This investigation is devoted to linear stability analysis within the solutal analog of Horton-Rogers-Lapwood (HRL) problem with sorption of solid particles. The solid nanoparticles are treated as solute within the continuous approach. Therefore, the infinite horizontal porous layer saturated with mixture (carrier fluid and solute) is considered. The solute concentration difference between the layer boundaries is assumed as constant. The solute sorption is simulated in accordance with the linear mobile/immobile media model. In the first part, the instability of steady net mass flow through this layer is studied analytically. The critical values of parameters have been found. It is known that for the HRL problem the seepage makes the critical mode oscillatory, but the stability threshold remains unchanged. In contrast, if the sorption is taken into account, the stability threshold varies. In the latter case, the critical value of solutal Rayleigh-Darcy number increases versus that for the standard HRL problem. The second part is devoted to investigation of instability for modulated in time horizontal net mass flow. The ordinary differential equation has been obtained for description of the behavior near the convection instability threshold. This equation is analyzed numerically by the Floquet method; the parametric excitation of convection is observed.