperature.

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