Problem 68 - General Chemistry: Principles and Modern Applications

Question

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.

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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.

Step 3: 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.

Step 4: 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.

Step 5: 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.

Key Concepts

Coupled Reactions

In the context of chemical processes, understanding the mechanism of coupled reactions is vital. Often, a reaction that wouldn't occur spontaneously can be driven by pairing it with a spontaneous one. This approach is called coupling reactions. By designing a suitable combination, the desired chemical reaction is facilitated. For instance, in metal oxide reduction, metal oxides like NiO or MnO react with a substance like carbon, resulting in the formation of pure metal and carbon monoxide.

Here, the Gibbs energy plays a crucial role. The basic idea is that the Gibbs energy change for the sum of the reactions should be negative. This signifies that the entire process, when reactions are coupled, proceeds spontaneously. The calculations involve subtracting the sum of the Gibbs energies of formation of the reactants from the sum of the products for each reaction. Thus, we can strategically combine reactions to achieve a negative Gibbs energy change, resulting in a viable chemical pathway.

• Requires an understanding of Gibbs energy changes
• Utilized in processes where direct spontaneous reactions are not feasible
• Enables harnessing the spontaneity of one reaction to drive another

Spontaneous Reactions

Spontaneous reactions are those that occur without any external input of energy. The change in Gibbs energy (\(\Delta G\)), is central to determining if a reaction is spontaneous. If \(\Delta G < 0\), the reaction naturally proceeds towards equilibrium.

In the exercise, a comparison was made between different metal oxides to see which could be reduced to metals using carbon — this involved calculating the \(\Delta G\) values. Two of the metal oxide reactions, those involving NiO and TiO₂, resulted in negative \(\Delta G\) values. This indicated that these reactions are spontaneous. MnO, on the other hand, had a different outcome with a positive \(\Delta G\), indicating no spontaneous reaction.

The conditions under which a reaction becomes spontaneous depend on a variety of factors, one primary factor being temperature. Spontaneity is a useful concept in predicting the behavior of chemical processes in industrial applications.

• Occurs without requiring external energy
• Negative Gibbs energy signifies spontaneity
• Temperature can affect the spontaneity of reactions

Metal Oxide Reduction

Metal oxide reduction involves transforming metal oxides into pure metals, often through a reaction with reducing agents like carbon. This process is significant in metallurgy and production industries because many metals are found in nature as oxides rather than pure metals.

In the exercise, the reduction reactions were examined for NiO, MnO, and TiO₂ using CO as a product. These reactions are:NiO + C → Ni + CO, MnO + C → Mn + CO, and TiO₂ + 2C → Ti + 2CO. The Gibbs energy calculations helped identify which of these processes could be spontaneous. For optimal efficiency and cost-effectiveness in industrial settings, it's beneficial to focus on those reactions with the most negative \(\Delta G\).

This process, alongside its coupling with carbon, offers valuable insight into the feasibility of reducing various metal oxides under standard conditions and influences their application in relevant industries.

• Transform oxide forms to pure metals
• Influences metallurgical processes
• Key in determining industrial applications of metals