# Enthalpy & Entropy

ENTHALPY AND ENTROPY OF ZINC WITH COPPER SULFATE The CCLI Initiative Computers in Chemistry Laboratory Instruction

LEARNING OBJECTIVES The learning objectives of this experiment are to. . . ! ! determine changes in enthalpy and entropy of the reaction of zinc with copper sulfate using two methods: electrochemistry and calorimetry. compare the enthalpy values obtained by the two methods. BACKGROUND Thermodynamics is concerned with energy changes that occur in chemical and physical process es. The enthalpy and entropy changes of a system undergoing such processes are interrelated by the change in free energy, ªG, according to the equation

ªG

=

ªH - T ªS

(1)

This investigation focuses on the reaction Zn(S ) + CuSO4(aq)

Y

ZnSO4(aq) + Cu(S )

(2)

ªG will be calculated from the ªH and ªS values obtained electrochemically. The validity of Equation (1) will be tested by comparing the value of ªH obtained electrochemically with the value of ªH obtained calorimetrically for the same reaction. The electrochemical method The electrochemical method offers simple and accurate means for the determination of thermodynamic quantities. A simple electrochemical cell is constructed in a Chem-Carrou-Cell™ plate as shown in Figure 1. Cu(S )/CuSO4 (aq) || Zn(S )/ZnSO4(aq) (3)

FiªG ure 1: Set-up for measuring E versus temperature.

1

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The overall galvanic cell reaction is Zn(S ) + Cu2+ (aq) Y Zn2+(aq) + Cu(S ) and it is essentially the same as that taking place in the calorimeter. The quantity of the electrical energy, F , produced or consumed during the electrochemical reaction is a constant measured per mole of electrons, and can be accurately measured. The free energy change, ªG , of an electrochemical reaction is related to the voltage, E, of the electrochemical cell by the equation (4)

ªG

where and

= -nFE n

(5)

F

= the number of moles of electrons transferred in a redox reaction. = Faraday's constant of 96,500 C/mole of electrons .

Combining equations (1) and (5), and dividing both sides by the constant “n,” we obtain a linear relationship between the voltage change, ªE, and the enthalpy and entropy changes at different temperatures E = -

ÎH

+ T ªS nF nF

Î

(6)

or E =

ÎS

(T) -

ÎH

nF

(7)

nF

By measuring the voltage E, of our electrochemical cell, at several temperatures, we can obtain a plot of the voltage versus temperature. Assuming that ªH and ªS remain constant over a small temperature range, we can calculate the ªS and ªH from the slope and the intercept of the straight line respectively slope =

ÎS

nF

(8)

and Y-intercept = -

ÎH

nF

(9)

ªG

can now be calculated by means of Equation (1). We can verify its value using Equation (5). Please note that in both cases, ªG must be calculated for the same temperature. If the calculations are done for 298 K (25 °C), we can also verify the experimental value of E° for this temperature by employing the Nernst equation (7) E = E° - RT ln [products ] nF [reactants ] 2 (10)

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where E° is the standard potential measured at 25 ° C and is 1.100V for the cell under consideration. When the concentrations of the ZnSO4 and CuSO4 solutions are equal, the log term of the Nernst equation becomes zero. Under these conditions, the standard voltage, E°, of the cell is equal to the measured voltage, E The calorimetric method The ideal calorimeter is a perfectly insulated vessel which contains a large known weight of solution in perfect thermal contact with an accurate thermometer and a small reaction tube (Figure 2). When measured quantities of reactants are introduced into the reaction tube, the heat of reaction changes the temperature of the calorimeter solution.

Figure 2. Diagram of Calorimeter

The heat of the chemical reaction is given by the equation

ÎH

H n K W Ti Tf

= (K + W)(Ti - Tf) n

(11)

is the heat of reaction at constant...

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