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ELECTRO CHEMISTRY.

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References:

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• Physical Chemistry by P. Atkins, J.D. Paula

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• Engg.Chemistry by Jain and Jain

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• Principles of Physical Chemistry by Puri and Sharma

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• Engg. Chemistry ( Vol I & II) by J.C. Kuriacose and J Rajaram

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Electrochemistry is a branch of chemistry which deals with the properties and behavior of electrolytes in solution and inter-conversion of chemical and electrical energies.

An electrochemical cell can be defined as a single arrangement of two electrodes in one or two electrolytes which converts chemical energy into electrical energy or electrical energy into chemical energy.

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It can be classified into two types:

• Galvanic Cells.
• Electrolytic Cells.

Galvanic Cells:

A galvanic cell is an electrochemical cell that produces electricity as a result of the spontaneous reaction occurring inside it. Eg.: Daniel cell.

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Daniel Cell.

Representation of galvanic cell.

• Anode Representation:

Zn│Zn²⁺ or Zn ; Zn²⁺

Zn │ ZnSO_{4 (1M)} or Zn ; ZnSO_{4 (1M)}

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• Cathode Representation:

Cu²⁺/Cu or Cu²⁺ ;Cu

Cu²⁺ _(1M) ; Cu or CuSO_4(1M)/Cu

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• Cell Representation:
• Zn │ ZnSO_{4 (1M)}║ CuSO_4(1M)/Cu

ELECTROLYTIC CELL

An electrolytic cell is an electro –chemical cell in which a non- spontaneous reaction is driven by an external source of current.

LIQUID JUNCTION POTENTIAL

• Potential difference across the interface of the two electrolytes.
• E_j = Ø soln, R - Ø soln,L
• The junction potential contributes to the cell emf.
• Generally, junction potentials are of the order of magnitude 10 to 30 mV.  

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Salt Bridge.

The liquid junction potential can be reduced (to about 1 to 2 mV) by joining the electrolyte compartments through a salt bridge.

Emf of a cell.

The difference of potential, which causes a current to flow from the electrode of higher potential to one of lower potential.

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E_cell = E_cathode- E_anode

The E _Cell depends on:

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• the nature of the electrodes.
• temperature.
• concentration of the electrolyte solutions.

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• Standard emf of a cell(E^o _cell) is defined as the emf of a cell when the reactants & products of the cell reaction are at unit concentration or unit activity, at 298 K and at 1 atmospheric pressure.

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• The emf of a galvanic cell can not be measured accurately using a voltmeter

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E_x α AD

E_s α AD¹

E_x ═ AD

E_s AD¹

E_x = AD x E_s

AD¹

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Weston Cadmium Cell

Sealed wax

Cork

Soturated solution of

CdSO₄.8/3H₂O

CdSO4.8/3H₂O

crystals

Cd-Hg

12-14% Cd

Paste of Hg₂SO₄

Mercury, Hg

• Capable of giving constant and reproducible emf.

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• Negligible temperature – coefficient of the emf.

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• Cd (s) → Cd²⁺ + 2e^- (At negative electrode)

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• Hg₂SO_4(s) + 2e^- → 2 Hg (l) + SO₄^2-_(aq) (At positive electrode)

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Energetics of Cell Reactions.

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ΔG = -nFE ( in k cal)

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ΔH = nF[T(δ E/ δT)_P –E]

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ΔS = nF (δE/ δT)_P

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Single electrode potential.

Electric layer on the metal has a potential Ø _(M).

Electric layer on the solution has a potential Ø _(aq)

Electric potential difference between the electric double layer existing across the electrode /electrolyte interface of a single electrode or half cell.

De-electronation

Electronation

Helmholtz double layer

Sign Of Electrode Potential.

The electrode potential of an electrode:

Is positive: If the electrode reaction is reduction when coupled with the standard hydrogen electrode

Is negative: If the electrode reaction is oxidation when coupled with standard hydrogen electrode. According to latest accepted conventions, all single electrode potential values represent reduction tendency of electrodes.

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Nernst Equation.

• It is a quantitative relationship between electrode potential and concentration of the electrolyte species.

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• Consider a general redox reaction:

Mⁿ⁺_(aq) + ne^- → M(s)

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At 298K,

E= E^o-0.0592/n log 1/[Mⁿ⁺]

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Classification of Electrodes.

• Gas electrode ( Hydrogen electrode)

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• Metal-metal insoluble salt (Calomel electrode).

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• Ion selective electrode.(Glass electrode).

Metal –metal salt ion electrode.

• These electrodes consist of a metal and a sparingly soluble salt of the same metal dipping in a solution of a soluble salt having the same anion.

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Eg: Calomel electrode.

Ag/AgCl electrode.

Construction.

The crystal structure of calomel(Hg₂Cl₂), which has limited solubility in water (Ksp = 1.8 ×10^–18).

• Representation: Hg; Hg₂Cl₂ / KCl

IAs anode: 2Hg + 2Cl^- → Hg₂Cl₂ + 2e^-

• As Cathode: Hg₂Cl₂ + 2e^- → 2Hg + 2 Cl^-

E= E^o -0.0591 log [Cl^-] at 298 K

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Its electrode potential depends on the concentration of KCl.

Conc. of Cl^- Electrode potential

0.1M 0.3335 V

1.0 M 0.2810 V

Saturated 0.2422 V

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Applications:

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• Since the electrode potential is a constant it can be used as a secondary reference electrode.

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• To determine electrode potential of other unknown electrodes.

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• To determine the pH of a solution.

Ion Selective Electrode

• It is sensitive to a specific ion present in an electrolyte.

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• The potential of this depends upon the activity of this ion in the electrolyte.

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• Magnitude of potential of this electrode is an indicator of the activity of the specific ion in the electrolyte.

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*This type of electrode is called indicator electrode.

Composition of glass membranes

70% SiO₂

30% CaO, BaO, Li₂O, Na₂O,

and/or Al₂O₃

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The overall potential of the glass electrode has three components:

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• The boundary potential E_b

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• Internal reference electrode potential E_ref.

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• Asymetric potential E_asy.

E_g = E_b + E_ref. + E_asy.

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Glass electrode is mainly used in the determination of pH of a solution.

• Applications.

• Determination of pH:

Cell: SCE ║Test solution / GE

E _cell = E_g – E_cal.

E _cell = E^o_g – 0.0592 pH – 0.2422

pH = E^o_g -E_cell – E_cal. / 0.0592

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Problems

The cell SCE ΙΙ (0.1M) HCl Ι AgCl(s) /Ag

gave emf of 0.24 V and 0.26 V with buffer having pH value 2.8 and unknown pH value respectively. Calculate the pH value of unknown buffer solution. Given E_SCE= 0.2422 V

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E^o_g= 0.0592pH +E_cell + E_cal.

= 0.0592x2.8 +0.24 + 0.2422

=0.648 V

pH = E^o_g -E_cell – E_cal. / 0.0592

= 0.648 -0.26-0.2422/0.0592

= 2.46

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POTENTIOMETRIC TITRATION

• Titrations carried out using potentiometric indicators are normally referred to as potentiometric titrations.
• involves the measurement of electrode potentials between indicator electrode and reference electrode, with the addition of titrant.

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Types of potentiometric titrations:

1) Acid-base titrations.

2) Redox titrations.

3)Precipitation titrations.

The electrode reaction is,

Mⁿ⁺ + ne^------>M

As the concentration of Mⁿ⁺ changes, the EMF of the cell also changes correspondingly.

1) Acid-base titrations. These titrations are based on the neutralization reaction that occurs between an acid and a base, when mixed in solution.

When more precise results are required, or when the titration constituents are a weak acid and a weak base, a pH meter or a conductance meter are used.

Common indicators, their colours, and the pH range in which they change colour,

basic

potentiometric cell

Measurement of Potential

To measure a potential we need to create a voltaic cell containing two electrodes, one of which is the indicator electrode and one of which is the reference electrode. We measure the voltage of the cell which is giving a reading of the potential of the indicator electrode relative to the reference electrode. This potential can be related to the analyte activity or concentration via the Nernst equation.

• General Principles
• Reference electrode | salt bridge | analyte solution | indicator electrode
• E_ref E_j E_ind

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• E_cell = E_ind – E_ref + E_j

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• Reference cell :(fixed potential)
• a half cell having a known electrode potential
• Indicator electrode:
• has a potential that varies in a known way
• with variations in the concentration of an analyte

• Determination of pH:

Cell: SCE ║Test solution / GE

E _cell = E_g – E_cal.

E _cell = E^o_g – 0.0592 pH – 0.2422

pH = E^o_g -E_cell – E_cal. / 0.0592

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Procedure

.The combined electrode is standardised by dipping in the buffer

solution of known pH.

.The emf of the cell containing the initial solution is determined.

.Relatively large amounts of the titrant solution are added until

the equivalence point is approached.

.The emf is determined after each addition.

.The approach of the end point is indicated by a somewhat more

rapid exchange of emf.

.Thus the pilot run is made to locate the end point.

Then again fresh solution is taken and in the vicinity of the end point, equal increments (0.1or 0.05ml) of titrant is added to locate where exactly the equivalence point lies.

Equivalent point or End point

Volume of NaOH,mL

The maximum point is the equivalence point

Volume of NaOH,mL

The equivalence point is the point on the curve with the

maximum slope

Titration curve

Derivative of Titration Curve

Derivatives method

Graph of voltage against volume added can be drawn and the end point of the reaction is half way between the jump in voltage.

Background

Valdosta State University

Consider the following graph:

CH₃COOH + NaOH^- → CH₃COO^- + Na⁺ + H₂O

For example;

Background

Valdosta State University

Consider the following graph:

In this region H⁺ dominates, the small change in pH is the result of relatively small changes in H⁺ concentration.

Background

Valdosta State University

Consider the following graph:

In this region, relatively small changes in H⁺ concentration cause large changes in pH, The midpoint of the vertical region is the equivalence point.

Background

Valdosta State University

Consider the following graph:

In this region OH^- dominates, the small change in pH is the result of relatively small changes in OH^- concentration.

Advantages

• The apparatus required is generally inexpensive, reliable and readily available.

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2. It is easy to interpret titration curves

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3. The method can be used for colored solutions.

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4. The method is applicable for analysis of dilute solutions

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5. Several components can be titrated in the same solution without the possibility of indicators interfering with each other. Eg bromide and iodide may be titrated together.

CONDUCTOMETRIC TITRATION

Conductance measurements are frequently employed to find the end points of acid-alkali and other titrations.

The principle involved is that electrical conductance depends upon the number and mobility of ions.

Conductance of electrolyte is directly propotional to:

• Mobility of ions
• No. of ions present in unit volume.

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Conductance of the titrating solution varies due to two reasons, namely:

• Dilution
• Replacement of molecular species by ionic species or one ionic species by another

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The concentration of the titrant must be 10 times as the solution being titrated. This is done to keep the volume changes small.

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The conductance of hydrochloric acid is due to the presence of hydrogen and chloride ions. As alkali is added gradually, the hydrogen ions are replaced by slow moving sodium ions, as represented below:

H⁺ (aq) + Cl^- (aq) + Na⁺ (aq) + OH^- (aq) → Cl^- (aq) + Na⁺ (aq) + H₂O(l)

(unionised)

Consider the titration of a strong acid(HCl) with a strong base(NaOH).

The acid is taken in the conductivity vessel &

the alkali in the burette.

The concentration of the titrant must be 10 times as the solution being titrated. This is done to keep the volume changes small.

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Hence, on continued addition of sodium hydroxide, the conductance will go on decreasing until the acid has been completely neutralized. The solution at neutralization ie. at end point containing only sodium and chloride ions., will have minimum conductivity.

Any subsequent addition of alkali will result in introducing fast moving hydroxyl ions. The conductance , therefore , after reaching a certain minimum value, will begin to increase.Thus a V-shaped graph is produced.

Strong acid x Strong base HCl Vs NaOH

Strong acid x Weak base ( HCl x NH₄OH)

Vol. of NH₄OH

H⁺ + Cl^- + NH₄⁺ + OH^- → NH₄Cl + H₂O

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When NH₄OH is added to HCl, the conductivity decreases because of replacement of highly conducting H⁺ ions by less conducting NH4⁺ ions. After the equivalence point is reached, the conductance remains almost constant, since the excess of NH₄OH added, does not ionize in presence of NH₄Cl. (Common ion effect)

When weak acid(CH₃COOH ) is titrated with NaOH, the conductivity decreases initially. (the anion formed suppresses the ionization of the weak acid, This is because the conversion of the non conducting weak acid into its conducting salt. The 2 opposing effects act here- decrease due to common ion effect and increase due to formation of conducting salt.) .the conductance increases with the further addition of NaOH due to the formation of Na+ & CH₃COO^- .

CH₃COO^- + H⁺ + Na⁺ + OH^- → CH₃COO^- + Na⁺ + H₂O

When the neutralization of acid is complete, further addition of NaOH produces excess of OH^{- &} the conductance of the solution increases more rapidly.

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Weak acid X Strong base (CH₃COOH x NaOH)

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Weak acid x Weak base (CH₃COOH x NH₄OH)

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The conductance decreases initially and then increase, the reason being the same as in the previous titration. After the end point an excess of NH₄OH solution has little effect on the conductance as its dissociation is suppressed by ammonium salt in the solution.

ADVANTAGES

• They can be used in the case of colored liquids where ordinary indicators cannot work

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• They can be used for the analysis of dilute solutions and also for v. weak acids.

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• It is not necessary to measure the actual conductance value because we can use any quantity that is proportional to it. Eg. The reading on a Wheatstone bridge. This can be directly plotted against the volume of the titrant.

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DISADVANTAGES

• It becomes less accurate and less satisfactory with increasing total electrolytic concentration. Actually, the change in conductance due to addition of titrant can become largely masked by high salt concentrations in the solution being titrated; under these circumstances, the method cannot be used.
• Although the method is potentially adaptable to all types of volumetric reactions, the number of useful applications to redox systems is limited. The reason for this is that the substantial excess of hydronium ion typically needed for such reactions tend to mask conductivity changes associated with volumetric reaction.

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CONCENTRATION CELLS.

• Two electrodes of the same metal are in contact with solutions of different concentrations.
• Emf arises due to the difference in concentrations.
• Cell Representation:

M/ Mⁿ⁺_[C1] ║ Mⁿ⁺/M_[C2]

Construction.

• At anode: Zn →Zn²⁺_(C1) + 2e^-
• At cathode: Zn²⁺_(C2) + 2e^-→ Zn
• E_cell = E_C-E_A

= E⁰ + (2.303RT/ nF)logC₂- [E⁰+(2.303RT/nF)logC₁]

• E_cell = (0.0592/n) log C₂/C₁

E_cell is positive only if C₂ > C₁

• Anode - electrode with lower electrolyte concentration.
• Cathode – electrode with higher electrolyte concentration.
• Higher the ratio [C₂/C₁] higher is the emf.
• Emf becomes zero when [C₁] = [C₂].

Concentration cell with transference

Consider a concentration cell formed by combining two hydrogen gas (1atm) electrodes in contact with HCl solutions of different concentrations, which are in direct contact.

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Pt, H₂(g), HCl(a₁) || HCl(a₂), H₂(g), Pt

At anode, ½ H₂(g) → H⁺(a₁) + e^- (1)

At cathode, H⁺(a₂) + e^- → ½ H₂(g) (2)

Since the solutions are in direct contact with each other, the ions are free to move from one solution to the other when current flows through the cell. Since anions move in the direction opposite to that in which cations move, Cl^- ions migrate from right to left.

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Transport number: The fraction of the total current carried by each ion is called its transport number.

Transport number of the cation,t₊=Current carried by the cation/Total current=u₊÷u₊ + u_-

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Let t_- be the transport number of Cl^- ion and t₊ (1- t_-) that of H⁺ ion in HCl.

Then for 1F of electricity passing through, t_- F will be carried by Cl^- ions and t₊ F by H⁺ ions.

According to Faraday’s second law, t_- equivalent of Cl^- ions will be transferred from the solution of activity a₂ to the solution of activity a₁. This may be represented as

t_- Cl^- (a_-)₂ → t_- Cl^- (a_-)₁ (3)

t₊ equivalent of H⁺ ions will be transferred from the solution of activity a₂ which is represented as

t₊ H⁺ (a₊)₁→ t₊ H⁺ (a₊)₂ (4)

The net result for flow of 1F electricity is

At anode,

Gain of 1 gram equivalent of H⁺ ions in anodic reaction (1) = Loss of t₊ gram equivalent of H⁺ ions (4)

Therefore, net gain of H⁺ ions = (1-t₊) gram equivalent

=t_- gram equivalent

At the cathode,

Net gain of Cl^- ions = t_- gram equivalent (3)

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Loss of 1 gram equivalent of H⁺ ions in cathodic reaction (2) = gain of t₊ gram equivalent of H⁺ ions (4)

Therefore, net loss of H⁺ ions = (1-t₊) gram equivalent

=t_- gram equivalent

At the same time,

Net gain of Cl^- ions = t_- gram equivalent (3)

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Thus for every 1F of electricity, there is net transfer of t_- gram equivalent of H⁺ ions and t_- gram equivalent of Cl^- ions from the solution in which activity of HCl is a₂ to that in which activity of HCl is a₁.

These changes are represented as

t_- H⁺ (a₊)₂ → t_- H⁺ (a₊)₁

t_- Cl^- (a_-)₂ → t_- Cl^- (a_-)₁

The EMF of concentration cell with transport is

E = t_- RT ln (a₊)₂ + t_- RT ln (a_-)₂

F (a₊)₁ F (a)₁

If (a_±)₁ and (a_±)₂ are the mean ionic activities of the two hydrochloric acid solutions, it follows that

(a_±)₁² = (a₊)₁(a_-)₁ and (a_±)₂² = (a₊)₂(a_-)₂

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Therefore, E = = t_- RT ln (a_±)₂²

F (a_±)₁²

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Knowing that activity of a univalent electrolyte, a, is

a = (a_±)²

E = t_- RT ln a₂

F a₁

Where a₂ and a₁ are activities of HCl at the cathode and anode respectively.

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Problems

• Zn/ZnSO₄(0.001M)||ZnSO₄(x)/Zn is 0.09V at 25˚C. Find the concentration of the unknown solution.

E_cell = 0.0592/n log C₂/C₁

0.09 =(0.0592/2) log ( x / 0.001)

x =1.097M

2. Calculate the valency of mercurous ions

with the help of the following cell.

Hg/ Mercurous || Mercurous /Hg

nitrate (0.001N) nitrate (0.01N) when the emf observed at 18˚ C is 0.029 V

E_cell=(2.303 RT/nF) log C₂/C₁

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E_cell=(2.303 RT/nF) log C₂/C₁

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0.029 = 2.303RT/n) log (0.01/0.001)

0.029 =0.057 x 1/ n

n = 0.057/0.029 =̃ 2

Valency of mercurous ions is 2, Hg₂ ²⁺

Hiii

Why don't you hear more about negative pH?

It's possible. If the molarity of hydrogen ions is greater than 1, you'll have a negative value of pH.

For example, you might expect a 12 M HCl solution to have a pH of -log(12) = -1.08.

Even strong acids don't dissociate completely at high concentrations. Some of the hydrogen remains bound to the chlorine, making the pH higher than you'd expect from the acid molarity. Because there are so few waters per acid formula unit, the influence of hydrogen ions in the solution is enhanced.

We say that the effective concentration of hydrogen ions (or the activity) is much higher than the actual concentration. The usual general chemistry text definition of pH as -log [H⁺] (negative the logarithm of the hydrogen ion molarity) is better written as pH = - log a_H⁺ (negative the logarithm of the hydrogen ion activity). This effect is very strong, and makes the pH much lower than you'd expect from the acid molarity.

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0 crossing is the equivalence point

The Second Derivative of Titration Curve

Extra slide: Not necessary