Osmotic Work in Biological Systems

If we assume that solutes in biological systems are at low enough concentrations to obey Henry s law, their chemical potentials are given individually as [Equation (15.11)] 

the change in the Gibbs function for the transfer of one mole of the solute from a molality m2 to a molality m is 

If m2 is greater than m2, then AGm is positive and work must be performed on the system by the surroundings to carry out the transfer. According to Equation (7.80) 

For example, if the molahty of glucose in blood is 5.5 x 10 mol kg and in urine is 5.5 X 10 mol kg, then to transport glucose back into the blood, the kidney must perform work against this gradient equal to at least 

Any mechanism suggested for carrying out the active transport of glucose in the kidney must provide at least this much work. 

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