Compositional displacements in porous media, where chemical components partition between phases during a displacement, occur in flow processes such as surfactant flooding and gas injection. We develop a new approach to solving compositional displacements with volume change on mixing. The result is a new condition on the local volumetric flux that is equivalent to the tangent construction (condition). We demonstrate how this works by solving for the shocks for the simplest case of a two-component, two-phase system. We discuss the use of this procedure for the more general case of arbitrary volume change on mixing and arbitrary number of components.