A linear and nonlinear stability analyses are carried out for a double‐diffusive chemically reactive fluid layer with viscosity being a function of temperature and pressure. The linear stability analysis is studied when the stabilizing salt gradient acts against the destabilizing thermal gradient. The effect of reaction parameters and variable viscosity on the stability of the system is studied for heated below, salted above, and the heated and salted below models with Rigid–Rigid boundary conditions. Chebyshev pseudospectral method is applied to determine the numerical solutions.