This work is devoted to the modelling of phase transition. The thermodynamic model for phase transition chosen is a model with two equations of state, each of them modelling one phase of a given fluid. The mixture equation of state is obtained by an entropy optimization criterion. Both equations of state are supposed to be convex and a necessary condition is found to ensure the convexity of the mixture equation of state. Then we investigate the Riemann problem for the Euler system with these equations of state. More precisely, we propose to take into account metastable states. We check that the Chapman-Jouguet theory can be applied in our context, and that it is consistent with the entropy growth criterion. As the characteristic Lax criterion does not hold for this solution, an additional relation, the kinetic closure is necessary. The common closure, i.e. the Chapman-Jouguet closure is proved to be uncorrect in general in that context.