The purpose of this series is to make a thermodynamic analysis of the Fe-C system with a minimum of assumptions and to revise the equilibrium diagram of the same system in the light of the results of this investigation. In this paper, the first of the series, activities in liquid Fe-C alloys have been evaluated up to saturation, using Richardson and Dennis' data123 on dilute solutions of carbon in liquid iron and Darken and Smith's model~([1]) for carbon dissolved in austenite with certain modifications.A parameter α_c defined as logγc/N_Fe~2 with reference to graphite as the standard state is plotted against N_c for both austenite and Fe-C melt in order to facilitate the evaluation of α_(Fe) by graphical integration. Smith's data~([1]) on equilibrium between austenite and gaseous mixtures (CO_2/CO, CH_4/H_2) are re-treated to yield α_c~γ-N_c~γ curves for 800° and 1000℃ as shown in Fig. 1. On the assumption that L_c~γ the relative partial molal enthalpy of carbon in austenite, does not chan preciably with temperature, the α_c~γ-V_c~γ curve for 1153℃, the iron-graphite eutectic temperature, is obtained by extrapolation and found to lie above the graphite saturation point. This fact seems to indicate that the limit of application of Darken and Smith's model is reached somewhere around N_c~γ=0.0661 (1.50%) and a point of inflection should occur at this concentration. The above-mentioned assumption has been semi-quantitatively proved in this paper and will be discussed further in another paper of this series.In a similar manner, α_c~l-N_c~l curves for liquid Fe-C alloys are drawn through the experimental points of Richardson and Dennis on equilibrium between CO_2/CO mixed gases and dilute solutions of carbon in liquid iron at 1560° and 1660℃ as shown in Fig. 1. The curves are extended up to N_c~1=0.15 on the basis of Darken and Smith's model using 3600 cals. as the energy of interaction at 1560℃ between carbon atoms in the neighbouring interstitial sites as recommended by Richardson and Dens. Then, a suitable curve is drawn between N_c~l=0.15 and the graphite saturation point for 1560℃ to meet certain requirements, and a corresponding curve for 1660℃ is obtained by extrapolation, assuming that L_c~l, the relative partial molal enthalpy of carbon in liquid iron, does not change appreciably with temperature. Thus, α_c~l-N_c~l curves for 1560° and 1660℃ are completed from low carbon concentrations up to saturation. The activities of carbon in Fe-C melts at 1600℃ with reference to graphite as the standard state are readily obtained at different carbon concentrations by interpolation, from which the reversible electromotive forces of a concentration cell of the type Fe,C