Entropy
introduction
The Gibbs’ Free Energy equation is:
∆G = ∆H - T∆S
In this experiment, you will measure the voltage over a 30°
range of temperature. After plotting E versus T, you will
measure the slope of the line. In equation (4),
∆S
slope =
(5)
nF After measuring the slope, multiplying by nF will give a
value for ∆S for the reaction.
(1)
Free energy, ∆G, is the maximum amount of work that
a reaction can perform on the surroundings. Free energy
equals the thermal energy change during the reaction minus
the energy of the entropy change during the reaction. The
thermal energy change is related to chemical bonding, while
the entropy change is related to the disorder of the system.
In today’s experiment, you will measure the entropy change
for the net ionic reaction:
Look at the balanced equation for the reaction. Ions in an
aqueous solution have more mobility than atoms in a metallic solid. Do you expect a positive or a negative value
for ∆S?
Cu(s) + 2Fe3+ (aq) → Cu 2+ (aq) + 2Fe 2+ (aq) (2)
To do this, an electrochemical cell will be constructed, and
its voltage measured over a range of temperatures. The
units for voltage are Joules per coulomb. A coulomb is
6.42 x 1018 electrons. Free energy is obtained from voltage
by the relationship:
∆G = -nFE
(3)
n = moles of electrons transferred in the reaction.
F = 96500 coulombs·mol-1.
E = voltage.
The slope is obtained from a graph of E versus T. The units
for the slope will be volts per K. Use the units for E, n, and
F, given below, to find the units obtained after multiplying
the slope by nF.
Units:
Joules
volts =
coulomb
n = moles
coulombs
F=
mole
For a reaction to be spontaneous, ∆G must be negative, and
E must be positive, hence the negative sign in equation (3).
If equation (3) is substituted into equation (1), then
-nFE = ∆H - T∆S
Dividing by (-nF), and rearranging:
∆S
∆H
E=
⋅T −
nF
nF (4)
Work in pairs
Supplies:
Special Equipment
• 1 platinum electrode (sign out for one)
• 1 copper electrode (scour bright with iron wool)
• 2 glass tubes
• 2 vinyl rings
• 1 bent paper clip
From your drawer
• 1-100 ml beaker
• 1-600 ml beaker
• 1 thermometer
Also
• 1 hotplate
• 1 pH/MV meter with electrical lead
• 2 dialysis membranes
This is a straight line equation of the form:
y = mx + b,
with E as y and T as x. The ∆H term is the constant. The
value of ∆H actually does vary somewhat with temperature,
but it is close to constant over a small temperature span.
Susan Logan helped develop this experiment
experiment
1
Construct two half-cells as follows:
clamp. Attach the clamp on the red lead to the piece of
platinum. Position the wire over the utility clamp on the
ringstand so that the platinum can dip into the Fe2+/Fe3+
half-cell, and the black clamp reaches the copper strip. Tape
the wire to the clamp.
Vinyl
ring
Dialysis
tubing
Electrochemical cells tend to build up polarity on the
electrodes, which causes problems when careful measurements are desired. To avoid this, you will pull the clamp
with the platinum wire out of the half-cell and detach the
clamp from the copper between readings. Suspend them
away from the hot plate. Put them back in the half-cell just
before the next reading.
Glass
tube
The full setup should look like this:
Thermometerhangsfromring
The dialysis tubing is porous to water molecules and small
ions. The vinyl ring should be pushed past the edge of the
glass. Add deionized water to each tube to check for leaks.
Pour out the deionized water.
Tape
p the wire
pe
i
to th
totheclamp
totheclam
tthe
h clam
Use the transfer pipets attached to the reagent bottles to
put 2 ml of 0.1M FeCl3 and 2 ml of 0.1M FeSO4 into one
of the half-cells, and 4 ml of 0.1M CuSO4 into the other
half-cell. Pour 60 ml of 0.1M KNO3 solution into a 100
ml beaker. Then set the half-cells in the beaker. The liquid
level in the beaker should be a bit higher than the liquid
levels in the half-cells.
4mlCu2+
Cu
strip
here,
bent as
shown
600mlbeaker
ml
2mlFe3+
2mlFe2+
Pt
wire
here,
alligator
clamp
attached
tEmp°c
40
60
cALiB
20
80
0
100
pH
tEmp
mV
Atc
With the hot plate off, attach the black clamp to the copper
strip, insert the platinum into the iron solution, turn the meter
to the MV function, and record the voltage (in millivolts)
from the meter, and the temperature (to the nearest degree)
from the thermometer. Remove the electrodes between
readings as described above.
100ml
beaker
Set the hot plate to 3 while you take the rest of the readings.
When the temperature reaches 25°, insert the electrodes,
record the voltage and the temperature, then remove the
electrodes. Repeat this procedure each 5°. Your last reading
should be at or near 50°.
60ml0.1MKNO3 solution
Set the 100 ml beaker into the 600 ml beaker. Add water
to the 600 ml beaker so that the water level is about 1 cm
higher than the level of the KNO3 solution in the 100 ml
beaker. Set the beaker assembly onto a hot plate. Use a ring
stand with a ring and paper clip to suspend a thermometer
into the KNO3 solution in the 100 ml beaker.
Turn off the hotplate and the meter. Pour the solutions into
the waste containers provided for each one of the solutions.
Take the half-cell apart. Dry and return the special equipment. Get signed off on the platinum wire. The membrane
is discarded into the garbage. Clean up, and go on to the
calculations.
Consult directions for the mV meter use. Attach the BNC
connector to the meter. Loop the wire up over the utility
2
Data T able and C alculations
Voltage/mV
Voltage/V
temp/°C
T emp/K
S lope and ∆S C alculation
Draw the best straight line through your data, and
K calculate the slope:
∆y ∆x = __________
K
Use the Entropy Excel template on the computer to graph
K your data. Print a copy, and attach it to the lab. Put names
and the date on the graph. How does the slope compare in
the computer and hand drawn versions of the graph?
K
mV
V
°C
mV
V
°C
mV
V
°C
mV
V
°C
mV
V
°C
Use the slope to calculate ∆S. See equation (5), page 1.
75.
K n = ____; F = 96500 C/mol
mV
V
°C
K ∆S = __________
Graph: Voltage vs T
0.420
0.410
E/volts
0.400
0.390
0.380
0.370
0.360
293
298
303
T/K
3
308
313
318
323
Name_________________________________________ Grade___________ Date ___________
questions
1. Refer to the question in the paragraph following equation (5) on page 1. From looking at the equation for the reaction, did you expect the ∆S to be positive or negative? Why? Show what the units for ∆S are using the units on E, n,
and F as directed in the paragraph.
2. A commonly used “button” battery uses the reaction: Zn(s) + Ag2O(s)
volts. What is ∆G for the reaction? (Hint: First find n.)
ZnO(s) + 2Ag(s). The battery gives 1.5
3. For the reaction used in this experiment, reaction (2) on page 1, give the setup for the Mass Action quotient, Q. The
concentrations of the iron solutions are 0.05M and the copper is 0.1M. Give the numerical value for Q.
4. On the graph for the experiment, go to 308K along the x axis, and find the corresponding voltage on the y axis. Use
equation (3) to find the ∆G. From the equation: ∆G = ∆H - T·∆S, find the value for ∆H for this reaction.
Use ∆S from the experiment, and T = 308K.
5. Measurements made in this lab are very rough. One of the problems lies in the difficulty in getting good voltages
from a simple setup. Another comes from the use of molarities rather than activities for the concentrations. The book
value of ∆S° for this reaction is 296 J·K-1. Did you notice that ∆S, not ∆S°, was used in the text of this lab?
a) What does the ° on the S signify?
b) To measure ∆S° rather than ∆S, the concentrations must be changed. How?
c) For your value of ∆S to move closer to the book value, would the slope of the line on the graph have to be more
or less steep?
4