Understanding the interactions of a solute with its environment is of fundamental importance in chemistry and biology. In this work, we propose a deep neural network architecture for atom type embeddings in its molecular context and interatomic potential that follows fundamental physical laws. The architecture is applied to predict physicochemical properties in heterogeneous systems including solvation in diverse solvents, 1-octanol-water partitioning, and PAMPA with a single set of network weights. We show that our architecture is generalized well to the physicochemical properties and outperforms state-of-the-art approaches based on quantum mechanics and neural networks in the task of solvation free energy prediction. The interatomic potentials at each atom in a solute obtained from the model allow quantitative analysis of the physicochemical properties at atomic resolution consistent with chemical and physical reasoning. The software is available at https://github.com/SehanLee/C3Net.