ENTROPY OF MIXING FROM EMF MEASUREMENTS (10/30/2012 11:57:00 AM)

INTRODUCTION

Your assignment is to measure the potential difference as voltages between two aqueous

solutions of potassium ferricyanide [K3Fe(CN)6] and potassium ferrocyanide [K4Fe(CN)6] at various

concentrations. The entropy of mixing for these two solutions will be calculated from the voltage

measurements assuming ideal conditions.

Background material for the relationship between electrochemical measurement and chemical

systems can be found in most Physical Chemistry textbooks or the provided references. The cell

diagram for this system is shown in equation 1.

Pt | K3Fe(CN)6 (m1), K4Fe(CN)6 (m2) || K4Fe(CN)6 (m3), K3Fe(CN)6 (m4) | Pt (1)

Using aqueous solutions containing both of these salts allows for the use of a simple Pt electrode.

The electrode reactions (both e- transfer reactions) are shown in equation 2 and 3.

Fe(CN)63- + e- � Fe(CN)64- (2)

Fe(CN)64- � Fe(CN)63- + e- (3)

By preparing cells in which the concentrations compliment each other (i.e. [Fe(CN)63-]cell 1 =

[Fe(CN)64-]cell 2 and [Fe(CN)63-]cell 2 = [Fe(CN)64-]cell 1), the overall cell reaction is simplified, as shown

in equation 4.

For cells in which m1 = m3, m2 = m4:

Fe(CN)63- (m1) + e- � Fe(CN)64- (m2)

Fe(CN)64- (m3) � Fe(CN)63- (m4) + e-

Fe(CN)63- (m1) + Fe(CN)64- (m1) � Fe(CN)63- (m2) + Fe(CN)64- (m2) (4)

Where m1 = the concentration for cell 1, m2 = the concentration for cell 2, etc. Under ideal

conditions, the Nernst equation relates the cell voltage to the concentrations according to equation

5.

2

1

20

)m()CN(Fe)m()CN(Fe

)m()CN(Fe)m()CN(Fe0 )m

mln(

n

RT

aa

aaln

n

RT

1461

36

2462

36

ℑ−ε≈

ℑ−ε=ε

−−

−−

(5)

Where R represents the gas constant, T is temperature in Kelvin, n is number of moles of e- in the

balanced half-cell reaction, ℑ is Faraday's constant, and aA(m1) represents the activity, or non-ideal

concentration, of solution A at a concentration of m1.

Using the relations ∆GMIX = -nℑε and G = H - TS, the cell voltage can be used to calculate the

entropy of mixing, as shown in equation 6.

Where ∆SMIX (m) = maximum molar entropy of mixing between x = x2 and x=0.5.

NOTE: Physical chemists use molalities (m) or mole/weight fractions (x/X) more often than

molarities (M) because mass measurements are not temperature dependent and therefore

measured more accurately than volume measurements. Use of molarities is recommended for this

experiment since m = M at low concentrations and ideal conditions. Also, measurements and

calculations are simplified if molarities are used for this procedure..

� The entropy for this experiment could not be determined if the following assumptions are

not made: ∆HMIX = 0 and qREV = wMAX

PRE LABORATORY EXERCISE

1. Write the form of the Nernst equation that applies to the above cell in terms of molalities. Also,

write it in terms of mole fractions. Include a calculation that shows the conversion of molalities

to mole fractions.

2. Find the standard EMF for the reaction. (Note: Standard states are usually defined as T =

25oC, P = 1atm).

3. Calculate the EMF for several values of xB, where 0.0 < xB ≤ 0.5. You may assume that the

activity coefficients cancel. You are to compare experimental measurements to these

calculations.

4. Plot the EMF values of step 3 versus xB (from xB > 0.0 to xB = 0.5) and determine the area

under the curve. Predict the entropy of mixing according to equation 6.

5. What is the EMF value at a mole fraction of 0.5? In your final report, compare your

experimental result to this calculation in your final report and explain any discrepancy.

∫ =

ℑ=∆

50.0

)( )6()(BXX

mMIXdxx

T

nS ε

LABORATORY EXERCISE

Figure 1. Example apparatus used for this experiment.

1. Prepare a salt bridge by mixing enough potassium chloride (to make a 1 molal solution) with

enough agar (3-5% by weight) in enough water (50mL) to fill several salt bridges and then

heating on a hot plate until the agar is completely dissolved. Draw the solution into tygon

tubing. Once cooled, the solution should gel and remain in the tubing. Cut the tubing into

~12cm lengths.

2. Prepare 0.100 M stock solutions of potassium ferrocyanide (available as the trihydrate,

K4Fe(CN)6.3H2O) and potassium ferricyanide. (Concentrations should be nearly identical.)

Make enough for 8 or 10 measurements (0.1 ≤ xB ≤ 0.9). Each half cell in your experimental

holds about 50mL (50gm).

3. Prepare by volume, several pairs of solutions that are complimentary to each other using the

above stock solutions.

Figure 2. An example pair of complimentary half cells

4. Place one solution in one half cell and the complimentary solution in the other half cell. Place

the half cells in holders in the constant temperature bath at 298 Kelvin. Place a salt bridge in

the half cells as shown in Figures 2 and 3. Connect each lead from the voltmeter to a piece of

platinum (electrode) and put one wire in each half cell. Make sure that the clips on the leads

do not touch the liquid. Read the voltage and record the results. Make sure that temperature

equilibrium has been reached.

Figure 3. Two half cells connected via a salt bridge, with one of the two platinum

electrodes (connected to alligator clip) visible.

Figure 4. Schematic drawing of an electrochemical cell.

5. Compare the measured EMF values with those calculated in the pre-lab (in step 3).

6. Repeat the experiment using a solution (quantitatively prepared) at a concentration less than

than 0.1M.

CLEAN-UP PROCEDURES

� Clean and rinse all glassware with distilled water. Never use a brush on volumetric glassware.

� Return burets upside down with stopcocks in the open position to a buret clamp in the

northern-most hood of the lab.

� Remove labels and other solid debris from the constant temperature bath.

� Empty the water bath and rinse with clean water if a compound is spilled into the constant

temperature bath.

� Turn off the instrument(s) and return all items to their original location.

� Clean up all spills, particularly on or around balances!

� Discard agar in solid waste receptacles, not in sinks.

REFERENCES

Barrow, Gordan M., Physical Chemistry, 6th ed., McGraw-Hill, New York, 1996 pp 386-412.

Selley, N.J., “Entropy of Mixing: An Electrochemical Measurement”, Journal of Chemical

Education, (1972), 49, 212-214.