ResistanceChoose a Value
amps

(amps x seconds)

coulombs

seconds
volts

(volts x coulombs)

joules
Description of the Apparatus         Suggested Operation



































Description:
        This apparatus consists of two ice calorimeters, which measure the amount of ice melted or frozen by heat transfer within the apparatus.  As ice melts or water freezes, there is a change in volume because of the differences in the densities of ice and water.  This change in volume causes mercury to flow into or out of the containers on the balances.  The amount of heat transferred can be calculated very accurately from the change in weight.
        The calorimeter on the left contains a battery with electrical connections to an ammeter (to measure the electrical current) and a switch.  The switch can be short-circuited so that the battery discharges without performing any electrical work, or the battery can be connected to a resistor (and a voltmeter) immersed in the calorimeter on the right.  The electrical work (Wel) may be measured directly as:
     Wel(joules) = volts x amps x seconds
or it may be observed as a heat equivalent based on the change in weight of mercury on the balance on the right.  The apparatus thus allows the heat transfer from the battery and the work performed by the battery to be observed simultaneously.

        The battery is composed of two Metal/Metal Salt Electrodes in aqueous solutions of the sodium salt, separated by an ion-selective membrane which allows only anions to be transferred between the solutions.  The net chemical reaction which occurs inside the battery is given at the top of the page.  The program has three different chemical reactions which may be changed by clicking the mouse on the reaction.  The net chemical reaction in each case involves only pure solid or liquid materials, so that the electrochemical force of the battery is not affected by concentrations.  This also minimizes the PdV work involved in the electrochemical reaction, so that there is effectively no difference between energy changes and enthalpy changes.  The use of an ion-selective membrane in place of a salt bridge eliminates junction potentials so that the Standard Electrochemical Potential of the cell may be determined.  Lastly, the immersion of the components in the ice calorimeters ensures that all observations will be at constant temperature and pressure.

     For this simulation, the batteries are "constructed" so that exactly 0.0100 moles of Lead (Pb) metal will react before the battery "burns out".
 

Process:
        The program allows the battery to be discharged through resistances of 0 ohms to 10,000 ohms.

    When the battery is short-circuited with a resistance of zero ohms, there is maximum current and no electrical work can be performed.  Zero voltage is observed.  In this case, all of the chemical energy of the battery is released as heat and is measured by the ice calorimeter on the left.

    When the battery is discharged through a measureable resistance, a voltage is measured, electrical work is performed, and the effect of this work is measured by the ice calorimeter on the right.

    The maximum electrical work can be performed and the maximum voltage can be observed when the battery is operated reversibly with minimum (zero) current, a state which is approached with a resistance of 10,000 ohms.  This maximum voltage is called the Electrochemical Potential (E) of the Chemical reaction.  For these reactions involving only pure solids and liquids, the Electrochemical Potential is identical to the Standard Electrochemical Potential (Eo).

    The First Law of Thermodynamics is demonstrated by the operation of this apparatus for a specific (complete) reaction with different resistances.  The heat (Q) equivalent and the work equivalent (W) observed in the two calorimeters are different when different resistances are used.  However, the sum of the two is always the same, totaling to the energy (U) or enthalpy (H) released by the chemical reaction.

DU = Q + W
    When no work is performed (resistance = 0), the heat (Q) is related to the energy change (constant volume) or enthalpy change (constant pressure):
DU = Qv     ;     DH = Qp






    The Second Law of Thermodynamics is demonstrated by the reversible discharge of the battery.  The heat equivalent does not approach zero as the battery is discharged reversibly, but approaches a limiting value which is the maximum value (the most positive value or the least negative value) observed for all of the conditions.

Qreversible = Qmaximum
Therefore, the maximum work which can be realized from the chemical reaction is not determined solely by the Energy/Enthalpy of the reaction, but though a combination of the Energy/Enthalpy and the reversible heat.  The definition of Entropy (S) relates the reversible heat to the entropy change at constant temperature:
TDS = Qreversible
For constant temperature,
Wreversible = DU - Qreversible = DU - TDS
and, for constant temperature and pressure,
Wreversible  + PDV= DH - Qreversible = DH - TDS
(in the cases here, DV = 0, so there is no difference between the two).
 
 

    The reversible work at constant temperature is equal to the Helmholtz Free Energy (DA = DU - TDS), and the quantity Wreversible  + PDV at constant temperature and pressure is equal to the Gibbs Free Energy change (DG = DH - TDS).
 

    The operation of this battery under its limiting conditions provides a direct measure of these thermodynamic properties:

     When the resistance is zero, no work is done on the right and the heat equivalent on the left is a measure of the enthalpy change (DH) for the chemical reaction.  Division of this value by the number of moles of Lead (the limiting reagent, 0.0100 moles) gives the standard enthalpy change (DHo) for the reaction of one mole of Lead.

    When the resistance approaches infinity, the battery performs its maximum, reversible work.  The heat equivalent on the left is the reversible heat (TDS) for the reaction.  Division of this value by the number of moles of Lead and the absolute temperature (273.15 K) gives the standard entropy change (DSo) for the reaction of one mole of Lead.
    The work equivalent on the right is the Gibbs free energy change for the reaction (DG).  Division of this value by the number of moles of Lead (the limiting reagent, 0.0100 moles) gives the standard Gibbs free energy change (DGo) for the reaction of one mole of Lead.


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Suggested Operation

Choose one of the programmed reactions to study.

Select the outputs of heat and work equivalences as "Joules".

Operate the simulation with Resistances of 0 ohms, 10000 ohms, and several other values.

In each case record the values of amps and volts,  plus the heat and work equivalences for the complete reaction.  Divide the heat and work equivalences (Joules) by the number of moles of Lead reacted (0.0100).
Note how these values vary with Resistance.

The Eo (Standard Electrochemical Potential) for this reaction  at 0oC is the limiting value of the Voltage as the Current approaches zero.
This may be obtained graphically, by linear regression (y = voltage, x = amps),
or simply by estimation.

The Heat equivalent (Joules/mole of Lead) with Resistance = 0 is equal to the Standard Enthalpy change (DHo) for this reaction at 0oC.

The limiting value of the Work equivalent (Joules/mole of Lead) as the current approaches zero is equal to the Standard Gibbs Free Energy change (DGo)for the reaction at 0oC.

The limiting value of the heat equivalent (Joules/mole of Lead) as the current approaches zero is equal to TDSo for the reaction at 0oC.

Observe the relationships between DHo, DGo, DSo, and Eo for this reaction.
 

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