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Chapter 17: Problem 29

Use standard entropies and heats of formation to calculate \(\Delta G_{i}^{\circ}\) at \(25^{\circ} \mathrm{C}\) for (a) cadmium(II) chloride (s). (b) methyl alcohol, \(\mathrm{CH}_{3} \mathrm{OH}(l)\). (c) copper(I) sulfide (s).

Short Answer

Expert verified
Question: Calculate the standard Gibbs free energy change, \(\Delta G_{i}^{\circ}\), for the following compounds at 25°C: (a) cadmium(II) chloride, (b) methyl alcohol, and (c) copper(I) sulfide.

Step by step solution

01

Obtain standard entropies and heats of formation

Gather the relevant thermodynamic information for cadmium(II) chloride and its constituents (cadmium and chloride ions) from standard thermodynamic tables.
02

Calculate the standard entropy change

Determine the standard entropy change, \(\Delta S_{i}^{\circ}\), for the formation of cadmium(II) chloride, using the standard entropies of the products and reactants: \(\Delta S_{i}^{\circ} = [S_{CdCl_{2}(s)} - (S_{Cd(s)} + 2S_{Cl_{2}(g)}/2)]\)
03

Calculate the standard heat of formation

Determine the standard heat of formation, \(\Delta H_{i}^{\circ}\), for the formation of cadmium(II) chloride, using the heats of formation of the products and reactants: \(\Delta H_{i}^{\circ} = [H_{CdCl_{2}(s)} - (H_{Cd(s)} + H_{Cl_{2}(g)})]\)
04

Calculate the standard Gibbs free energy change

Plug the calculated values of \(\Delta S_{i}^{\circ}\) and \(\Delta H_{i}^{\circ}\), as well as the temperature (25°C = 298K) into the equation to find the standard Gibbs free energy change: \(\Delta G_{i}^{\circ} = \Delta H_{i}^{\circ} - T \cdot \Delta S_{i}^{\circ}\) (b) Methyl alcohol, CH3OH(l):
05

Obtain standard entropies and heats of formation

Gather the relevant thermodynamic information for methyl alcohol and its constituents (carbon, hydrogen, and oxygen) from standard thermodynamic tables.
06

Calculate the standard entropy change

Determine the standard entropy change, \(\Delta S_{i}^{\circ}\), for the formation of methyl alcohol, using the standard entropies of the products and reactants: \(\Delta S_{i}^{\circ} = [S_{CH_{3}OH(l)} - (S_{C(s)} + 2S_{H_{2}(g)} + S_{O_{2}(g)}/2)]\)
07

Calculate the standard heat of formation

Determine the standard heat of formation, \(\Delta H_{i}^{\circ}\), for the formation of methyl alcohol, using the heats of formation of the products and reactants: \(\Delta H_{i}^{\circ} = [H_{CH_{3}OH(l)} - (H_{C(s)} + 2H_{H_{2}(g)} + H_{O_{2}(g)})]\)
08

Calculate the standard Gibbs free energy change

Plug the calculated values of \(\Delta S_{i}^{\circ}\) and \(\Delta H_{i}^{\circ}\), as well as the temperature (25°C = 298K) into the equation to find the standard Gibbs free energy change: \(\Delta G_{i}^{\circ} = \Delta H_{i}^{\circ} - T \cdot \Delta S_{i}^{\circ}\) (c) Copper(I) sulfide (s):
09

Obtain standard entropies and heats of formation

Gather the relevant thermodynamic information for copper(I) sulfide and its constituents (copper and sulfur) from standard thermodynamic tables.
10

Calculate the standard entropy change

Determine the standard entropy change, \(\Delta S_{i}^{\circ}\), for the formation of copper(I) sulfide, using the standard entropies of the products and reactants: \(\Delta S_{i}^{\circ} = [S_{Cu_{2}S(s)} - (2S_{Cu(s)} + S_{S_{8}(s)}/8)]\)
11

Calculate the standard heat of formation

Determine the standard heat of formation, \(\Delta H_{i}^{\circ}\), for the formation of copper(I) sulfide, using the heats of formation of the products and reactants: \(\Delta H_{i}^{\circ} = [H_{Cu_{2}S(s)} - (2H_{Cu(s)} + H_{S_{8}(s)})]\)
12

Calculate the standard Gibbs free energy change

Plug the calculated values of \(\Delta S_{i}^{\circ}\) and \(\Delta H_{i}^{\circ}\), as well as the temperature (25°C = 298K) into the equation to find the standard Gibbs free energy change: \(\Delta G_{i}^{\circ} = \Delta H_{i}^{\circ} - T \cdot \Delta S_{i}^{\circ}\)

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Most popular questions from this chapter

On the basis of your experience, predict which of the following reactions are spontaneous. (a) \(\mathrm{CO}_{2}(s) \longrightarrow \mathrm{CO}_{2}(g)\) at \(25^{\circ} \mathrm{C}\) (b) \(\mathrm{NaCl}(s) \longrightarrow \mathrm{NaCl}(l)\) at \(25^{\circ} \mathrm{C}\) (c) \(2 \mathrm{NaCl}(s) \longrightarrow 2 \mathrm{Na}(s)+\mathrm{Cl}_{2}(g)\) (d) \(\mathrm{CO}_{2}(g) \longrightarrow \mathrm{C}(s)+\mathrm{O}_{2}(g)\)

Given the following standard free energies at \(25^{\circ} \mathrm{C}\), $$ \begin{array}{ll} \mathrm{SO}_{2}(g)+3 \mathrm{CO}(g) \longrightarrow \operatorname{COS}(g)+2 \mathrm{CO}_{2}(g) & \Delta G^{\circ}=-246.5 \mathrm{~kJ} \\ \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) & \Delta G^{\circ}=-28.5 \mathrm{~kJ} \end{array} $$ find \(\Delta G^{\circ}\) at \(25^{\circ} \mathrm{C}\) for the following reaction. $$ \mathrm{SO}_{2}(g)+\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{COS}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) $$

Predict the sign of \(\Delta S\) for the following. (a) a lake freezing (b) precipitating lead chloride (c) a candle burning (d) weeding a garden

Show by calculation whether the reaction $$ \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}(a q) \quad \Delta G^{\circ}=+27.2 \mathrm{~kJ} $$ is spontaneous at \(25^{\circ} \mathrm{C}\) (a) when \(\left[\mathrm{H}^{+}\right]=\left[\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}\right]=0.85 M_{;}\left[\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right]=0.15 \mathrm{M}\). (b) when \(\left[\mathrm{H}^{+}\right]=\left[\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}\right]=2.0 \times 10^{-3} \mathrm{M} ;\left[\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right]=1.0 \mathrm{M}\).

Discuss the effect of temperature change on the spontaneity of the following reactions at 1 atm. (a) \(\mathrm{Al}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Fe}(s) \longrightarrow 2 \mathrm{Al}(s)+\mathrm{Fe}_{2} \mathrm{O}_{3}(s)\) $$ \Delta H^{\circ}=+851.5 \mathrm{~kJ} ; \Delta S^{\circ}=+38.5 \mathrm{~J} / \mathrm{K} $$ (b) \(\mathrm{N}_{2} \mathrm{H}_{4}(l) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2}(g)\) $$ \Delta H^{\circ}=-50.6 \mathrm{~kJ} ; \Delta S^{\circ}=0.3315 \mathrm{~kJ} / \mathrm{K} $$ (c) \(\mathrm{SO}_{3}(g) \longrightarrow \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g)\) $$ \Delta H^{\circ}=98.9 \mathrm{~kJ} ; \Delta S^{\circ}=+0.0939 \mathrm{~kJ} / \mathrm{K} $$
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