The mass flux of a species can be written using the chemical potential as a driving force. Consider the simple case of binary diffusion in an ideal mixture of liquids. If the chemical potential is given by:

\[\mu_{i}^{c}=\mu_{i o}^{c}+R T \ln x_{i}\]

prove that the total flux $\boldsymbol{j}_{a}+\boldsymbol{j}_{b}=0$. What must hold true if the chemical potentials are given by the equation below and the sum of the fluxes is to be zero?

\[\mu_{i}^{c}=\mu_{i o}^{c}+R T \ln \left(\gamma_{i} x_{i}\right) \quad \gamma_{i} \text { is the activity coefficient }\]