If the macromolecule is uncharged, the second term in Eq (11.50) vanishes. The charge effect, whether it arises from added electrolyte or from a positive charge on the macromolecule, increases the osmotic pressure. Problem 11.2 deals with Eq (11.50a)

Example: A macromolecule with a charge of+10 and a concentration of 10- M is dissolved in the solution on one side of a membrane, while a 10"3 M sodium chloride solution initially fills the other side. At equilibrium, the osmotic pressure is:

11.7.4 Membrane potential difference

Because of the imbalance in the Na+ and Cl" concentrations on the two sides of an osmotic cell, there exists an electric potential difference across the semipermeable membrane. The potential difference is determined by equating the chemical potentials of Na+ on the left and right sides of the membrane:

m Na += m Na++ RT ln[ Na + ]l + Ff m N += m o, + + RT ln[ Na + ]r+ Ff r (11.51)

where F is Faraday's constant. Equating and solving for the potential difference yields:

RT ,.,( [Na + ]R | RT ,J [NaCl]o f, - fR _ _lnl --^ I _ —lnl-L-^-I (11.52)

The same result is obtained by equating the chemical potentials of Cl" on the two sides, recognizing that because of the change in sign of the ion, the plus sign in front of the last terms in Eq (11.51) becomes a minus sign. That the same electric potential difference is obtained from either ion is simply a consequence of the Donnan equilibrium, Eq (11.46).

Example: A macromolecule with a charge of+10 is on one side of a membrane at a concentration of 10-4 M while a 10" M sodium chloride solution occupies the other side. The electric potential difference between the solutions on either side of the membrane is:


How can the existence of a potential difference across the membrane be reconciled with the condition of electrical neutrality of solutions on both sides? The answer is that the charge difference is localized at the membrane, which acts as a capacitance. The membrane potential difference has profound implications in mammalian cells because it permits species to be transferred into and out of the cell against concentration gradients.

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