Chemical Equilibrium Example Program

In the program below, the equilibrate method is called to set the gas to a state of chemical equilibrium, holding the temperature and pressure fixed.

#include "cantera/thermo.h"

using namespace Cantera;

void equil_demo()
    std::unique_ptr<ThermoPhase> gas(newPhase("h2o2.cti","ohmech"));
    gas->setState_TPX(1500.0, 2.0*OneAtm, "O2:1.0, H2:3.0, AR:1.0");
    std::cout << gas->report() << std::endl;

int main()
    try {
    } catch (CanteraError& err) {
        std::cout << err.what() << std::endl;

The program output is:

      temperature            1500  K
         pressure          202650  Pa
          density        0.316828  kg/m^3
 mean mol. weight         19.4985  amu

                         1 kg            1 kmol
                      -----------      ------------
         enthalpy    -4.17903e+06       -8.149e+07     J
  internal energy    -4.81866e+06       -9.396e+07     J
          entropy         11283.3          2.2e+05     J/K
   Gibbs function     -2.1104e+07       -4.115e+08     J
heat capacity c_p         1893.06        3.691e+04     J/K
heat capacity c_v         1466.65         2.86e+04     J/K

                          X                 Y          Chem. Pot. / RT
                    -------------     ------------     ------------
               H2       0.249996        0.0258462         -19.2954
                H    6.22521e-06        3.218e-07         -9.64768
                O    7.66933e-12      6.29302e-12         -26.3767
               O2     7.1586e-12      1.17479e-11         -52.7533
               OH    3.55353e-07      3.09952e-07         -36.0243
              H2O       0.499998         0.461963          -45.672
              HO2    7.30338e-15       1.2363e-14          -62.401
             H2O2    3.95781e-13      6.90429e-13         -72.0487
               AR       0.249999          0.51219         -21.3391

How can we tell that this is really a state of chemical equilibrium? Well, by applying the equation of reaction equilibrium to formation reactions from the elements, it is straightforward to show that:

\[\mu_k = \sum_m \lambda_m a_{km}.\]

where \(\mu_k\) is the chemical potential of species k, \(a_{km}\) is the number of atoms of element m in species k, and \(\lambda_m\) is the chemical potential of the elemental species per atom (the so-called “element potential”). In other words, the chemical potential of each species in an equilibrium state is a linear sum of contributions from each atom. We see that this is true in the output above—the chemical potential of H2 is exactly twice that of H, the chemical potential for OH is the sum of the values for H and O, the value for H2O2 is twice as large as the value for OH, and so on.

We’ll see later how the equilibrate() function really works.