COLLEGE OF SAINT MARY   FALL 2008       BIOPHYSICAL CHEMISTRY      INSTRUCTOR: DR. PETER ILICH

    HOMEWORK # 05

TOPIC:    ION ACTIVITY     MEMBRANE POTENTIAL    GALVANIC CELLS

Copyright © 2008/2010 by Peter Ilich

A pickling solution.

1.    (25 pts) A small amount of concentrated HCl is added to a millimolal (NOTE: "m", not "M") solution of GdCl₃ to bring the HCl concentration of the solution to 0.01 m.   (a) Use the Debye-Hückel Limiting Dilution Law to calculate the activities of both cations in the solution.  (b) What is the actual pH of the GdCl₃ solution?  [Hint: Refer to the WEB lecture pages.]

STRATEGY & ASSUMPTIONS:

      For the problems involving concentrations, activities and equilibrium constants of relatively diluted electrolyte solutions we use the Debye-Hückel Limiting Dilution Law.   We will use this strategy to first calculate the "average" ionic activity coefficient to find out the proton activity in the 0.01 M solution of HCl.

CALCULATION:

We assume that HCl at this concentration is completely dissociated and the concentrations of H⁺ and Cl^- are 0.01 M.

K_eq = [H⁺][A^-] / [HA]

We will then use the Debye-Huckel Limiting Dilution Law to calculate the "average" activity coefficient of the ions:

lg g(H⁺) = -0.509 * z(H⁺)² * I^1/2

and the expression for the ionic strength of the solution, I:

I = 0.5 * {c(H⁺)*z(H⁺)² + c(Cl^-)*z(Cl^-)² + c(Gd⁺³)*z(Gs⁺³)² + 3* c(Cl^-)*z(Cl^-)²}

In this expression for I, "c" is concentration, usually molar.

I = 0.5*{{0.01 * 1² + 0.01^* 1² } + {0.001 * 3² + 3* 0.001^* 1²} = 0.01 + 0.006 = 0.016

and

lg g(H⁺) = -0.509 * 1² * (0.016^)1/2 = -6.44*10^-2 = -0.0644

which gives for the ion activity coefficient,

g_(H+)= 10^-0.0644 = 0.862  -- close to one

For gadolinium we have:

lg g(Gd⁺³) = -0.509 * 3² * (0.016^)1/2 = -5.79*10^-2 = -0.0579

g_(Gd+3) = 10^-0.0579 = 0.263  -- much smaller than one

Now we can calculate the actual pH of the HCl solution:

pH = -lg a(H⁺) = - lg {g(H⁺) * [H⁺]} = -lg g(H⁺) -lg [H⁺] = -0.0644 - lg 0.01  = + 1.94

It's all electrical

2.    (25 pts) A 0.0028 M solution of charged peptide, Z_M = 21, dialyzed against 0.0813 M CsCl, shows Donnan potential of + 9.10 mV.   At what approximate polypeptide concentration will the membrane potential be twenty times lower?  [Hint: Refer to the WEB lecture pages.]

Habeas corpus: DUI

3.    (25 pts) The "Breathalyzer test" -- used by law enforcement agents to detect the presence of ethanol vapors in the "expired" air of vehicle drivers -- is based on the oxidation of ethanol to acetaldehyde, E^ө₂₉₈ (CH₃CHO/CH₃CH₂OH) -0.197 V, and the reduction of (orange) bichromate, Cr₂O₇^-2,  to (green) Cr⁺³ salt. [Check the textbook for the standard potential.]  (a) Write down an acceptable stoichiometric equation for this reaction.  (b) Calculate the E^ө, DG^ө and K_eq for this reaction.  (c) Is the reaction  spontaneous?

You don't need pH paper

4.    (25 pts) A hydrogen electrode and a normal calomel electrode give an electromotive force, E = 0.435 V, at certain solution at 25 °C.  (a) What is the pH of the solution? (b) What is the value of a_H+?