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/core.h"
#include <iostream>

using namespace Cantera;

void equil_demo()
{
    // Create a new Solution object
    auto sol = newSolution("h2o2.yaml");
    auto gas = sol->thermo();

    gas->setState_TPX(1500.0, 2.0*OneAtm, "O2:1.0, H2:3.0, AR:1.0");
    gas->equilibrate("TP");
    std::cout << gas->report() << std::endl;
}

int main()
{
    try {
        equil_demo();
    } catch (CanteraError& err) {
        std::cout << err.what() << std::endl;
        return 1;
    }
    return 0;
}

The program output is:

 ohmech:

      temperature   1500 K
         pressure   2.0265e+05 Pa
          density   0.31683 kg/m^3
 mean mol. weight   19.499 kg/kmol
  phase of matter   gas

                         1 kg             1 kmol
                    ---------------   ---------------
         enthalpy       -4.1789e+06       -8.1485e+07  J
  internal energy       -4.8186e+06       -9.3957e+07  J
          entropy             11283        2.2001e+05  J/K
   Gibbs function       -2.1104e+07        -4.115e+08  J
heat capacity c_p              1893             36912  J/K
heat capacity c_v            1466.6             28597  J/K

                     mass frac. Y      mole frac. X     chem. pot. / RT
                    ---------------   ---------------   ---------------
               H2          0.025847              0.25           -19.295
                H        3.2181e-07        6.2252e-06           -9.6477
                O        6.2927e-12        7.6693e-12           -26.377
               O2        1.1747e-11        7.1586e-12           -52.753
               OH        3.0994e-07        3.5535e-07           -36.024
              H2O           0.46195               0.5           -45.672
              HO2        1.2362e-14        7.3034e-15           -62.401
             H2O2         6.904e-13        3.9578e-13           -72.049
               AR           0.51221              0.25           -21.339
               N2                 0                 0

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:

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.