Problem 68 - General Chemistry: Principles and Modern Applications

Question

An aluminum production cell of the type pictured in Figure \(21-24\) operates at a current of \(1.00 \times 10^{5} \mathrm{A}\) and a voltage of 4.5 V. The cell is \(38 \%\) efficient in using electrical energy to produce chemical change. (The rest of the electrical energy is dissipated as thermal energy in the cell.) (a) What mass of \(\mathrm{Al}\) can be produced by this cell in \(8.00 \mathrm{h} ?\) (b) If the electrical energy required to power this cell is produced by burning coal \((85 \%\) C; heat of combustion of \(C=32.8 \mathrm{kJ} / \mathrm{g}\) ) in a power plant with \(35 \%\) efficiency, what mass of coal must be burned to produce the mass of Al determined in part (a)?

Step-by-Step Solution

Answer

The mass of aluminum produced by the cell in 8.0 hours is 337.8 kg and the mass of coal that must be burned to produce this amount of \(\mathrm{Al}\) is 1129.62 kg.

Step 1: Calculate the power and energy produced by the cell

Using the formula \(P=VI\), where P is power, V is voltage, and I current, the power produced by the cell can be calculated as \(P=1.00 \times 10^{5} \mathrm{A} \times 4.5\mathrm{V} = 450000 \mathrm{W}\) or \(450 \mathrm{KW}\). To calculate the energy produced in 8 hours, use the formula \(E=Pt\), where E is energy, P power and t time (in seconds). Therefore \(E=450 \mathrm{KW} \times 8 \times 3600 \mathrm{s} = 12960000 \mathrm{KJ}\).

Step 2: Calculate the mass of Al produced

Given the efficiency of the cell as 38%, the actual energy used in producing the Al is \(0.38 \times 12960000 \mathrm{KJ} = 4924800 \mathrm{KJ}\). The reaction for the production of Al from Al2O3 is 2Al2O3 → 4Al + 3O2, where \(2 \mathrm{mol} \mathrm{Al2O3} = 4 \mathrm{mol} \(\mathrm{Al} = 393.5 \mathrm{KJ}. Therefore, the number of moles of Al produced is \(4924800 \mathrm{KJ}\) / \(393.5 \mathrm{KJ/mol}\) = \(12511.15 \mathrm{mol} . The mass of Al produced can be found using the molar mass of Al, 27 g/mol: 12511.15 mol x 27g/mol = 337801.5 g or 337.8 kg .

Step 3: Find the mass of Coal required to produce the energy

The total energy required, given the efficiency of the power plant is 35%, is \(E_{total} = 12960000 \mathrm{KJ}\) / \(0.35 = 37028571.43 \mathrm{KJ} . Since the heat of combustion of coal is 32.8 kJ/g, the mass of coal required is \( m = 37028571.43 \mathrm{KJ}\) / \(32.8 \mathrm{KJ/g} = 1129620.04 g or 1129.62 \(\mathrm{Kg}\).

Key Concepts

Aluminum production

Aluminum production is a fascinating process involving several steps and reactions. The extraction of aluminum from its oxide involves an electrolytic process. Primarily, aluminum is produced from bauxite ore, which is refined to obtain alumina (Al2O3).
This alumina is then subjected to electrolysis in an electrolytic cell known as the Hall-Héroult cell. In this cell, aluminum ions are reduced to aluminum metal at the cathode, while oxygen is released at the anode.

• The key reaction is: 2Al2O3 → 4Al + 3O2
• This method requires significant electrical energy, highlighting the necessity of energy efficiency improvements in production processes.

The efficiency of this process is only about 38%, which means a considerable portion of electrical energy is wasted as heat. Hence, technological innovations are critical for making aluminum production more sustainable, especially given its extensive use in industries.

Energy efficiency

Energy efficiency is a crucial factor in aluminum production because it directly affects the cost and environmental impact of the process. In the context of electrochemical cells, efficiency indicates the proportion of electrical energy used effectively for chemical reactions compared to the total input energy.
For instance, in the aluminum production cell described, only 38% of the electrical energy is utilized for producing aluminum, with the rest dissipated as heat. Improving efficiency can significantly reduce energy consumption and production costs.

• Increasing efficiency can be achieved through better material designs that reduce energy losses.
• Optimizing the design of cells and using innovative technology can help minimize thermal loss.

Moreover, using energy-efficient methods also reduces emissions when the energy is derived from fossil fuels. Eventually, integrating renewable energy sources directly to such processes could further enhance sustainability.

Thermodynamics

Thermodynamics plays a pivotal role in understanding processes like aluminum production. It dictates how energy is converted and transferred during chemical reactions. In electrochemical cells, thermodynamics helps predict cell potentials and assess energy changes.
During aluminum production, the reaction's enthalpy change ( ΔH ) represents the energy needed to break bonds in Al2O3 and form new bonds in metallic aluminum. Aluminum production is endothermic, meaning it requires continuous supply of energy.

• Thermodynamics helps calculate efficiencies, energy needs, and optimization potential.
• The concept of Gibbs free energy ( ΔG ) shows whether the production process is feasible and spontaneous under certain conditions.

These principles not only aid in understanding but are vital for improving industrial processes and for engineers working on maximizing output relative to energy input.

Chemical reactions

Chemical reactions are at the heart of aluminum production. The primary reaction involves the decomposition of aluminum oxide to produce aluminum metal via electrolysis.
In the Hall-Héroult process, alumina dissolved in molten cryolite is subjected to a current, causing decomposition of Al2O3 into Al and O2.

• This process simplifies to: Al2O3 🡪 2Al + 1.5O2
• Electrolysis is a crucial step, involving electron transfer, which requires careful control of electrical input to optimize the yield.

Understanding these chemical reactions is essential, as it affects the design of the cell, choice of input materials, and ultimately, determines the efficiency and sustainability of the production process. At a greater scale, these reactions highlight the significance of chemistry in advancing industrial processes.