James Richard Fromm

A living organism requires energy simply to survive as an organized structure, let alone to perform any useful functions. In this section we explore the energy usage of organisms in a particular area of chemistry, osmotic work.

Membranes, or separators, are found in all living systems, and are usually made up of lipids. Artificial membranes can also be fabricated and are of great industrial utility (for example, in the electrolytic chloralkali industry). One place where membranes occur naturally is in the walls of cells.

These natural and artificial membranes are called semipermeable membranes because some species dissolved in aqueous or other solutions can move (permeate) through them while others cannot. In general, small entities (perhaps ions such as sodium ion, potassium ion, chloride ion, and carbonate ion; perhaps only water molecules; or perhaps both) can permeate through them to a greater or lesser extent while larger entities such as proteins cannot. This difference can give rise to an osmotic pressure if the concentrations of ions or solvent are different on the two sides of such a membrane.

Suppose we have a perfect semipermeable membrane through which only solvent, which in biological systems means water, can pass. On side A of the membrane let there be an aqueous NaCl solution whose concentration is 0.1 molar, while on side B let there be a similar aqueous NaCl solution whose concentration is 0.01 molar. Obviously, the spontaneous reaction is the passage of water from B to A to equalize the concentration of NaCl, or more accurately the concentrations of Na+(aq) and Cl-(aq), on both sides. This will increase the amount of water in A and decrease that in B.

This difference in height of water is a pressure, called the osmotic pressure. It is found to follow the ideal gas, or ideal solution, law pV = nRT, where n is now the number of moles of solute present, p is now the osmotic pressure of the solution, and the other quantities have their usual meaning. In this case,

pos,A = RT x n/V = 0.08206 L-atm/K mole x 298.15 K x 0.1 mol/L x 2, since we get two particles, one sodium ion and one chloride ion, per mole of sodium chloride. As a consequence, pos,A = 24.45 x 0.2 atm = 4.89 atm and pos,B = 24.45 x 0.02 atm = 0.049 atm. The osmotic pressure difference is then 4.40 atm, with p(A) greater than p(B). Water will therefore spontaneously permeate from B into A until the pressure of the water column is 4.40 atmospheres, which will then oppose and stop the flow driven by 4.40 atm of osmotic pressure. This is about equivalent to the pressure head developed by forty meters of water.

A difference in osmotic pressure can be expressed as a free energy difference as well. Since -DG0 = RT ln K, where K can be expressed in any concentration unit such as pressure or molarity, -DG0 = RT ln c(2)/c(1) = 5.70 kJ/mole. The free energy change for transfer of the solute salt from B to A is -5.70 kJ/mole and the free energy change for transfer from A to B is +5.70 kJ/mole.

The importance of concentration differences across cell walls can be seen from the information below. Active and passive pumping are the processes which establish these gradients by moving materials across a semipermeable membrane; active pumping is against the concentration gradient, while passive pumping is with the concentration gradient.

Human kidneys process by this active pumping about 190 liters/day of fluid, reducing its volume to about 1.5 liters of urine per day. They recycle one or more kg/day of NaCl, about 0.5 kg/day of NaHCO3, about 0.15 kg/day of glucose, and many other components. This is active pumping since it consists of the removal of water against a salt gradient. The process by which the stomach secretes 0.2 molar HCl, which also occurs against a concentration gradient, is similar. Both active pumping processes require energy, which is supplied by ATP. The method of coupling between the exergonic use of ATP and the endergonic active pumping is not yet clearly understood.

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Copyright 1997 James R. Fromm