Turns' book - Calculation of the Gibbs function of formation for compounds

[Marie Meulemans]

Hello all, 

I am hitting a wall, but it might be silly.

I am trying to find a way to obtain de Gibbs function of formation of species dependent of temperature, to then be able to calculate the Gibbs energy of a reaction, and then Kp. 

In Turn's book, Appendix A, it is explained the following:

I have been trying to re-calculate the tabulated values, but it does not match!

For example, taking H for simplicity, at 298K:

g = h-Ts = 217,977  -(298 * 114.605)= 183,825 kJ/(kmol.K), which is not the tabulated g of 203,276 kJ/(kmol.K).

How is that calculated then? I have tried many things, but I don't seem to ever fall back on the right value.

Another question, in Cantera, we can access the function '.standard_gibbs_RT' : Array of nondimensional species standard-state Gibbs free energies at the current temperature and pressure.

The values are far from the tabulated ones in Turns. I don't understand what the nondimensional means here... Any help on that too?

Is there a way to obtain the gibbs function of formation for the elements and species in Cantera, or in a tabulated manner ?

My idea was to calculate them based on the Nasa thermodynamic properties (with h and s), but no luck in getting the right calculation methodology.

Thanks for your help!

Looking forward to reading you,

Marie

[Ray Speth]

Hi Marie,

You’re neglecting the last term in the given expression for the standard Gibbs free energy of formation, the sum over the elements in their standard states. This is explained in more detail in Turns’ book in Chapter 2, in the “Chemical Equilibrium” section. Here, the term that needs to be introduced includes the stoichiometric coefficient on H2 (standard state) in the formation reaction for H ( 1/2 H2 -> H ), i.e 1/2, and the standard enthalpy of formation for H2 at 298 K, from table A.3 (130.595 kJ/kmol-K). The calculation is then:

217,977 - 114.605*298.15 - 0.5 * (- 130.595 * 298.15) = 203,276

Which is exactly in agreement with the value given in Table A.4.

For the Cantera properties, “nondimensional” means that the values are nondimensionalized by R or R * T, as appropriate (that is, R * T for enthalpy, enthalpy, and Gibbs free energy and R for entropy and specific heat capacities). If you multiply these out, you’ll get values in line with those in the table:

>>> import cantera as ct >>> gas = ct.Solution('h2o2.yaml') >>> gas.TPX = 298.15, ct.one_atm, {'H': 1.0} # Standard enthalpy (J/kmol) >>> print(gas['H'].standard_enthalpies_RT * ct.gas_constant * gas.T) [2.17997186e+08] # Standard entropy (J/kmol/K) >>> print(gas['H'].standard_entropies_R * ct.gas_constant) [114717.20938001] # Standard Gibbs free energy (J/kmol) >>> print(gas['H'].standard_gibbs_RT * ct.gas_constant * gas.T) [1.8379425e+08]

Note that the Gibbs free energy here is not the Gibbs free energy of formation; it is just h - T*s, and does not include the extra terms in the formula for the formation quantity.

Cantera does include a database of the standard entropies of formation, element-standard-entropies.yaml. However, there isn’t an interface to these values from Python.

Regards,
Ray

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