A chemical activity can be defined as a=γ*x, a=γ*m/mo or a=γ*c/co, where γ is activity coefficient, x is mole fraction in mol/mol, m is molality in mol/kg, c is molarity in mol/L. The mo and co are often described as standard state which equals to 1 mol/kg or 1 mol/L.
However, these three definitions do not give the same activity, chemical potential, Gibbs energy, dissociation constant, ...
Isn't it better to marry they together by selecting the more reasonable standard state values?
For example the ideal gas at pressure of p=101.325kPa and temperature T=298.15K will have molar concentration n/V = p/(RT). So the standard state of ideal gas should be co = 101.325/(8.314*298.15) mol/L. Using this value of co is the activity a=γ*c/co compatible with a=γ*x. There is also possible to express the co and mo of solutions with known properties as total molar mass and density at defined temperature and pressure to be consistent with activity defined as a=γ*x.
Has the multiple definitions of activities, chemical potentials, dissociation constants and so on reasonable background? Or is it only misunderstanding of the standard state of the solution?
the standard state of gas is defined as : gas to be ideal at pressure 1 bar and temperature T.
for solutions you can use different scale for standard state and it means different scale for activity. in each scale you compare chemical potential of the solution with the corresponding standard state and in thermodynamic this difference is important not absolute value of chemical potential.
Does this different scaling for standard state realy scale the activity resulting in shift of chemical potential, in shift of free Gibbs energies of formation, in shift of enthalpy of formation and/or in shift of entropy of formation of each substance composed with more than one atom? So each value from physical chemistry must have the reference to selected standard state?
Formation quantities compare two states the scale is not important but the scale afect chemical potential. We define chemical potential by comparing the system with a reference state (standard state). You can find more details in physical chemistry by Levine.
If you compare the state of the same amount of substances before and after reaction then the change of chemical potential (change of free Gibbs energies) is independent on selected standard state. However if the free Gibbs energy of the reaction is calculated from Hess law with different number of products and different number of reactants then there could be the strong dependence on selected standard state. As a result I expect the different values of free Gibbs energies of formation for substances containing more than one atom in the molecule using different reference states.
Let us have three definitions of activity ac = gamma * c, am = gamma * m and ax = gamma * x, where c is molarity (mol/L), m is molality (mol/kg), x is mole fraction (mol/mol) and gamma is activity coefficient of the substance. Typically are these values different, e.g. in water solution of density 0.997 kg/L at 25°C and molar mass of 18 g/mol the comparison of the values are 0.01805*ac = 0.018*am = ax. If we assume that the dissociation constant can be defined also using different activities then we can have also three different dissociation constants Kc,Km and Kx. E.g. reaction A B + C in water solution of density 0.997 kg/L at 25°C and molar mass of 18 g/mol, where Kc = ac(B)*ac(C)/ac(A), Km = am(B)*am(C)/am(A) and Kx = ax(B)*ax(C)/ax(A), the comparison of the values are 0.01805*Kc = 0.018*Km = Kx. And because there is a relation between dissociation constant and free Gibbs energy of the reaction ΔrG° expressed as -R*T*ln(K) = ΔrG°, there must be also three different denifitions of ΔrGc°, ΔrGm°, ΔrGx° with three different values in our solution, where ΔrGc° + RT*ln(0.01805) = ΔrGm° + RT*ln(0.018) = ΔrGx°. And the result of the Hees law is that there must be also three different definitions of free Gibbs energies of formation of the substance... Crazy, isn't it?
The Hess law deals with reaction enthalies! Note, that in most of the thermodynamic tables the enthalpies of formation Hf follow Hess, the entropies Sf - the III. principle. If you calculte properties of solutions the definition of activity is important, but it is not very difficult to calculate Km, Kx or Kc.
The free entropy of formation is not the entropy from the III. law of thermodynamics for the same substance!!! And I am sure that you can use Hess law for entropies of formation and for free Gibbs energies of formation in the same patern as you use Hess law for enthalpies of formation to reach the enthalpy change of reaction. That is the base of these formation values, isn't it? Please note, that dfG=dfH-T*dfS where T is temperature in K, dfG is free Gibbs energy of formation in J/mol, dfH is free enthalpy of formation in J/mol and dfS is free entropy of formation in J/(mol.K).
Dear Marek
you can find your answer in chaters 11.1 and 11.2 of the physical chemistry by Levine.
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