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Chapter 19: Problem 68

Following are some standard Gibbs energies of formation, \(\Delta G_{f}^{2},\) per mole of metal oxide at \(1000 \mathrm{K}: \mathrm{NiO},\) \(-115 \mathrm{kJ} ; \mathrm{MnO},-280 \mathrm{kJ} ; \mathrm{TiO}_{2},-630 \mathrm{kJ} .\) The standard Gibbs energy of formation of \(\mathrm{CO}\) at \(1000 \mathrm{K}\) is \(-250 \mathrm{kJ}\) per mol CO. Use the method of coupled reactions (page 851 ) to determine which of these metal oxides can be reduced to the metal by a spontaneous reaction with carbon at \(1000 \mathrm{K}\) and with all reactants and products in their standard states.

Short Answer

Expert verified
At 1000 K, NiO and TiO2 can be reduced to the metal by a spontaneous reaction with carbon, while MnO can not.

Step by step solution

01

Understand the method of coupled reactions

The method of coupled reactions involves adding the reactions together in such a way that the resulting reaction is the one of interest. It’s crucial to comprehend the idea of spontaneous reactions in terms of Gibbs energy. A spontaneous reaction happens if the Gibbs energy change (ΔG) is negative.
02

Analyze the given Gibbs energies of formation

The given standard Gibbs energies of formation (per mole) at 1000 K are -115 kJ for NiO, -280 kJ for MnO, -630 kJ for TiO2, and -250 kJ for CO.
03

Formulate coupled reactions for each metal oxide

The required reactions to reduce metal oxides to pure metal using carbon (C) are: NiO + C → Ni + CO, MnO + C → Mn + CO, and TiO2 + 2C → Ti + 2CO. We can calculate the Gibbs energy for each reaction by subtracting the sum of the Gibbs energies of formation of the reactants from the sum of the Gibbs energies of formation of the products.
04

Calculate the Gibbs energy for each reaction

For NiO: ΔG = ΔGf(Ni) + ΔGf(CO) - ΔGf(NiO) - ΔGf(C) = 0 + (-250 kJ) - (-115 kJ) - 0 = -135 kJ. For MnO: ΔG = ΔGf(Mn) + ΔGf(CO) - ΔGf(MnO) - ΔGf(C) = 0 + (-250 kJ) - (-280 kJ) - 0 = +30 kJ. For TiO2: ΔG = ΔGf(Ti) + 2*ΔGf(CO) - ΔGf(TiO2) - 2*ΔGf(C) = 0 + 2*(-250 kJ) - (-630 kJ) - 2*0 = -130 kJ.
05

Determine which reactions are spontaneous

Since a reaction is spontaneous if ΔG is negative, NiO and TiO2 can be reduced to the pure metal form by carbon, while MnO can't.

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Most popular questions from this chapter

At \(1000 \mathrm{K},\) an equilibrium mixture in the reaction \(\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \quad\) contains \(0.276 \mathrm{mol} \quad \mathrm{H}_{2}, 0.276 \mathrm{mol} \mathrm{CO}_{2}, \quad 0.224 \mathrm{mol} \mathrm{CO}, \quad\) and \(0.224 \mathrm{mol} \mathrm{H}_{2} \mathrm{O}\) (a) What is \(K_{\mathrm{p}}\) at \(1000 \mathrm{K} ?\) (b) Calculate \(\Delta G^{\circ}\) at \(1000 \mathrm{K}\). (c) In which direction would a spontaneous reaction occur if the following were brought together at 1000 K: \(0.0750 \mathrm{mol} \mathrm{CO}_{2}, 0.095 \mathrm{mol} \mathrm{H}_{2}, 0.0340 \mathrm{mol} \mathrm{CO},\) and \(0.0650 \mathrm{mol} \mathrm{H}_{2} \mathrm{O} ?\)

Which of the following changes in a thermodynamic property would you expect to find for the reaction \(\mathrm{Br}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{Br}(\mathrm{g})\) at all temperatures: \((\mathrm{a}) \Delta H<0\) (b) \(\Delta S>0 ;\) (c) \(\Delta G<0 ;\) (d) \(\Delta S<0 ?\) Explain.

For one of the following reactions, \(K_{c} K_{p}=K .\) Identify that reaction. For the other two reactions, what is the relationship between \(K_{c}, \bar{K}_{\mathrm{p}},\) and \(K ?\) Explain. (a) \(2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{g})\) (b) \(\mathrm{HI}(\mathrm{g}) \rightleftharpoons \frac{1}{2} \mathrm{H}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{I}_{2}(\mathrm{g})\) (c) \(\mathrm{NH}_{4} \mathrm{HCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{NH}_{3}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(1)\)

For the reaction \(2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{g})\) all but one of the following equations is correct. Which is incorrect, and why? (a) \(K=K_{\mathrm{p}} ;\) (b) \(\Delta S^{\circ}=\) \(\left(\Delta G^{\circ}-\Delta H^{\circ}\right) / T ;\left(\text { c) } K_{\mathrm{p}}=e^{-\Delta G^{\circ} / R T} ;(\mathrm{d}) \Delta G=\Delta G^{\circ}+\right.\) \(R T \ln Q\).

For the dissociation of \(\mathrm{CaCO}_{3}(\mathrm{s})\) at \(25^{\circ} \mathrm{C}, \mathrm{CaCO}_{3}(\mathrm{s})\) \(\rightleftharpoons \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) \Delta G^{\circ}=+131 \mathrm{kJ} \mathrm{mol}^{-1} .\) A sample of pure \(\mathrm{CaCO}_{3}(\mathrm{s})\) is placed in a flask and connected to an ultrahigh vacuum system capable of reducing the pressure to \(10^{-9} \mathrm{mmHg}\) (a) Would \(\mathrm{CO}_{2}(\mathrm{g})\) produced by the decomposition of \(\mathrm{CaCO}_{3}(\mathrm{s})\) at \(25^{\circ} \mathrm{C}\) be detectable in the vacuum system at \(25^{\circ} \mathrm{C} ?\) (b) What additional information do you need to determine \(P_{\mathrm{CO}_{2}}\) as a function of temperature? (c) With necessary data from Appendix D, determine the minimum temperature to which \(\mathrm{CaCO}_{3}(\mathrm{s})\) would have to be heated for \(\mathrm{CO}_{2}(\mathrm{g})\) to become detectable in the vacuum system.
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