Second law analysis (entropy generation) for the steady two-dimensional laminar forced convection flow, heat and mass transfer of an incompressible viscous fluid past a nonlinearly stretching porous (permeable) wedge is numerically studied. The effects of viscous dissipation, temperature jump, and first-order chemical reaction on the flow over the wedge are also considered. The governing boundary layer equations for mass, momentum, energy and concentration are transformed using suitable similarity transformations to three nonlinear ordinary differential equations (ODEs). Then, the ODEs are solved by using a Keller’s box algorithm. The effects of various controlling parameters such as wedge angle parameter, velocity ratio parameter, suction/injection parameter, Prandtl number, Eckert number, temperature jump parameter, Schmidt number, and reaction rate parameter on dimensionless velocity, temperature, concentration, entropy generation number, and Bejan number are shown in graphs and analyzed. The results reveal that the entropy generation number increases with the increase of wedge angle parameter, while it decreases with the increase of velocity ratio parameter. Also, in order to validate the obtained numerical results of the present work, comparisons are made with the available results in the literature as special cases, and the results are found to be in a very good agreement.