Unit 4: Electrochemistry - Subjective Questions

Cell constant () is the ratio of the distance between the electrodes () to the area of cross-section of the electrodes ():

Its unit is .

Relation with conductance:

where is specific conductance, is conductance and is resistance.

Experimental determination:

• The exact geometry ( and ) of a conductivity cell is difficult to measure directly.
• A solution of known specific conductance (standard KCl solution, e.g. 0.1 N KCl whose is accurately known from tables) is taken in the cell.
• The resistance of this solution is measured using a Wheatstone bridge (conductivity bridge).
• The cell constant is then calculated:

• Once the cell constant is known, the same cell can be used to find the specific conductance of any unknown electrolyte solution.

Specific Conductance ():

• It is the conductance of a solution placed between two electrodes of area separated by distance.
• It is the reciprocal of specific resistance (resistivity).

• Unit: (or )

Molar Conductance ():

• It is the conducting power of all the ions produced by dissolving one mole of electrolyte in solution.

where is concentration in mol/litre.

• Unit:

Key differences:

Relationship:

Given:

• Resistance,
• Cell constant,
• Concentration,

Step 1 — Specific conductance:

Step 2 — Molar conductance:

Result:

• Specific conductance
• Molar conductance

An electrolyte is a substance that dissociates into ions when dissolved in water (or melted) and conducts electricity.

Classification:

• Strong Electrolytes:

  • Almost completely ionised in solution.
  • Examples: , , , , .
  • High conductance even at moderate concentration.
  • Molar conductance increases slightly with dilution (limited by inter-ionic forces).

• Weak Electrolytes:

  • Only partially ionised in solution.
  • Examples: , , .
  • Low conductance.
  • Molar conductance increases sharply with dilution due to increase in degree of dissociation.

Conduction behaviour difference:

Note: For strong electrolytes Debye-Hückel-Onsager equation () applies.

Galvanic (Voltaic) Cell:

• Converts chemical energy into electrical energy.
• Based on a spontaneous redox reaction ().
• Anode is negative, cathode is positive.
• Example: Daniell cell ().

Electrolytic Cell:

• Converts electrical energy into chemical energy.
• Drives a non-spontaneous reaction using external EMF.
• Anode is positive, cathode is negative.
• Example: Electrolysis of water, electroplating.

Comparison Table:

Common feature: In both, oxidation occurs at anode and reduction occurs at cathode.

The electrochemical series (or activity series) is the arrangement of various electrodes (elements) in the increasing order of their standard reduction potentials ().

• At the top: strong reducing agents (most negative , e.g. , , ).
• At the bottom: strong oxidising agents (most positive , e.g. , ).
• Standard hydrogen electrode (SHE) is taken as reference with .

Applications:

• Predicting cell EMF: .
• Relative oxidising/reducing power: Higher → stronger oxidising agent.
• Predicting spontaneity of redox reactions: A metal displaces another metal ion below it in the series.
• Displacement reactions: Metals higher in series (more negative ) displace metals lower down.
• Reactivity of metals with acids: Metals above hydrogen liberate from acids.
• Predicting products of electrolysis and corrosion tendency.

Example: Since and , zinc can displace copper from solution.

Consider a general electrode reaction (reduction):

The free energy change is related to the reaction quotient by the Van't Hoff isotherm:

Since and :

Dividing by :

For a single electrode:

At 298 K, converting to log base 10 ():

For a complete cell:

This is the Nernst equation, relating cell potential to concentration of species.

Step 1 — Standard cell EMF:

Step 2 — Cell reaction:

Step 3 — Nernst equation:

Result:

The electrical work done by a reversible galvanic cell equals the decrease in Gibbs free energy.

1. Free energy and EMF:

The maximum useful (electrical) work obtainable:

Since :

Under standard conditions:

2. Entropy and EMF:

From the Gibbs-Helmholtz relation, :

where is the temperature coefficient of EMF.

3. Enthalpy and EMF:

Using :

Significance:

• If temperature coefficient is positive → cell absorbs heat.
• These relations allow determination of thermodynamic quantities from EMF measurements.

Origin of single electrode potential:

When a metal electrode is dipped in a solution of its own ions, two opposing tendencies occur:

• Oxidation (dissolution): Metal atoms lose electrons and go into solution as ions:
  
  This leaves the metal negatively charged and enriches solution with positive ions.

• Reduction (deposition): Metal ions in solution gain electrons and deposit on the metal:
  

Depending on the nature of the metal, one tendency dominates, developing a potential difference between the metal and solution. This is the single electrode potential.

Electrical Double Layer (Helmholtz Double Layer, HDL):

• Due to charge separation, a layer of charge forms on the metal surface and an oppositely charged layer of ions accumulates in solution close to the electrode.
• This arrangement of two oppositely charged layers is called the electrical double layer.
• Helmholtz model: treats it like a parallel-plate capacitor — one layer of charge on the metal and a rigidly held layer of counter-ions in solution.
• The potential difference across this double layer constitutes the electrode potential.

Note: The absolute value cannot be measured; only relative to a reference electrode (SHE).

Reversible Cell:

A cell is reversible if it satisfies the conditions of thermodynamic reversibility.

Conditions:

• When EMF of an external source is exactly equal and opposite to cell EMF, no current flows.
• If external EMF is infinitesimally smaller, the cell reaction proceeds in the forward direction (produces current).
• If external EMF is infinitesimally larger, the reaction reverses exactly.

Example: Daniell cell (under balanced conditions):

Irreversible Cell:

• Does not obey the conditions of reversibility.
• Reversing the current does not reverse the original chemical reaction.

Example:

• On discharge:
• On applying reverse EMF: a different reaction occurs (hydrogen not converted back).

Comparison:

Construction:

The Daniell cell consists of two half-cells:

• Zinc electrode dipped in solution (anode compartment).
• Copper electrode dipped in solution (cathode compartment).
• The two solutions are connected by a salt bridge (KCl in agar) which maintains electrical neutrality and completes the circuit.

Working:

Because zinc is more electropositive than copper, oxidation occurs at zinc and reduction at copper.

Electrode reactions:

• At anode (oxidation):
  

• At cathode (reduction):
  

• Overall reaction:
  

Cell representation:

Standard EMF:

Function of salt bridge:

• Completes the internal circuit.
• Maintains electrical neutrality of both half-cells.
• Prevents liquid junction potential.

Given:

Step 1 — Degree of dissociation:

Step 2 — Dissociation constant (Ostwald's dilution law):

Result:

• Degree of dissociation, (1.33%)
• Dissociation constant,

A reference electrode is an electrode whose potential is accurately known and constant, used to measure the potential of other (indicator) electrodes.

Standard Hydrogen Electrode (SHE):

It is the primary reference electrode with an assigned potential of exactly 0.00 V at all temperatures.

Construction:

• A platinum foil coated with platinum black (to increase surface area and adsorb ).
• The foil is immersed in a solution of ions at unit activity (1 M HCl).
• Pure hydrogen gas at 1 atm pressure is bubbled over the platinum electrode at 298 K.

Electrode representation:

Electrode reaction:

• As anode (oxidation):
• As cathode (reduction):

Working:

• When coupled with another electrode, it acts as anode or cathode depending on the standard potential of the other electrode.
• The measured EMF directly gives the electrode potential of the other electrode.

Limitations: Difficult to maintain unit activity and 1 atm pressure; hence secondary electrodes like calomel electrode are often used.

Variation of molar conductance with dilution:

As a solution is diluted, the molar conductance () increases because the total number of ions responsible for conduction increases per mole (or ionic mobility increases).

For strong electrolytes:

• increases slightly and linearly with .
• Follows the Debye-Hückel-Onsager equation:
  
• obtained by extrapolation to zero concentration.

For weak electrolytes:

• is low at high concentration and rises steeply on dilution due to increasing degree of dissociation.
• cannot be found by extrapolation; found using Kohlrausch's law.

Kohlrausch's Law of Independent Migration of Ions:

At infinite dilution, each ion migrates independently of its co-ion, and the molar conductance of an electrolyte at infinite dilution is the sum of the individual ionic contributions.

Applications:

• Calculating for weak electrolytes.
• Determining degree of dissociation ().
• Calculating solubility of sparingly soluble salts.

Step 1 — Identify electrodes:

• Anode (oxidation):
• Cathode (reduction): (×2 to balance electrons)

Overall reaction:

Step 2 — Standard cell EMF:

Step 3 — Gibbs free energy:

Result:

• (negative → spontaneous reaction)

Why not a voltmeter?

• An ordinary voltmeter draws current from the cell to give a reading.
• When current flows, the cell is no longer at equilibrium and internal resistance causes a voltage drop.
• Hence the voltmeter measures the terminal potential (), not the true (reversible) EMF.

Potentiometric method (Poggendorff's compensation method):

• Based on balancing the unknown cell EMF against a known, opposing potential difference so that no current flows — a truly reversible measurement.

Principle:

• A uniform resistance wire carries a steady current from a working battery.
• The potential drop is uniform along the wire.
• The unknown cell is connected opposing this drop through a galvanometer.
• The balance point (null point) is located where the galvanometer shows zero deflection.

Working:

• First a standard cell (e.g. Weston cell) of known EMF is balanced at length .
• Then the unknown cell is balanced at length .
• Since EMF ∝ balancing length:

Advantage: At balance no current is drawn, so the true reversible EMF is measured.

Given:

Relation between and equilibrium constant:

At equilibrium, and . From the Nernst equation:

Rearranging:

Therefore:

Result: The very large value of indicates the cell reaction () is essentially complete and highly spontaneous.

IUPAC conventions for cell representation:

• The anode (oxidation, negative electrode) is written on the left.
• The cathode (reduction, positive electrode) is written on the right.
• A single vertical line ( | ) represents a phase boundary (electrode–solution interface).
• A double vertical line ( || ) represents the salt bridge.
• Concentrations / pressures of species are indicated in brackets.

General form:

Daniell cell representation:

Sign conventions for EMF:

• (both as reduction potentials).
• If is positive, the reaction is spontaneous as written ().
• If is negative, the reaction is non-spontaneous and actually proceeds in reverse.

For Daniell cell:

Positive value confirms spontaneity.

Concentration cell:

A cell in which both electrodes are of the same material and the EMF arises only due to a difference in concentration of the electrolyte (or electrode material) in the two half-cells. Here .

Derivation (electrolyte concentration cell):

Consider:

• At anode (dilute, ):
• At cathode (conc., ):

Net:

Applying the Nernst equation with :

Numerical:

• (cathode), (anode),

Result: