For an ideal dilute solution, $\mathrm{\Delta }{\mathit{\Phi }}_{\text{d}}$ is the integral of $\mathrm{\nabla }\mathit{\Phi }$ (given by the following equation) across the boundary between two regions of different concentrations. $$\mathrm{\nabla }\mathit{\Phi }=\frac{RT\sum D_i{z}_i\mathrm{\nabla }{c}_i}{F\sum s_i^2{D}_i{c}_i}$$ where $D_i$ is the diffusion coefficient of species $i$, $z_i$ is the charge number of species $i$, $c_i$ is the concentration of species $i$, $R$ is the gas constant, $T$ is the thermodynamic temperature, and $F$ is the Faraday constant.