16.4 Free Energy

A reaction has $\Delta H °$ = 100 kJ/mol and $\Delta S ° = \text{250 J}/\text{mol}\cdot\text{K}.$ Is the reaction spontaneous at room temperature? If not, under what temperature conditions will it become spontaneous?

Use the standard free energy of formation data in Appendix G to determine the free energy change for each of the following reactions, which are run under standard state conditions and 25 °C. Identify each as either spontaneous or nonspontaneous at these conditions.

(a) $\text{MnO}_{2} \left(s\right) \rightarrow \text{Mn} \left(s\right) + \text{O}_{2} \left(g\right)$

(b) $\text{H}_{2} \left(g\right) + \text{Br}_{2} \left(l\right) \rightarrow \text{2HBr} \left(g\right)$

(c) $\text{Cu} \left(s\right) + \text{S} \left(g\right) \rightarrow \text{CuS} \left(s\right)$

(d) $\text{2LiOH} \left(s\right) + \text{CO}_{2} \left(g\right) \rightarrow \text{Li}_{2} \text{CO}_{3} \left(s\right) + \text{H}_{2} \text{O} \left(g\right)$

(e) $\text{CH}_{4} \left(g\right) + \text{O}_{2} \left(g\right) \rightarrow \text{C} \left(s , \text{graphite}\right) + \text{2H}_{2} \text{O} \left(g\right)$

(f) $\text{CS}_{2} \left(g\right) + \text{3Cl}_{2} \left(g\right) \rightarrow \text{CCl}_{4} \left(g\right) + \text{S}_{2} \text{Cl}_{2} \left(g\right)$

Given:
$\text{P}_{4} \left(s\right) + \text{5O}_{2} \left(g\right) \rightarrow \text{P}_{4} \text{O}_{10} \left(s\right) \Delta G ° = −\text{2697}.\text{0 kJ}/\text{mol}$
$\text{2H}_{2} \left(g\right) + \text{O}_{2} \left(g\right) \rightarrow \text{2H}_{2} \text{O} \left(g\right) \Delta G ° = −\text{457}.\text{18 kJ}/\text{mol}$
$\text{6H}_{2} \text{O} \left(g\right) + \text{P}_{4} \text{O}_{10} \left(s\right) \rightarrow \text{4H}_{3} \text{PO}_{4} \left(l\right) \Delta G ° = −\text{428}.\text{66 kJ}/\text{mol}$

(a) Determine the standard free energy of formation, $\Delta G_{\text{f}}^{\circ} ,$ for phosphoric acid.

(b) How does your calculated result compare to the value in Appendix G? Explain.

Consider the decomposition of red mercury(II) oxide under standard state conditions.
$\text{2HgO} \left(s , \text{red}\right) \rightarrow \text{2Hg} \left(l\right) + \text{O}_{2} \left(g\right)$

(a) Is the decomposition spontaneous under standard state conditions?

(b) Above what temperature does the reaction become spontaneous?

Calculate ΔG° for each of the following reactions from the equilibrium constant at the temperature given.

(a) $\text{N}_{2} \left(g\right) + \text{O}_{2} \left(g\right) \rightarrow \text{2NO} \left(g\right) \text{T} = 2000 °\text{C} K_{p} = 4.1 \times 10^{−\text{4}}$

(b) $\text{H}_{2} \left(g\right) + \text{I}_{2} \left(g\right) \rightarrow \text{2HI} \left(g\right) \text{T} = 400 °\text{C} K_{p} = 50.0$

(c) $\text{CO}_{2} \left(g\right) + \text{H}_{2} \left(g\right) \rightarrow \text{CO} \left(g\right) + \text{H}_{2} \text{O} \left(g\right) \text{T} = 980 °\text{C} K_{p} = 1.67$

(d) $\text{CaCO}_{3} \left(s\right) \rightarrow \text{CaO} \left(s\right) + \text{CO}_{2} \left(g\right) \text{T} = 900 °\text{C} K_{p} = 1.04$

(e) $\text{HF} \left(a q\right) + \text{H}_{2} \text{O} \left(l\right) \rightarrow \text{H}_{3} \text{O}^{+} \left(a q\right) + \text{F}^{−} \left(a q\right) \text{T} = 25 °\text{C} K_{a} = 7.2 \times 10^{−\text{4}}$

(f) $\text{AgBr} \left(s\right) \rightarrow \text{Ag}^{+} \left(a q\right) + \text{Br}^{−} \left(a q\right) \text{T} = 25 °\text{C} K_{sp} = 3.3 \times 10^{−\text{13}}$

Calculate the equilibrium constant at 25 °C for each of the following reactions from the value of ΔG° given.

(a) $\text{O}_{2} \left(g\right) + \text{2F}_{2} \left(g\right) \rightarrow \text{2OF}_{2} \left(g\right) \Delta G ° = −\text{9}.\text{2 kJ}$

(b) $\text{I}_{2} \left(s\right) + \text{Br}_{2} \left(l\right) \rightarrow \text{2IBr} \left(g\right) \Delta G ° = \text{7}.\text{3 kJ}$

(c) $\text{2LiOH} \left(s\right) + \text{CO}_{2} \left(g\right) \rightarrow \text{Li}_{2} \text{CO}_{3} \left(s\right) + \text{H}_{2} \text{O} \left(g\right) \Delta G ° = −\text{79 kJ}$

(d) $\text{N}_{2} \text{O}_{3} \left(g\right) \rightarrow \text{NO} \left(g\right) + \text{NO}_{2} \left(g\right) \Delta G ° = −\text{1}.\text{6 kJ}$

(e) $\text{SnCl}_{4} \left(l\right) \rightarrow \text{SnCl}_{4} \left(l\right) \Delta G ° = \text{8}.\text{0 kJ}$

Calculate the equilibrium constant at the temperature given.

(a) $\text{O}_{2} \left(g\right) + \text{2F}_{2} \left(g\right) \rightarrow \text{2F}_{2} \text{O} \left(g\right) \left(\text{T} = 100 °\text{C}\right)$

(b) $\text{I}_{2} \left(s\right) + \text{Br}_{2} \left(l\right) \rightarrow \text{2IBr} \left(g\right) \left(\text{T} = 0.0 °\text{C}\right)$

(c) $\text{2LiOH} \left(s\right) + \text{CO}_{2} \left(g\right) \rightarrow \text{Li}_{2} \text{CO}_{3} \left(s\right) + \text{H}_{2} \text{O} \left(g\right) \left(\text{T} = 575 °\text{C}\right)$

(d) $\text{N}_{2} \text{O}_{3} \left(g\right) \rightarrow \text{NO} \left(g\right) + \text{NO}_{2} \left(g\right) \left(\text{T} = −10.0 °\text{C}\right)$

(e) $\text{SnCl}_{4} \left(l\right) \rightarrow \text{SnCl}_{4} \left(g\right) \left(\text{T} = 200 °\text{C}\right)$

Consider the following reaction at 298 K:
$\text{N}_{2} \text{O}_{4} \left(g\right) \rightleftharpoons \text{2NO}_{2} \left(g\right) K_{P} = 0.142$

What is the standard free energy change at this temperature? Describe what happens to the initial system, where the reactants and products are in standard states, as it approaches equilibrium.

Under what conditions is $\text{N}_{2} \text{O}_{3} \left(g\right) \rightarrow \text{NO} \left(g\right) + \text{NO}_{2} \left(g\right)$ spontaneous?

Hydrogen sulfide is a pollutant found in natural gas. Following its removal, it is converted to sulfur by the reaction $\text{2H}_{2} \text{S} \left(g\right) + \text{SO}_{2} \left(g\right) \rightleftharpoons \frac{3}{8} \text{S}_{8} \left(s , \text{rhombic}\right) + \text{2H}_{2} \text{O} \left(l\right) .$ What is the equilibrium constant for this reaction? Is the reaction endothermic or exothermic?

In the laboratory, hydrogen chloride (HCl(g)) and ammonia (NH₃(g)) often escape from bottles of their solutions and react to form the ammonium chloride (NH₄Cl(s)), the white glaze often seen on glassware. Assuming that the number of moles of each gas that escapes into the room is the same, what is the maximum partial pressure of HCl and NH₃ in the laboratory at room temperature? (Hint: The partial…

Carbon dioxide decomposes into CO and O₂ at elevated temperatures. What is the equilibrium partial pressure of oxygen in a sample at 1000 °C for which the initial pressure of CO₂ was 1.15 atm?

Determine ΔGº for the following reactions.

(a) Antimony pentachloride decomposes at 448 °C. The reaction is:
$\text{SbCl}_{5} \left(g\right) \rightarrow \text{SbCl}_{3} \left(g\right) + \text{Cl}_{2} \left(g\right)$

An equilibrium mixture in a 5.00 L flask at 448 °C contains 3.85 g of SbCl₅, 9.14 g of SbCl₃, and 2.84 g of Cl₂.

(b) Chlorine molecules dissociate according to this reaction:
$\text{Cl}_{2} \left(g\right) \rightarrow 2 \text{Cl} \left(g\right)$

1.00% of Cl₂ molecules dissociate at 975 K and a pressure of 1.00 atm.

Determine the standard free energy change, $\Delta G_{\text{f}}^{\circ} ,$ for the formation of S²⁻(aq) given that the $\Delta G_{\text{f}}^{\circ}$ for Ag⁺(aq) and Ag₂S(s) are 77.1 kJ/mole and −39.5 kJ/mole respectively, and the solubility product for Ag₂S(s) is 8 $\times$ 10⁻⁵¹.

The evaporation of one mole of water at 298 K has a standard free energy change of 8.58 kJ.
$\text{H}_{2} \text{O} \left(l\right) \rightleftharpoons \text{H}_{2} \text{O} \left(g\right) \Delta G ° = \text{8}.\text{58 kJ}$

(a) Is the evaporation of water under standard thermodynamic conditions spontaneous?

(b) Determine the equilibrium constant, K_P, for this physical process.

(c) By calculating ∆G, determine if the evaporation of water at 298 K is spontaneous when the partial pressure of water, $P_{\text{H}_{2} \text{O}} ,$ is 0.011 atm.

(d) If the ev…

One of the important reactions in the biochemical pathway glycolysis is the reaction of glucose-6-phosphate (G6P) to form fructose-6-phosphate (F6P):
$\text{G6P} \rightleftharpoons \text{F6P} \Delta G ° = \text{1}.\text{7 kJ}$

(a) Is the reaction spontaneous or nonspontaneous under standard thermodynamic conditions?

(b) Standard thermodynamic conditions imply the concentrations of G6P and F6P to be 1 M, however, in a typical cell, they are not even close to these values.…

When ammonium chloride is added to water and stirred, it dissolves spontaneously and the resulting solution feels cold. Without doing any calculations, deduce the signs of ΔG, ΔH, and ΔS for this process, and justify your choices.

What happens to $\Delta G$ (becomes more negative or more positive) for the following chemical reactions when the partial pressure of oxygen is increased?

(a) $\text{S} \left(s\right) + \text{O}_{2} \left(g\right) \rightarrow \text{SO}_{2} \left(g\right)$

(b) $\text{2SO}_{2} \left(g\right) + \text{O}_{2} \left(g\right) \rightarrow \text{2SO}_{3} \left(g\right)$

(c) $\text{HgO} \left(s\right) \rightarrow \text{Hg} \left(l\right) + \text{O}_{2} \left(g\right)$