We present the first density functional theory (DFT) molecular dynamics (MD) study of metal-molten-salt solutions using the isobaric-isothermal (NpT) ensemble. We study solutions of excess sodium in molten sodium chloride of concentrations ranging from 0 to 11% Na. We use the Widom particle insertion method to calculate the chemical potential of sodium across this concentration range, and find the solubility limit to be between 3 to 6%, in excellent agreement with the experimental solubility limit. We use the same particle insertion method to calculate the standard reduction potential of sodium in molten sodium chloride as 3.9 +/- 0.6 V, in good agreement with the experimental value of 3.18 V. We demonstrate the robustness of our DFT-MD particle insertion method, and discuss applications of our method to modeling electrowinning recycling processes of rare earth metals. (C) 2014 The Electrochemical Society. All rights reserved.