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Lodz University of Technology, Faculty of Chemistry, Institute of Applied Radiation Chemistry, Laboratory
II. ELECTROCHEMISTRY
Introduction In 1812 Humphry Davy wrote: “ If a piece of zinc and a piece of copper be brought in contact with each other, they will form a weak electrical combination, of which the zinc will be positive, and the copper negative; this may be learnt by the use of a delicate condensing electrometer ”. One can consider what happens when electrodes (zinc and copper in Davy’s experiment) are immersed in electrolyte solutions and connected via an external metallic conductor. Such an arrangement is a typical electrochemical cell.
Electromotive force (EMF) of the cell One can consider a cell built from a zinc electrode immersed into a solution of ZnSO 4 and a copper electrode immersed in CuSO 4 (Daniel’s cell). The two solutions are separated by a porous barrier, which allows electrical contact but prevents excessive mixing of the solutions by interdiffusion. This cell can be represented by a scheme:
Zn|Zn2+|Cu2+|Cu
where vertical line denotes phase boundaries. According to definition given by IUPAC the electromotive force (emf), E, is defined as follows: the emf is equal in sign and in magnitude to the electrical potential of the metallic conducting lead on the right when that of the similar lead on the left is taken as zero, the cell being open. Thus it can be written that: E Eright Eleft 1
where Eright and Eleft would be the potentials of the right and left leads relative to some common standard. The meaning of left and right refers to the cells as written.
Measurement of emf – the potentiometer The definition of emf states that the potential difference is measured while the cell is open, i.e., while no current is being drawn from the external leads. In practice E is being measured under conditions in which the current drawn from the cell is so small as to be negligible. The
Lodz University of Technology, Faculty of Chemistry, Institute of Applied Radiation Chemistry, Laboratory
method, devised by POGGENDORF used a circuit known as potentiometer (a basic one is shown in Figure 1).
Figure 1. Potentiometer scheme
The slide wire is calibrated with a scale so that any setting of the contact corresponds to a certain voltage. With a double through switch in the standard cell position S, slide wire is set to the voltage reading of standard cell, and rheostat is being adjusted until no current flows through the galvanometer G. At this point the potential difference between A and B, the IR along the section AB of the slide wire, just balances the emf of the standard cell. Then switch of the unknown cell is being set to the X position and slide wire is being readjusted until no current flows through galvanometer. From the new setting the emf of the cell can be read directly from the scale of the slide wire. The most widely used standard is the Weston cell written as: Cd(Hg)|CdSO 4 · 8/3 H 2 O|CdSO 4 (sat.sol.)|Hg 2 SO 4 |Hg The cell reaction is:
Cd s Hg 2 SO 4 s 38 H 2 O l CdSO 4 38 H 2 O s 2 Hg l
The accuracy of the compensation method for measuring an emf is limited only by the accuracy of the standard E and of the various resistances in the circuit. The precision of the method is determined mainly by the sensitivity of the galvanometer used to detect the balance between unknown and standard emf.
Reversible cells An electrode immersed in a solution is said to constitute a half cell. The typical cell is combination of two half cells. One should be primarily interested in so called reversible cells, which can be recognized by the following criterion: the cell is connected with a potentiometer arrangement for emf measurement by compensation method. The emf of the cell is measured:
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electrodes either to accept electrons from, or to donate electrons to ions in the solution they are all in the sense oxidation-reduction electrodes. Metal, insoluble salt electrodes consist of a metal in contact with one of its slightly soluble salts; in the half cell, this salt is in turn in contact with a solution containing common anion. An example is the silver, silver chloride half cell Ag|AgCl|Cl-(c 1 ) and overall electrode
reaction is AgCl s e Ag s Cl .
Metal, insoluble oxides electrodes are similar to the metal, insoluble salt one e.g. antimony, antimony trioxide electrode with a scheme Sb|Sb 2 O 3 |OH—and an overall reaction
Sb s 3 OH 21 Sb 2 O 3 23 H 2 O l 3 e. An antimony rod is covered with a thin layer of
oxide and dips into a solution containing OH-^ ions.
Classification of cells When two suitable cells are connected an electrochemical cell is given. The connection is made by bringing the solutions in the half cells into contact so that ions can pass between them. If these two solutions are the same, there is no liquid junction, and one can have a cell without transference. If the solutions are different, the transport of ions across the junction will cause irreversible changes in the two electrolytes, and one can have a cell with transference. Cells in which the driving force is the change in concentration are called concentration cells. The change in concentration can occur either in the electrolyte or in electrodes. The variety of electrochemical cells is given in Figure 2.
Electrochemical cells
Chemical cells Concentrationl cells
Without transference
With transference
Electrolyte Concentration cells
Electrode Concentration cells
Without transference
With transference
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Figure 2. Electrochemical cells
Emf and standard emf of the cell For generalized cell reaction:
aA bB cC dD
free-energy change in terms of the activities of the reactants is:
aA Bb Cc Dd a a G G^0 RT ln a a 3
Since G=-|z|FE, division by -|z|F gives
aA bB
cC Dd a a
a a zF E E^0 RT ln 4
called Nernst equation. E^0 is called a standard emf of the cell. Determination of this value is one of the most important procedures in electrochemistry. As an example lets consider cell consisting of a hydrogen electrode and a silver-silver chloride electrode immersed in a solution of hydrochloric acid: Pt(H 2 )|HCl(m)|AgCl|Ag. The overall reaction is:
AgCl 21 H (^2) H Cl Ag
The emf of the cell is
21
0 2
ln AgCl H
Ag Cl H a a
a a a F
E E RT 5
Setting the activities of the solid phases equal to the unity, and choosing hydrogen pressure so that aH2=1 (for ideal gas P=1atm) following reaction can be obtained:
E E^0 RTF ln aCl aH 6
Introducing the mean activity of the ions defined by a±=±m one can obtain
E E^0 ^2 RT^ F ln a E^0 ^2 FRT ln m 7
E ^2 RTF ln m E^0 ^2 RT F ln 8
According to the Debye-Hückel theory, in dilute solutions ln ±=Am1/2, where A is a constant. Hence the equation becomes:
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W X W X R
E E R 13
Experimental procedure:
- Prepare electrolyte solutions of given concentrations.
- Connect electrochemical cell as given in the scheme
Scheme 1. Daniel’s cell scheme
- Measure electromotive force of the tested cell. Repeat measurement 3 times. Data analysis:
- Put emf of tested cell into the table.
- Calculate emf of tested cell by using Nernst equation. Standard electrode potentials and mean activity coefficients are given in the tables.
- Calculate relative error of emf measurement (%) and put it to a table.
Cell EEXPERIMENT [V] ET HEORY [V] E E E 100% THEORY
EXPERIMENT THEORY
Standard electrode potentials, E^0 Electrode Zn, Zn2+^ Cu, Cu2+ E^0 [V] - 0.763 0.
Mean activity coefficients, γ for electrolyte solutions at 25ºC Electrolyte Molality [mol/kg] 0.005 0.01 0.02 0.05 0.1 0.2 0.5 1 CuSO 4 0.573 0.438 0.317 0.217 0.154 0.104 0.062 0. ZnSO 4 0.477 0.387 0.298 0.202 0.15 0.104 0.062 0.
Lodz University of Technology, Faculty of Chemistry, Institute of Applied Radiation Chemistry, Laboratory
Lodz University of Technology, Faculty of Chemistry, Institute of Applied Radiation Chemistry, Laboratory
For determining end points in neutralization it is possible to bubble oxygen or even air over a platinized electrode. Since the oxygen electrode is not reversible, it is not possible to set – nFE equal to F, and no theoretical significance can be attached to the absolute voltages. But when addition of reagents leads to a rapid change of OH-^ concentration and potential the end point can be identified. It is also possible to obtain end points in precipitation reactions. Let us consider determination of AgNO 3 concentration with a concentration cell:
Ag|AgCl|AgCl (sat. sol.) (mAg+) 1 ||AgNO 3 (mAg+) 2 |AgCl|Ag
where (mAg+) 1 is Ag+^ concentration in AgCl saturated solution and (mAg+) 2 is unknown concentration of AG ions in AgNO 3 solution. To the right half-cell, containing AgNO 3 solution, NaCl solution of known concentration is being added:
AgNO 3 + NaCl NaNO 3 + AgCl(s)
Ag+^ concentration in titrated solution decreases as a result of AgCl precipitation. Before titration silver ion concentration in titrated solution is higher than in saturated solution:
(mAg+) 2 > (mAg+) 1
In stoichiometric point concentrations of Ag ions in both solutions are equal: (mAg+) 2 = (mAg+) 1
After this point Ag+^ concentration in titrated solution is smaller than in saturated one,
(mAg+) 1 > (mAg+) 2 m Cl
L
where L= (mAg+) 1 = (mCl-) 1 is AgCl solubility product. According to Nernst equation following dependency of emf in function of molality can be presented:
2 1
ln 2 ln
Ag
Ag Ag
Ag m
m F
RT
a
a F
E RT 14
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According to this equation with decrease of along with (mAg+) 2 concentration cells emf decreases, whereas for (mAg+) 1 > (mAg+) 2 there is a change in emf sign, E<0, which decribes change in character of reaction proceeding on electrodes. Scheme of the setup is shown below.
Experimental procedure:
- Connect electrochemical cell as given in the scheme
- Read value of EMF on the voltage meter.
- Add aqueous solution of NaCl (portions 0.2-0.5 mL) to AgNO 3 solution and mix it precisely
- Read value of EMF on the voltage meter after every addition of another portion of NaCl solution
- After change of the EMF value to the negative one add another 2 mL of NaCl (portions of 0.5 mL) Data analysis:
- Prepare a titration graph EMF=f(VNaOH)
- For exact determination of stoichiometric point prepare derivative graph ( (^) NaCl ) NaCl
EMFV (^) f V
- From the graph read stoichiometric point and calculate number of moles of AgNO 3 in titrated solution
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It is common to report values of Ka in terms of its negative logarithm, pKa, which gives an insight into strength of the acid (high pKa => low Ka => weak acid). For a base B in water, the characteristic proton transfer equilibrium is
B HO
HB OH a a Baq HOl HB aq OH aq K a a 2
2
^
where HB+^ is is the conjugate acid of the base B. In dilute solutions, where activity of water is 1, one can express this equilibrium in terms of the basicity constant Kb:
a B
K aHB aOH b
^6
Similarly to acidic constant, basicity constant can be used to assess the strength of a base. It is common to express proton transfer equilibrium involving a base in terms of its conjugate acid:
HB
HO B a (^) a
a a HB aq H 2 Ol H 3 O aq Baq K^37
The acidity constant of the conjugate acid HB+^ is related to the basicity constant of the base B, which may be verified by multiplying the expressions for Ka and Kb:
K (^) a Kb Kw^8 where Kw is the autoprotolysis constant of the water:
2 H 2 O l ^ H 3 O aq OH aq Kw aH 3 O a OH ^9
At 25ºC, Kw=1.008 × 10-14^ (pKw=14), showing that only a few of a water molecules are ionized. If, in analogy to pH, pOH=-log aOHˉ will be introduced, then it follows that pKw pH pOH 10
and because molar concentrations of H 3 O+^ and OH-^ are equal in pure water then in 25ºC
pH=½pKw 7.00.
Acid base titrations One method a chemist can use to investigate acid-base reactions is a titration. The word "titration" comes from the Latin word "titalus", meaning inscription or title. The French word, titre, also from this origin, means rank. Titration is by definition the determination of rank or concentration of a solution. The origins of volumetric analysis are in late 18th century French chemistry. Francois ANTOINE HENRI DESCROIZILLES developed the first burette (which looked more like a graduated cylinder) in 1791. JOSEPH LOUIS GAY-LUSSAC developed an improved version
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of the burette that included a side arm, and coined the terms "pipette" and "burette" in a 1824 paper about on the standarization of indigo solutions. A major breakthrough in the methodology and popularization of volumetric analysis was due to KARL FRIEDRICH MOHR, who redesigned the burette by placing a clamp and a tip at the bottom, and wrote the first textbook on the topic, Lehrbuch der chemisch-analytischen Titrirmethode ( Textbook of analytical-chemical titration methods ), published in 1855. A pH titration is performed by adding small, accurate amounts of standard base to an acid of unknown concentration. The pH is recorded methodically and is plotted vs. the volume of base added to the acid solution. The result of this plot is an "S" shaped curve. The inflection point of this curve (middle of the "S") is indicative of the equivalance (stoichiometric) point. This point occurs when the acid and base in solution are stoichiometrically equivalent. An equivalance point can be very useful in determining the concentration of an acid or base. Chemists can also titrate using an indicator to determine the end point of a titration. An indicator contains a molecule that exists in at least two different forms which have different colors. The forms differ by the addition or removal of a hydrogen ion. Thus, the color of the indicator solution changes when the pH changes past a certain point. Let one consider titration of a weak acid (such as CH 3 COOH) and strong base (NaOH)
- the analyte (the solution being titrated). At the stoichiometric point their mixtures become an aqueous solution of the weak acid-strong base salt (sodium acetate). It also contains ions streaming from autoprotolysis. The presence of the Brønsted base CH 3 COO-^ means that pH greater then 7 can be expected (see Figure 1).
Figure 1. pH-metric titration of strong and weak acid with a strong base
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]=S. The number of OH-^ ions arise from the proton transfer equilibrium greatly outnumber those produced by the water autoprotolysis, that is why one can set [HA]=[OH-]:
S
OH
a K a a A
b HA OH
^2
At this point pH can be calculated as:
pH 21 pKa 21 pKw ^12 log S 16
When surplus of strong base has been added that the titration has been carried out well past stoichiometric point, the pH is determined by the excess base present. Then, [H 3 O+] = Kw/[OH-] and pH pKw log B ' 17
where B’ is the molar concentration of excess base.
Experimental procedure:
- Calibrate a pH-meter with a phthalate buffer (pH=4)
- Prepare an aqueous solution of strong acid (10 mL of strong acid, 20 mL of acetone and 20 mL of distilled water)
- Fill a burette with a NaOH solution (0.2 mol/L)
- Titrate an acid solution by adding 0.1-0.5 mL of a base
- Prepare an aqueous solution of weak acid (10 mL of strong acid, 20 mL of acetone and 20 mL of distilled water)
- Fill a burette with a NaOH solution (0.2 mol/L)
- Titrate an acid solution by adding 0.1-0.5 mL of a base
Strong acid - HCl Weak acid - CH 3 COOH VNaOH [mL] pH VNaOH
pH
( ) VNaOH [mL] pH VNaOH
pH
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Data analysis:
- Prepare a titration graph pH=f(VNaOH) for a strong and weak acid separately. Inflexion point of titration curve denotes stoichiometric point.
- For exact determination of stoichiometric point prepare derivative graph ( ) ( NaOH ) NaOH VpH^ f^ V
- Calculate number of moles and concentrations of acids in solution
4. For a weak acid prepare a graph ^ ^ NaOH
NaOH
NaOH NaOH fV V log V^^0 V and determine its
pKa. Compare it with theoretical one (hint: you can find it in chemical tables).
Problems to solve:
- Estimate the pH of 0.1M HClO(aq). pKa=7.
- The stoichiometric point of a titration of 25 mL of 0.1M HClO(aq)with 0.1M NaOH(aq) occurs when the molar concentration of NaClO is 0.05M (volume of the solution increased to 50 mL). Calculate pH.
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Conductance and conductivity The electric current in an electrolyyic solution consist of a flow of ions; in a metal, it consists of a flow of electrons. The fundamental measurement used to study the motion of ions is that of the electrical resistance, R, of the solution. The standard technique is to incorporate a conductivity cell into one arm of the resistance bridge (Figure 1) and to search for the balance point.
Figure 1. Conductometer scheme
The conductance, Γ, of a solution is the inverse of its resistance R: Γ=1/R. As resistance is expressed in ohms, Ω, the conductance of a sample is expressed in Ω-1, which officially is designated as siemens, S, and 1 S = 1 Ω-1. The conductance of a sample decreases with its length l and increases with its cross-sectional area A. Therefore one can write:
l
^ A 1
where κ is the conductivity in siemens per meter, S m-1. The conductivity of a solution depends on the number of ions present, and it is normal to introduce the molar conductivity, Λm, which is defined as
m c
^ 2
where c is the molar concentration of the added electrolyte. The SI unit of molar conductivity is siemens metre-squared per mole (S m^2 mol-1). The molar conductivity of an electrolyte would be independent of concentration if κ were proportional to the concentration of the electrolyte. However, in practice, the molar conductivity is found to vary with the concentration. One reason for this variation is that the number of ions in the solution might not be proportional to the concentration of the electrolyte. For instance, the concentration of ions in the solution of weak acid depends on the concentration of acid in a complicated way, and doubling the concentration of the acid added
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does not double the number of ions. Secondly, because ions interact strongly with one another, the conductivity of a solution is not exactly proportional to the number of ion present. The concentration dependence of molar conductivities indicates that there are two classes of electrolyte. The characteristics of a strong electrolyte is that its molar conductivity decreases only slightly as its concentration is increased. The characteristic of a weak electrolyte is that its molar conductivity is normal at concentrations close to zero, but decreases sharply to low values as the concentration increases. The classification depends on the solvent employed as well as the solute: e.g. lithium chloride is strong electrolyte in water but a weak one in propanone.
Strong electrolytes Strong electrolytes are substances that are virtually fully ionized in solution, and include ionic solids and strong acids. As a result of their complete ionization, the concentration of ions in solution is proportional to the concentration of strong electrolyte added. In an extensive series of measurements during the XIXth century, FRIEDRICH KOHLRAUSCH showed that at low concentrations the molar conuctivities of strong electrolytes vary linearly with the square root of the concentration:
(^) m ^0 m K c 3
This variation is called Kohlrausch’s law. The constant ^0 m is the limiting molar conductivity,
the molar conductivity in the limit of zero concentration (when the ions are effectively infinitely apart from each other and do not interact with one another). The constant K is found to depend more on the stoichiometry of the electrolyte (that is, whether it is of the form MA, or M 2 A, etc.) than on its specific identity.
Kohlrausch was also able to show that ^0 m can be expressed as the sum of contributions from
individual ions. If the limiting molar conductivity of the cations is denoted and of the
anions , then his law of the independent migration of ions states that
^0 m 4
where and are the numbers of cations and anions per formula unit of electrolyte.
