A novel geometric method based on a sequential slope-intercept approach is derived for estimation of concentration-dependent diffusion, gas absorption, and gas dissolution concentration in gas-liquid binary systems. The gas absorption and diffusion are modeled using an inverse free boundary problem governed by Fick's second law of diffusion and Henry's absorption law. An unknown gas-liquid interface is governed by the Stefan's type boundary condition. Implementation of the estimation method involves piecewise linear approximation of the transformed concentration data and sequential application of the estimated slopes and intercepts from this approximation. Application and validation of the developed estimation method is given for synthetic concentration profiles and for real concentration measurements for a dimethyl ether-bitumen binary system obtained using computer tomography. The developed estimation method overcomes the existing estimation methods derived from polynomial approximations that significantly underestimate or overestimate the diffusion coefficients at very low dissolved gas concentrations.