This paper presents residual values of Helmholtz energy (A(r)/(RT)), entropy (S-r/R), and internal energy (U-r/(RT)) for a ternary mixture that resembles a distribution natural gas between 223.15 K and 303.15 K up to 20 MPa. The methodology uses isochoric and isothermal density measurements to apply corrections to the residuals for Helmholtz energy (delta A(r)/(RT)), entropy (delta S-r/R), and internal energy (delta U-r/(RT)) calculated using an equation of state. The method is demonstrated for three representative equations of state: REFPROP, Peng-Robinson, and Redlich-Kwong. Accurate (p-rho-T) isochoric and isothermal data provide experimental values of the compression factor (Z) and the derivative of pressure with respect to temperature at constant density (partial derivative(p)/partial derivative(T))(rho) which are used to calculate residual entropies and energies. The results obtained by using different equations of state at the same conditions have slight differences in the residual values. It is possible to represent those differences by equivalent changes in temperature for entropy (delta T-S) and internal energy (delta T-U) that are <= 0.5 K for temperatures above 225 K. For this mixture, the values of delta A(r)/(RT), delta S-r/R, and delta U-r/(RT) determined from REFPROP are sufficiently small that no corrections are required. For the Peng-Robinson and Redlich-Kwong equations of state, a global fit describing the residual corrections presents a practical application. The residual deviations of the plots lie within +/- 0.0005, +/- 0.001, and +/- 0.002 in the residuals for delta A(r)/(RT), delta S-r/(RT), and delta U-r/(RT), respectively.