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• Table of Contents
• Principles Hall-Héroult
• Mass Balance
• Electrolyte Properties
• Cell Voltage
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• Current Efficiency

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2.2 Principal Equation

Alumina (aluminum oxide or Al₂O₃) is decomposed in an electrolytic process to produce aluminum. At the positive electrode, the anode, oxygen (O₂) is formed which reacts immediately with the carbon anode (C) to carbon dioxide (CO₂). Aluminum (Al) is deposited at the negative electrode, the cathode, which is the already produced aluminum pool. This process is described by the

Principal Equation:

The Principal Equation means that two moles Al₂O₃ react with three moles C to four moles Al and three moles CO₂. The Mole is defined as the amount of substance (symbol: n, unit: mol) which contains as many elementary entities as there are atoms in 0.012 kg ¹²C. This number N_A = 6.022·10²³ mol^-1 (more exactly 6.02214179·10²³ mol^-1) is called Avogadro Constant.
During chemical processes particles (atoms, molecules) are reacting with each other. By using mole expressions formulating chemical reactions become independent of the properties of the reacting substances and are valid (with reservations) for every system. For technical applications a more practical unit namely the molecular weight of a substance is applied. The Molecular Weight (Molar Mass) of a substance is defined as the mass of the substance divided by its amount of substance:

	(2.2)

Where the Atomic Weight (Relative Atomic Mass) is defined as the ratio of the average mass per atom of an element to 1/12 of the mass of an atom of the nucleide ¹²C and the Molecular Weight (Relative Molecular Mass) as ratio of the average mass per molecule or specified entity of a substance to 1/12 of the mass of an atom of the nucleide ¹²C.
You find relative atomic masses (values were taken from IUPAC (2007)) and molecular masses of elements and compounds which are important for the Hall-Héroult Process in Table 2.1 and Table 2.2 .

Table 2.1: Atomic Weights (Relative Atomic Masses) of some Elements.

Table 2.2: Molecular Weights (Relative Molecular Masses) of some Chemical Compounds.

2.3 Theoretical Productions (TP) and Consumptions (TC)

Faraday's Laws of electrolysis are saying that:

Equivalent Weight of a substance is its atomic or molecular weight divided by its electrochemical valence e.g. the ions Na⁺, 1/2Ca²⁺, and 1/3Al³⁺ are electrochemically equivalent. The Gram Equivalent Weight is the mass in grams numerically equal to the equivalent weight.
The unit of the electric charge is the Coulomb (1 C = 1 As). One mole of electrons has the electric charge of 96485 C. This value F = 96485 Cmol^-1 (more precisely 96485.3399 Cmol^-1) is called the Faraday Constant.

During electrolysis the electric charge of the aluminum ion is changed from positive three plus to electrical neutral. Accordingly three electrons are used per aluminum ion or three moles of electrons per one mole of aluminum:

One writes for the Theoretical Consumptions of Aluminum Oxide:

	(2.4)

According to Equ. 2.3 and the Principal Equation (Equ. 2.1) 4·3·F of electric charge are necessary to react two molecules of alumina (2Al₂O₃):

Putting in the values one gets:

and for the Theoretical Consumptions of Carbon:

	(2.5)

According to Equ. 2.3 and the Principal Equation (Equ. 2.1) 4·3·F of electric charge are necessary to react three atoms of carbon (3C):

Putting in the values one gets:

The Theoretical Production of Aluminum is:

	(2.6)

To discharge four aluminum ions (4Al³⁺) according to Equ. 2.3 and the Principal Equation (2.1) 4·3·F of electric charge are necessary. When a current I during the time t is flowing through the electrolytic cell the theoretical production of aluminum is:

Putting in the values one gets:

and the Theoretical Production of Carbon Dioxide (CO₂) is:

	(2.7)

To produce three molecules of carbon dioxide (3CO₂) according to the Principal Equation (2.1) 4·3·F of electric charge are necessary:

Putting in the values one gets:

According to the Principal Equation 2.1 the following relations must hold:

(2.8)

2.4 Reoxidation of Aluminum

In practice an electrolysis cell produces always less aluminum than is calculated according to Faraday's Laws. The current efficiency is the ratio of actually produced aluminum over theoretically produced aluminum. This value is called

Fractional Current Efficiency:

	(2.9)

Normally the current efficiency is expressed in percent:

Current Efficiency in Percent:

	(2.10)

Issues with Current Efficiency:

The current efficiency is a main factor to judge the quality of cell operation. There are two factors that influence the CE:

With AlPrg you may select the metal quality or the production factor:

2.1 Metal Quality and Production Factor. On the Aluminum Production page of AlWeb or AlPrg you may change the metal quality i.e. the content of pure aluminum in the actually tapped metal (PAl) or the factor to calculate the theoretical aluminum production (TPAl).

The electrolyte dissolves aluminum which is transported to the anode. There it reacts with carbon dioxide to alumina according to the

Reoxidation Reaction Equation:

Pearson and Waddington [Lit.] assume that the loss in current efficiency is only due to the reaction of aluminum with CO₂. To the Principal Equation:

the Reoxidation Reaction Equation is added:

considering that (1-η) fractions of aluminum are lost if η fractions are produced. That results in the

Electrolysis Equation:

Remark: You can add (or subtract) chemical equations like mathematical equations. You have to consider, however, that the sign has to be changed when you shift one component to the other side of the equation:

2.5 Electrolytic Productions (EP) and Consumptions (EC)

According to the Electrolysis Equation 2.8 e.g. according to the theory of Pearson and Waddington the expressions for the theoretical productions and consumptions (Equation 2.4 to 2.7) must be modified.
One writes for the Electrolytic Consumptions of Aluminum Oxide:

	(2.13)

Putting in the values one gets:

and for the Electrolytic Consumptions of Carbon:

	(2.14)

Putting in the values one gets:

The Electrolytic Production of Aluminum is:

	(2.15)

Putting in the values one gets:

the Electrolytic Production of Carbon Dioxide is:

	(2.16)

Putting in the values one gets:

the Electrolytic Production of Carbon Monoxide is:

	(2.17)

To produce 6(1-η) molecules of carbon monoxide (CO) according to the Electrolysis Equation 4·3·F of electric charge are necessary:

Putting in the values one gets:

2.6 Specific Electrolytic Productions (SEP) and Consumptions (SEC)

The practice uses also specific values e.g. values related to a reactant of the Principal Equation, normally to one kilogram of aluminum. The values of the specific productions (SEP) and consumptions (SEC) are calculated by dividing the kilograms of produced or consumed material by the kilograms of produced aluminum.
One can write for the Specific Electrolytic Consumptions of Aluminum Oxide:

	(2.18)

for the Specific Electrolytic Consumptions of Carbon:

	(2.19)

and for the Specific Electrolytic Production of Carbon Dioxide:

	(2.20)

and finally for the Specific Electrolytic Production of Carbon Monoxide:

	(2.21)

According to the Electrolysis Equation (2.8) the following relations must hold:

(2.22)

and:

(2.23)