Equilibrium Composition Calculation - Boudouard Reaction

This example illustrates the simulation of chemical equilibrium by solving reaction extent to minimize the system change in Gibbs energy. This functionality of the app is illustrated using the Boudouard reaction system as an example, where solid graphite (C(s)) reacts with CO2(g) to form CO(g) at elevated temperatures. The app is used to find the equilibrium gas composition as a function of temperature.

This examples requires a process system to be created with the following components and chemical reactions (see Get Started Guide):

Components: CO(g), CO2(g), C(s)

Chemical Reactions: CO2(g) + C(s) → 2 CO(g)

Process systems view with the process system listed for the current calculation example.

Process systems view with the process system listed for the current calculation example.

Process system view configured with components and reactions for the current calculation example.

Process system view configured with components and reactions for the current calculation example.

Vary reaction extent and product system composition at 700°C

This examples illustrates calculating the equilibrium gas composition for the Boudouard reaction occurring at elevated temperature. This is simulated by finding the extent of the specified Boudouard reaction that would result in the lowest negative value of the change in Gibbs energy.

Before using the app functionality to solve the reaction extent for minimized Gibbs energy, the calculation is defined to vary the reaction extent at a specific temperature and visualize the point where the change in Gibbs energy reaches a minimum. The change in Gibbs energy is calculated between the initial and final states at the specified temperature for the reactants transformed to products.

For this example, temperature is set as the calculation target with a value of 700°C. The component amounts of reactants CO2(g) and C(s) are both set to 1 mol, the reaction extent (fraction) varied between 0 and 1 in steps of 0.1.

In the Calculation view, configure the new calculation as follows:

  • Keep Initial Conditions off.
  • Keep the Calculation Target on Temperature, and enter the Temperature value as 700°C. 
  • Keep the units of the gas components as mol, and change the units of solids components to mol.
  • Set the component amounts for CO2(g) and C(s) both as 1 mol, and that of CO(g) as 0 mol.
  • Change the reaction extent to a range input and enter the FROM, TO, and STEP values as 0, 1, and 0.1
Calculation view with temperature configured.

Calculation view with temperature configured.

Calculation view with component amounts and reactions configured.

Calculation view with component amounts and reactions configured.

After configuring the calculation, tapping on the Calculate button would display the Results view as below. The plot button can be selected for ΔGibbs Free Energy and ΔEnthalpy with the plots generated to illustrate the calculated change in Gibbs energy and heat of reaction as a function of varied reaction extent.

The results display that for reaction extents between 0 and 1 and a temperature of 700°C, the change in Gibbs energy is negative, indicating the reaction to be spontaneous. The change in Gibbs energy reaches a minimum value around a reaction extent of between 0.4 and 0.5. The results also indicate the change in enthalpy to increase linearly with reaction extent, and as would be expected more energy is consumed as the reaction progresses.

The gas composition can be derived from the calculation results illustrated below. For the results illustrated here for a reaction extent of 0.4, only 40% of the CO2(g) and C(s) reactants would react. The product gas would be composed of 57.1 vol.% of CO(g), and 42.9 vol. % of CO2(g). And, of the 1 mol of reactant C(s), 0.6 mol would remain.

Calculation result values for a reaction extent of 0.4.

Calculation result values for a reaction extent of 0.4.

Results plot of the change in Gibbs energy and enthalpy as a function of reaction extent.

Results plot of the change in Gibbs energy and enthalpy as a function of reaction extent.

Calculation result component amounts for a reaction extent of 0.4.

Calculation result component amounts for a reaction extent of 0.4.

Determining the equilibrium product system composition over a range of temperatures

It was illustrated above that for varying reaction extents at a specified temperature the change in Gibbs energy reaches a minimum, indicating the equilibrium point for the specific temperature. This part of the example illustrates the app functionality to determine the equilibrium point by solving the reaction extent that gives the minimum change in Gibbs energy at a specific temperature. 

The calculation used above can again be used to find the equilibrium compositions over a range of temperatures between 25 and 1000°C, in steps of 50°C.

In the calculation view, the Temperature is changed to a range input, and the values for FROM, TO, and STEP entered as 25, 1000, and 50°C. Then, the option below the chemical reaction Calculate extent for equilibrium is selected, which hides any extent inputs as it will be calculated. The calculation configuration is illustrated below.

Calculation view with temperature configured.

Calculation view with temperature configured.

Calculation view with component amounts and reactions configured.

Calculation view with component amounts and reactions configured.

Tapping on the Calculate button would display the Results view as below. On the Results view the plot button is selected for ΔEnthalpythe reaction extent, as well as the molar amount fraction of CO2(g).

For the first temperature step of 25°C, and for temperatures up to around 450°C, it can be observed that the achieved reaction extent is reported as zero. This implies that in this temperature range no reaction extent would result in a negative change in Gibbs energy, and therefor the reaction would not occur spontaneously. From temperatures of around 450 to 1000°C the equilibrium reaction extent is calculated to increase from zero to one.

The heat of reaction is illustrated as ΔEnthalpy to increase from zero to 165.4 kJ per 1 mol of C(s) and CO2(g) for the completed reaction at 1000°C. This represents only the heat of reaction at the relevant temperature, and heating of reactants to the reaction temperature should be included by using the initial conditions option on the calculation configuration.

The equilibrium gas composition as a function of temperature is also illustrated in terms of the volume fraction of CO2(g) in the product gas. The fraction CO2(g) in the product gas decreases from one to zero in relation to the increasing reaction extent calculated as a function of temperature.

Calculation result values calculated for a reaction extent of 0.

Calculation result values calculated for a reaction extent of 0.

Results plot of the equilibrium conditions varying temperature.

Results plot of the equilibrium conditions varying temperature.