J . T o u š e k ú l o h a
/17/
3.a-c
3. Thermochemical measurement
3.a. Excerpt from Chapter 3a
The total amount of the released heat Q during reaction in the calorimeter is
determined by the temperature rise in the calorimeter according to the formula:
HTCQ ∆−=∆⋅= (3.1.)
where ∆T is the temperature rise during neutralization, C is the heat capacity of the
calorimeter, which indicates the amount of heat required to heat the calorimetric vessel
with its content of 1
o
C. In the case of an aqueous solution experiment, the C constant
depends mainly on the amount of water (𝑐𝑐𝐻𝐻2 𝑂𝑂
𝑝𝑝
)1,25( AtmC° =4,1796 J K-1
kg-1
).
We calibrate the heat capacity of the calorimeter C by measuring the temperature rise
∆T' in the calorimeter after releasing heat QE , which is produced by the passage of the
current I through the electrical resistor immersed in the calorimeter filling. The heat
capacity is given by eqn
C
Q
T
E I t
T
E
=
′
=
⋅ ⋅
′∆ ∆
(3.2.)
where E is the voltage at the resistance heater terminals and t is the flow time of the
electric current I.
3.b. Determination of thermodynamic functions of galvanic cell
Chemical reactions associated with electron transfer can be realized in
electrochemical cells. For example reaction:
CuZnCuZn +←→→+ ++ 22
(3.3.)
where equilibrium is shifted to the benefit of substances on the right side of the
equation, can be done in the so-called Daniel's cell:
Zn/0,1M ZnSO4 // saturated aq. solution of KCl // 0,1M CuSO4 /Cu (3.4.)
The cell potential of the Daniel's cell is standard cell potential ∆E
o
=1,097 V if the
pressure is 1Atm, t=25°C, and the cationic activities 2+
Cu a 2+
Zn are equal to “1”. The
cation activities usually differ from "standard" conditions, then the cell gives
electromotive voltage:
+
+
+∆=∆
2
2
ln0
Zn
Cu
a
a
nF
RT
EE (3.5.)
where R is the universal gas constant, T is the temperature in Kelvin, n is the number of
electrons transferred in the overall cell reaction (3.3), F=96485 C/mol is the Faraday
constant and 𝑎𝑎𝑖𝑖 is the activity of cation i.
The activities of the 2+
Cu and 2+
Zn cations can be calculated according to the relation
𝑎𝑎𝑖𝑖 = 𝑐𝑐𝑖𝑖 γ𝑖𝑖
±
. The tabulated mean ion activity coefficients are γ𝐶𝐶𝐶𝐶2+
±
= 0,154 and γ𝑍𝑍𝑍𝑍2+
±
=
0,150 for the cationic concentrations of 0,1𝑀𝑀 (see cell note (3.4.)).

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ú l o h a J . T o u š e k
/18/
3.a-c
Electrical work 𝑊𝑊𝑒𝑒 usable from a galvanic cell of voltage ∆𝐸𝐸 is equal to the change in the
molar Gibbs energy ∆𝐺𝐺 that accompanies the electrochemical processes in the cell:
EnFGWe ∆=∆−= (3.6.)
If the article provides a standard electromotive voltage ∆E 0
, then this relationship
applies:
00
EnFG ∆=∆− (3.7.)
where 0
G∆− is standard change of molar reaction Gibbs energy (3.3.), which is related
to the equilibrium thermodynamic constant K of the reaction (3.3) as follows:
ln K
nF E
RT
G
RT
=
⋅
=
−∆ ∆0 0
(3.8.)
Changes in both the molar enthalpy H∆ and the molar entropy S∆ of the reaction in the
cell are linked to the change in molar Gibbs energy ∆G by:
STHG ∆−∆=∆ (3.9.)
The enthalpy change H∆ can be experimentally determined, for example from the
thermal effect of the reaction (3.3) in the calorimeter. The reaction entropy change in the
galvanic cells is given by relation:
pT
G
S 




 ∆
−=∆
δ
δ
(3.10.)
Considering the expression (3.6.), we can make an adjustment and to obtain:
pT
E
nFS 




 ∆
⋅=∆
δ
δ
(3.11.)
This relationship can be used to theoretically calculate the change in the molar entropy
of the reaction in the cell if we evaluate its dependence on temperature (ie, the
sensitivity of voltage ∆𝐸𝐸 to change of T).
The voltage sensitivity to the temperature for the Daniel cell under standard pressure
has a table value:
KV
T
E
P
/1029,4 4−
⋅−=




 ∆
δ
δ
(3.12.)
TASK: Determine the change of the thermodynamic functions and the equilibrium
constant K for the Daniel cell using the calorimetric and potentiometric
measurements of the reaction inside. Compare the theoretical and experimental values
of the reaction entropy (eqns (3.11.)and (3.12.)).
LABORATORY AIDS AND CHEMICALS: zinc and copper electrodes, salt bridge,
2 beakers (150 ml), millivolt meter, calorimeter with accessories according to
exercise 3a, powder zinc, weighting bottle (25 g), pipettes (25 a 50 ml), graduated
cylinder (100 ml), spoon, 0,1M ZnSO4
, 0,1M CuSO4
, saturated KCl.
INSTRUCTIONS: The aim is to obtain a change in the molar reaction enthalpy by
calorimetric experiment at room temperature and to determine the standard
reaction Gibbs energy of the same reaction that occurs in Daniel's cell.
?


J . T o u š e k ú l o h a
/19/
3.a-c
1. Calorimetric measurement. Proceed similarly to the neutralization heat experiment
according to exercise 3a with the following differences: pipette 50 ml 0,1 M CuSO4
into the calorimeter vessel and dilute with 150 ml of water. Insert the cup holder for
powder zinc into the calorimeter stopper instead of the dosing capillary. Put an overstoichiometric
amount (about 3 g) of powdered zinc to the cup. Close the vessel with
the stopper and make sure that the cup involving zinc powder is placed above the
solution and that no zinc fell in solution. The recommended times of temperature
data collection are: initial relaxation 5-7 min, after inserting all zinc in the solution stir
gently few times with the cup holder, and collect temperature data for 10 min.
Switch on the heater element for a time sufficient to increase the temperature by
approx. 0,7ºC . Write down the exact time you switch on and off the heating element
on your computer monitor! Watch the final thermal relaxation for about 10 minutes.
In this way, we get finally a record similar to the dependency on FIGURE 2, EXERCISE
3.A. Visually inspect the course of the reaction (discoloration of the solution) after the
experiment. Empty the calorimeter vessel and rinse it with distilled water.
2. MEASUREMENT OF CELL VOLTAGE. Clean the electrodes with emery paper and rinse
them. Assemble Daniel's cell according to the record (3.4.) and measure its voltage
using a millivolt meter. Check the voltage after 5 min.
REPORT: Graph 1: the time dependent record of the temperature inside the
calorimeter. NEXT: Daniel's cell voltage, electric current and voltage on heating
element used in eqn (3.2.), thermal capacity of the calorimeter C, enthalpy change ∆H,
molar amount of substance Cu2+ reacted in calorimeter vessel, change of molar
enthalpy, cell temperature, electromotive voltage ∆E and standard cell potential ∆E0,
changes in molar Gibbs energy: ∆G a ∆Go, equilibrium reaction constant K .
Comparison of the value ∆S calculated according to eqn (3.9.) with the theoretical value
calculated from the temperature coefficient (eqns (3.11.), (3.12.)).
