<p>Derivation of exact explicit Einstein-Smolukhowski (ES) relations for non-ideal real gases is purpose of this paper. The ES method of the derivation was modified for this purpose. The new method is based on the rule of differentiation of inverse functions known in mathematics. The modified method turned out to be more effective than the traditional one: the fact is that the modified method always works, while the traditional method is effective only for a small number of simple equations of state (EoS). The method has been tested for four popular EoS: the Lorentz EoS, the Van der Waals EoS, the Peng-Robinson EoS, and the Dieterici EoS. As a result, exact explicit ES formulas for gases obeying these EoS were derived. It was found that the ratio of the diffusion coefficient to the particle mobility coefficient depends not only on the gas temperature, but also on its concentration for all examples of gases. The derived exact formulas can be used to debug codes that simulate molecular dynamics.</p>