Lab 8 (T) Flashcards
The Nernst Equation
Ecello = Eredo(cathode) - Eredo(anode) (1)
When the concentration of dissolved entities is not 1.00 mol/L and the pressures of gases differ
from 1 bar, the cells are called nonstandard.
The potentials of the half-cells vary with the concentrations and pressures of entities involved as described by the Nernst equation, which at 25.0 °C has the form:
E298 K = Eo -0.05916V / n log Q (2)
When equation (2) is applied to a full cell, Q is the reaction quotient, n represents the number of moles of electrons exchanged in the balanced redox reaction, and E° is the difference between the
two standard half-cell potentials as given in equation (1). For a general equation:
aA = bB ⇌ cC + dD (3)
the reaction quotient, Q, is defined as:
Q = [C]c[D]d / [A]a[B]b
where a, b, c and d are stoichiometric coefficients in the balanced equation. If the concentrations are all 1.00 mol/L, then Q = 1, log Q = 0, and E = E°.
Spontaneous Cell Reactions
For the reaction to occur spontaneously under standard conditions, E°cell must be positive. A spontaneous reaction will always result when the oxidation half-cell has a more negative reduction
potential than the reduction half-cell.
Cell Notation
Half-cells are sometimes written as: Ag(s)|Ag+(aq, 0.10 mol/L). This describes a half-cell consisting
of a silver electrode placed in a 0.10 mol/L silver nitrate solution. The symbol | separates the different phases (solid, liquid, and gas).
When this notation is used to describe a complete cell, the cell notation is written in the direction
of electron flow through the external circuit.
For example, in the electrochemical cell constructed
from two half-cells: Zn(s)|Zn2+(aq, 1.00 mol/L) and Cu(s)|Cu2+(aq, 1.00 mol/L), the reduction potential of the copper half-cell is more positive and this half-cell will be the cathode.
The zinc half- cell will be the anode where electrons are produced (Zn(s) → Zn2+(aq) + 2 e–) so the electron flow in the external circuit is from zinc to copper. The symbol || is used to represent a salt bridge.
The cell will thus be written as:
Zn(s)|Zn2+(aq, 1.00 mol/L)||Cu2+(aq, 1.00 mol/L)|Cu(s)
Calculation of the Cell Potential at Nonstandard Conditions
To write a balanced chemical equation for the overall cell reaction, we must first balance the
number of electrons gained in the reduction process with the number of electrons lost in the
oxidation process.
Recall that solids and liquids are not included in the reaction quotient.
Note that E° for a half-cell reaction is not changed even if the half-cell is multiplied by an integer.
Electrode potentials and cell potentials are intensive quantities like density.
Density is mass per unit volume, so values of density are independent of the volume of the sample.
A volt is 1 Joule of work per unit of charge transferred so values of E° are independent of the number of charges or electrons transferred.
Reference and Test Solutions to determine Solubility Products and Formation Constants
An alternate use of the Nernst equation is to use a measured cell potential along with equation (5)
to determine unknown concentrations of a metal ion.
Assume that you want to determine the concentration of the metal ion in a test solution.
First, you must determine which half-cell is the anode and which is the cathode.
Solubility product constants,
In this experiment, dipping a metal electrode into a 1.00 mol/L solution of its own metal cations will form the reference half-cell.
Solubility product constants, Ksp, and formation constants, Kf, are equilibrium constants for specific
kinds of reactions.
The only difference is whether the complex formed is charged (remaining in solution) or neutral (precipitating from solution).
Determination of Anode and Cathode
Before you start the experiment, you will determine which of the leads is connected to the more positive terminal.
To do this, recall that the cathode always has the more positive reduction potential when compared
to the anode in a voltaic cell.
Set up your half-cells. Then connect the voltmeter to the electrodes so that you get a positive reading on the voltmeter (if your first connection gives a negative reading, reverse the leads to the meter).
This procedure allows you to identify which electrode is the cathode, since it will be the one connected to the positive red lead. The other electrode is the anode.
Effect of Concentration on Electrode Potentials
will prepare a series of Ag/Ag+ half-cells using silver nitrate (AgNO3) solutions of different concentrations.
A strip of silver metal will be put into each solution, in turn, to form the test half-cells.
You will compare the potentials of these half-cells to a reference half-cell containing 1.00 mol/L AgNO3 A 1.00 mol/L AgNO3 solution compared to a reference 1.00 mol/L AgNO3 solution has a potential of 0.000 V, E°cell = 0.0.
The slope of a plot of the cell potential (Ecell) versus log Qcell is related to the Nernst equation constant.
Since both half-reactions involve Ag+(aq)|Ag(s), the only driving force for reaction is the difference
in silver ion concentrations.
The cell is moving towards equilibrium where the two concentrations are equal.
To achieve equilibrium, the larger concentration must be decreased which occurs at the cathode (silver ions are reduced to solid silver).
Similarly, the smaller concentration must be increased by production of more silver ions which occurs at the anode.
Cathode: Ag+ (aq, 1.00 mol/L) + e- → Ag(s)
Anode: Ag(s) → Ag+ (aq, x mol/L) + e-
Overall equation: Ag+ (aq, 1.00 mol/L) → Ag+ (aq, x mol/L)
Qcell = [Ag+]anode /[Ag+]cathode = [Ag+]anode /1.00 mol/L
Determination of an Equilibrium Constant
At equilibrium, Ecell (nonstandard cell potential) is equal to zero (no driving force for reaction in
either direction) and the reaction quotient, Q, is equal to the thermodynamic equilibrium constant, Keq.
Substituting these values into equation (9) gives the following equation at equilibrium.
Ecello = 0.05916V / n log Keq
The theoretical value for Keq is calculated using the standard cell potential in the above equation.
The following reaction will be studied in this experiment:
2 Ag+(aq) + Cu(s) → 2 Ag(s) + Cu2+(aq)
The reference half-cell is Cu2+(aq)|Cu(s) which is maintained at standard conditions (1.00 mol/L)
and the test half-cell is Ag+(aq)|Ag(s). The silver ion concentration in the test solution is varied and the cell potential is measured.
A plot of Ecell versus log Qcell is plotted where Qcell = [Cu2+(aq)]/[Ag+(aq)]2.
When the cell potential equals zero, the reaction is at equilibrium and Qcell equals Keq.
The graph is extrapolated to the point when Ecell equals zero to find the value of Keq for reaction (16).
It is compared to the theoretical
value of the equilibrium constant obtained from equation (15).
Determination of a Solubility Product
you will prepare a saturated solution of silver carbonate (Ag2CO3) and determine the
solubility product constant of Ag2CO3.
Ag2CO3(s) ⇌ 2 Ag+(aq) + CO32-(aq)
In making the solution, 1.0 mL of 0.10 mol/L AgNO3 will be added to specified volumes of 1.00
mol/L Na2CO3.
The limiting reagent in this reaction will be the silver ions.
Use of an excess amount
of anion allows for a relatively simple calculation of the anion concentration after reaction using
the stoichiometry of the reaction and the amounts of reagents mixed together.
Assuming that most of the silver nitrate reacts, the concentration of silver ions after reaction is
very small (≈ 0).
Using Ag+(1.00 mol/L)|Ag(s) as the reference half-cell, the cell potential is measured.
The equilibrium [Ag+]in the silver carbonate solution is calculated using the Nernst equation and an ICE table used to determine the equilibrium concentrations.
The error in the determined value for the silver ion concentration will depend on the error in measuring Ecell, which will be much larger than the error in measuring the volume of Na2CO3.
The measurement of Ecell will therefore determine the error in the calculated value of Ksp.
