• Table of Contents
• Introduction
• Plant Data
• Electrolyte Properties
• Concentration Converter
• Cell Voltage
• Anode Table Layout
• Alumina Feeding

• Table of Contents
• Introduction
• How to Use AlPrg
• Plant Data
• Alumina Feeding
• Electrolyte Properties
• Cell Voltage

• Table of Contents
• Introduction
• ATab Version 2
• Layout-View
• Evaluation-View
• 3D-View
• Floating Windows
• Optimization Window
• Examples
• Downloads

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

• Current Efficiency

• Raw Materials

• Cell Operation

• Measurements

• Environment, Emissions
• Examples, Exercises
• Literature

• News and Events
• Name Index
• Subject Index
• Sitemap
• Recreation

2.7 Ideal Gas

An ideal gas is regarded as one for which the molecular attraction is negligibly small and in which the actual volume of the molecules is small in comparison with the space they inhibit. The Ideal Gas Equation describes the state of such an ideal gas.

Ideal Gas Equation:

	(2.24)

The gas pressure and temperature are measured in different units. The following tables inform how to convert those units:

Table 2.3: Conversion of Temperatures.

Table 2.4: Conversion Factors for Pressure.

The value of the Molar Gas Constant is:

(2.25)

Table 2-5 shows the values of the gas constant in different unit systems:

Table 2.5: Values of the Gas Constant.

The volume of one mole of ideal gas at the Standard State namely a temperature of T₀ = 273.15 K (0 °C) and a pressure of p₀ = 101 325 Pa (1 atm) is called Molar Volume (V_m) of the ideal gas. Its value is:

(2.26)

If you want to calculate the volume of an ideal gas at a different temperature (t) or pressure (p) other than an initial state (t₀, p₀) use the

Conversion Equation for the Volume of an Ideal Gas:

	(2.27)

2.8 Electrolytic Volume Production

Using Equation 2.2 one writes for the number of moles of carbon dioxide produced during electrolysis:

	(2.28)

With Equation 2.16 and Equation 2.24 one finds the following relations for the
Electrolytic Volume Productions of Carbon Dioxide:

	(2.29)

and with Equation 2.17 the Electrolytic Volume Productions of Carbon Monoxide:

	(2.30)

at standard conditions:T₀ = 273.15 K (0 °C), p₀ = 101 325 Pa (1 atm).

The production values of VP_CO2 and VP_CO are in cubic meters (m³). If you want them in kilograms (EP_CO2, EP_CO) please use Equation 2.16 and 2.17 of the electrolytic productions.

Similarly to the specific electrolytic consumptions and productions one writes using Equation 2.20 for the
Specific Electrolytic Volume Productions of Carbon Dioxide:

	(2.31)

and with Equation 2.21 the Specific Electrolytic Volume Productions of Carbon Monoxide:

(2.32)

The calculated values of SVP_CO2 and SVP_CO are in cubic meters per kilogram (m³/kgAl). If you want them in kilograms per kilogram (kg/kgAl) please use Equation 2.20 (SEP_CO2) and 2.21 (SEP_CO).

2.9 Pearson Waddington Equation

The content of the components in a system (A, B) are given in fractions. The following values are used:

Mass Fraction:

	(2.33)

Mole Fraction:

	(2.34)

Volume Fraction:

	(2.35)

For the volume fraction and for the corresponding mole fractions of carbon dioxide in the anode gas one writes by using the Ideal Gas Equation 2.24:

	(2.36)

Taking the values from the Electrolysis Equation 2.12 one continues:

	(2.37)

Rearranging for the current efficiency η yields the

Pearson Waddington Equation: [Lit.]

	(2.38)

or

	(2.39)

by using

(2.40)

Remark: According to the Pearson Waddington Equation the current efficiency can not be less than 50%. The content of carbon monoxide in the anode gas is about half the loss of current efficiency.