### Entropy of Mixing

Author: J. M. McCormick

Last Update: October 13, 2013

**Introduction**

In this exercise you will first determine the entropy of mixing (Δ_{mix}*S*) by measuring the potential for a series of complementary solutions of potassium hexacyanoferrate(III) and potassium hexacyanoferrate(II) (i. e., potassium ferricyanide and potassium ferrocyanide, respectively). You are referred to experiment 7 in Halpern and McBane for more background on the theory of this exercise.^{1} Equation 6 (and also 3b) in experiment 7 in Halpern and McBane describes ideal mixing, that is one in which there are no intermolecular interactions and so the enthalpic contribution to Δ_{mix}*G* is 0. If instead of an ideal solution we consider our system to be a regular solution (the excess entropy of mixing, *S ^{E}*, equals 0, but the excess enthalpy,

*H*, does not equal 0),

^{E}^{2}then there is an additional term in the equation for Δ

_{mix}*G*due to

*H*that reflects the interactions between the solute with the solvent and between solute particles in the solution.

^{E}^{2}The goal of this exercise is to evaluate the assumption that was made in Halpern and McBane that the ferricyanide and ferrocynanide solutions are ideal by finding a method to evaluate

*H*. You should remember that Δ

^{E}

_{mix}*G*should depend on the temperature and that, since ionic compounds are involved, the ionic strength may play a role in mixing as it affects the solute activities.

^{3}

*Procedure*

The procedure is essentially identical to that given in the literature.^{1} However, you will be using two button platinum electrodes instead of platinum wire or platinum sheet electrodes. A digital voltmeter to measure the potential and a water bath to provide a constant temperature will be available.

**Results and Discussion**

Analyze your data according to the literature procedure.^{1} You can transfer your data to LoggerPro and use its fitting capabilities instead of Excel, if you wish. How well do your data match the ideal case? Can you use the method you developed to find *H ^{E}*? If so what is the value (and the uncertainty) in

*H*? You should present a graph of the cell potentials as a function of mole fraction, and your data for the dependence of Δ

^{E}

_{mix}*G*as a function of either ionic strength or temperature (the form is left up to you, but you should take care as a table may

__not__be the best way to present the data). Note that a quantitative propagation of error analysis will be essential to determine whether your value of

*H*is meaningful.

^{E}

- 1. Halpern, A. M. and McBane, G. C.
*Experimental Physical Chemistry, 3*; W. H. Freeman: New York, 2006, p. 7.1-7.10.^{rd}Ed. - 2. Atkins, P. and de Paula, J.
*Physical Chemistry, 8*; W. H. Freeman: New York, 2006, p. 148-150.^{th}Ed. - 3. Atkins, P. and de Paula, J.
*Physical Chemistry, 8*; W. H. Freeman: New York, 2006, p. 163-166.^{th}Ed.