Usually you can look up Gibbs Free energy in this form to get  -Delta G/RT or Ln( Keq). Sometimes you will only find  expression in the form A + B/T  for those case C and D = 0. What equilibrium constants are you trying to calculate?

I have attached a link to the JANAF table of thermodynamic properties which may help you find the Gibbs Free energies that you are interested in.

http://kinetics.nist.gov/janaf/

Having Keq vs. T use linear regresion.

y = ao + a1x1 + ...., A = (a1, a2...) = (XTX)-1XTY,  y = ln (Keq), x1= (1/T) etc

Regards,

Typically, such temperature dependency coefficients are aimed to be derived from published thermochemical data and not to be directly fitted to equilibrium experimental data. Indeed, for the last case, Van't Hoff equation could, in principle, provide a preferable approach.

Note that ΔG = - RT·ln(Keq) and ΔG = ΔH - T·ΔS, from what it can be seen that the temperature dependency expected for ΔH and ΔS imparts on that predicted for Keq. We may, in principle, apply Hess's law to derive ΔH for the reaction at some given temperature by referring also to temperature-dependency correlations for the molar heat capacity, whose fitting coefficients, given in terms of powers of T, can be found tabulated at well-known reference thermochemical data sources.

Such correlations can be integrated between the reference temperature (Tº) and some higher temperature (Kirchhoff's equation) to derive the reaction enthalpy for the last temperature (T). We can also calculate the entropy of reaction (ΔS) for that temperature based on temperature-dependency correlations for the specific heat. For each (i) reactant or product with molar heat capacity Cpi: SiT = Siº + ∫Tº,T (Cpi / T)dT, except when additional entropic contribution(s) arising from phase transitions are also to be accounted for.

It follows that the temperature dependency predicted for Keq can be derived from that tabulated for the molar heat capacity of reactants and products, which is commonly expressed as Cp = a + b·T + c·T2 + d·T-2. Both ∫CpdT and T·∫(Cp/T)dT terms contribute to express the ΔG temperature dependency. Integration leads to ∫CpdT = a·T + (1/2)b·T2 + (1/3)c·T3 - d·T-1 + k1, and T·∫(Cp/T)dT = (a/K)·T·ln(T/K) + b·T2 + (1/2)·c·T3 - (1/2)d·T-1 + k2·T, where k1 and k2 are (integration) constants and K stands for the temperature unit (kelvin). From that, it is show that we can generally expect a ΔG temperature dependency of the kind ΔG = A·T + B·T2 + C·T·ln(T/K) + D·T3 + E·T-1 + F. That yields a -R·ln(Keq) = A + B·T + C·ln(T/K) + D·T2 + E·T-2 + F/T temperature dependency for the equilibrium constant.

This kind of temperature correlation reduces to that proposed at the enunciate by neglecting the contribution of the parcels that express the quadratic dependency on T2 and T-2. That would be the case when both these contributions are small or jointly tend to compensate each other. By neglecting the quadratic contributions for Cp, so that Cp = a + b·T, we are also conducted to the expression given in the enunciate.

For constant Cp, the temperature dependency for the equilibrium constant could just conform to: ln(Keq) = A' + B'·ln(T/K) + C'/T.

You need equilibrium data at 4 different temperatures. Then it is 4 equations and 4 unknowns in a matrix inversion or the solution in parts given by other comments.

Make regression to the K vs T data using Excel, SPSS, Quatropro,  mathlab,..

Four temperatures are sufficient - a system of four linear equations with four unknown parameters - but usually you need more.

Regards,

Four data points are only sufficient is you  want to produce a correlation that only fits 4 points exactly.  If you only have four points you should use ln (Keq) = A + B / T .Equilibium/gibbs free energy data is readilly available for most systemsyou should almost always have much more than 4 data points.

One simple linear function (with respect to parameters) and so wide discussion. I am surprised.

In addition, a square term and a cubic term can be included, and use the stepwise regression to determine the value of the equation parameters. Why not?

Regards,