Unit4 - Subjective Questions

1. Specific Conductance ():
It is defined as the conductance of a solution of 1 cm length and having 1 sq. cm as the area of cross-section. In other words, it is the conductance of 1 cm of the electrolytic solution.

• Unit: Ohm cm or Siemens per meter (S m).

2. Molar Conductance ():
It is defined as the conducting power of all the ions produced by dissolving one gram mole of an electrolyte in a solution.

• Unit: Ohm cm mol or S cm mol.

Relationship:

Where:

• = Specific conductance
• = Molarity of the solution (mol/L)

The cell constant () is the ratio of the distance between electrodes () to the area of cross-section (). Since and are difficult to measure physically, it is determined indirectly.

Procedure:

1. Selection of Electrolyte: A standard solution of KCl (usually N/10 or N/50) is used because its specific conductance () is known accurately at various temperatures.
2. Measurement of Resistance: The resistance () of the KCl solution is measured using a Wheatstone bridge circuit.
3. Calculation:
   • We know that Specific Conductance () = Cell Constant () Observed Conductance ().
   • Therefore,

Once is determined using the standard KCl solution, it remains constant for that specific cell and can be used to determine the specific conductance of other unknown electrolytes.

Given:

• Molarity () = 0.05 M
• Resistance () = 31.6
• Cell Constant () = 0.367 cm

Step 1: Calculate Specific Conductance ()

Step 2: Calculate Molar Conductance ()

Answer: The molar conductance is 232.2 S cm mol.

Electrolytic Cell:

• Function: Converts electrical energy into chemical energy.
• Spontaneity: The redox reaction is non-spontaneous and requires an external power source.
• Electrodes: The Anode is Positive (+), and the Cathode is Negative (-).
• Example: Electrolysis of water, electroplating.

Galvanic (Electrochemical) Cell:

• Function: Converts chemical energy into electrical energy.
• Spontaneity: The redox reaction is spontaneous.
• Electrodes: The Anode is Negative (-), and the Cathode is Positive (+).
• Example: Daniel Cell, Dry cell, Lead-acid battery.

Consider a general reversible cell reaction:

From thermodynamics, the change in free energy () is related to the standard free energy change () and the reaction quotient () by:

where .

The relation between free energy and cell EMF is:

Substituting these into the thermodynamic equation:

Dividing the whole equation by :

Converting natural log (ln) to log base 10:

At 298 K (C), substituting values (, , ):

According to Nernst, the electrode potential arises due to two opposing tendencies when a metal rod is dipped in a solution of its own ions:

1. Solution Pressure ():

   • The tendency of the metal atoms to lose electrons and pass into the solution as cations ().
   • This oxidation process leaves electrons on the metal rod, making it negatively charged.

2. Osmotic Pressure ():

   • The tendency of the metal ions from the solution to take up electrons from the metal rod and deposit as metal atoms ().
   • This reduction process takes electrons from the rod, making it positively charged.

Outcome:

• If : Oxidation occurs, the electrode becomes Anode (-ve).
• If : Reduction occurs, the electrode becomes Cathode (+ve).
• If : Equilibrium is established (Null potential).

The potential difference developed at the interface between the metal and the solution due to charge separation is the Single Electrode Potential.

1. Determine Cell Reaction:
Anode (Oxidation):
Cathode (Reduction):
Overall:
Number of electrons transferred, .

2. Calculate Standard EMF ():

3. Apply Nernst Equation:

Substituting values:

Answer: The EMF of the cell is 1.13 V.

Reversible Cell:
A cell is thermodynamically reversible if it satisfies three conditions:

1. If an opposing EMF exactly equal to the cell EMF is applied, no current flows and no reaction occurs.
2. If the opposing EMF is infinitesimally smaller than the cell EMF, current flows largely, and the cell reaction occurs in the forward direction.
3. If the opposing EMF is infinitesimally larger than the cell EMF, the current flows in the opposite direction, and the cell reaction is reversed.
   • Example: Daniel Cell ().

Irreversible Cell:
A cell that does not satisfy the conditions of reversibility. Even if the external EMF is increased, the reaction does not reverse; instead, a different reaction may occur (like electrolysis of water).

• Example: A cell consisting of Zinc and Copper electrodes dipped in dilute . When external EMF is applied to reverse it, hydrogen evolution at copper stops, but zinc does not deposit back; instead, copper might dissolve.

In a reversible cell, the electrical work done () is equal to the decrease in Gibbs Free Energy ().

1. Free Energy Change ():
If moles of electrons are transferred and is Faraday's constant:

For standard conditions:

2. Entropy Change ():
From thermodynamics, , and the Maxwell relation gives:

Substituting :

Where is the Temperature Coefficient of the cell.

3. Enthalpy Change ():
Using the Gibbs-Helmholtz equation:
Substituting the expressions for and :

These equations allow the calculation of thermodynamic parameters solely from EMF measurements.

Definition: The arrangement of various elements (electrodes) in the increasing order of their standard reduction potentials () is called the Electrochemical Series.

Applications:

1. Comparison of Oxidizing and Reducing Power: Substances with high negative potentials are strong reducing agents (e.g., Li). Substances with high positive potentials are strong oxidizing agents (e.g., ).
2. Predicting Spontaneity of Cell Reaction: A reaction is spontaneous if the calculated is positive. If is negative, the reaction is non-spontaneous.
3. Displacement Reactions: A metal with a lower reduction potential (more negative) can displace a metal with a higher reduction potential from its salt solution (e.g., Zn displaces Cu from ).
4. Displacement of Hydrogen: Metals with negative reduction potentials (placed above Hydrogen) can displace hydrogen gas from dilute acids.

Concept:
When a metal electrode is dipped in an electrolyte, a potential difference develops due to the separation of charges. This interface is modeled as a capacitor, known as the Electrical Double Layer.

Helmholtz Model:

1. Inner Layer: The metal surface acquires a charge (say, positive due to ionization leaving the electrode or adsorption of ions).
2. Outer Layer: A layer of oppositely charged ions (counter-ions) from the solution lines up parallel to the metal surface to neutralize the charge.
3. Rigidity: Helmholtz proposed that this layer of counter-ions is firmly held (fixed) at a molecular distance () from the metal surface.
4. Potential Drop: The electrical potential drops linearly across this double layer, similar to a parallel plate capacitor.

While this model explains the basic capacity, it was later modified (by Gouy-Chapman and Stern) to include a diffuse layer where ions are mobile due to thermal agitation, but the Helmholtz layer represents the compact layer directly at the interface.

Given:

• Distance () = 1.80 cm
• Area () = 5.4 cm
• Resistance () = 32
• Concentration = Decinormal ( N)

1. Calculate Cell Constant ():

2. Calculate Specific Conductance ():

3. Calculate Equivalent Conductance ():
Formula:

Answer: Specific Conductance is 0.0104 S cm and Equivalent Conductance is 104 S cm equiv.

Why Voltmeter fails:
A voltmeter draws a small amount of current from the cell to deflect the needle. Due to the internal resistance of the cell, a voltage drop () occurs. Thus, the voltmeter measures the terminal voltage () rather than the true EMF ().

Poggendorff's Compensation Method (Potentiometer):

• Principle: The EMF of the unknown cell is opposed by a known EMF from a standard source. When the two are exactly equal and opposite, no current flows through the circuit (Null point).
• Setup: A battery drives a constant current through a long uniform wire. The test cell is connected in opposition. The sliding contact is moved until the galvanometer shows zero deflection.
• Calculation: At the null point, the EMF is proportional to the balancing length (). By comparing with a standard cell () with balancing length ():
  
• Since no current is drawn from the test cell at the null point, the true EMF is measured.

Formula:
At equilibrium, . The Nernst equation becomes:

Calculation:

1. Identify : Copper goes from 0 to +2, and Silver from +1 to 0 (times 2). Thus, electrons transferred, .
2. Substitute values:
   
   
   
   
3. Take Antilog:
   
   

Answer: The equilibrium constant is .

1. Nature of Electrolyte:
   • Strong Electrolytes: Ionize completely (e.g., HCl, NaCl), providing high conductance.
   • Weak Electrolytes: Ionize partially (e.g., CHCOOH), providing low conductance.
2. Concentration/Dilution:
   • Specific Conductance () decreases with dilution (fewer ions per unit volume).
   • Molar Conductance () increases with dilution (reduced interionic attraction in strong electrolytes; increased degree of dissociation in weak electrolytes).
3. Temperature:
   • Conductance increases with temperature due to decreased viscosity of the solvent and increased kinetic energy of ions.
4. Size of Ions and Solvation:
   • Smaller ions usually conduct faster, but if a small ion is heavily hydrated (solvated), its effective size increases, reducing mobility and conductance.
5. Viscosity of Solvent: Higher viscosity resists ion movement, lowering conductance.

Given:

• V
• Temperature Coefficient V K
• K (Standard assumption if not given)
• (Zn valency is 2)
• C

Formula:

Calculation:

1. Calculate the term inside brackets:
   
   
   

2. Calculate :
   
   
   
   

Answer: The enthalpy change is -167.1 kJ.

IUPAC rules for cell notation:

1. Anode (Oxidation): Written on the Left. The metal electrode is written first, followed by the electrolyte (ion) with its concentration.
   • Format:
   • Example:
2. Cathode (Reduction): Written on the Right. The electrolyte (ion) is written first, followed by the metal electrode.
   • Format:
   • Example:
3. Salt Bridge: Represented by two vertical parallel lines () separating the anode and cathode compartments.
4. Phase Boundary: A single vertical line () separates different phases (solid electrode and liquid electrolyte).

Full Example (Daniel Cell):

Given:

• Temperature = C
• pH = 10
• Standard Hydrogen Electrode Potential V

Reaction:

.

Formula:
Using Nernst Equation:

Since :

Calculation:

Answer: The reduction potential is -0.591 V.

Definition:
Electrolytes are substances that conduct electricity in their molten state or aqueous solution due to the dissociation into ions, accompanied by chemical decomposition.

Classification:

1. Strong Electrolytes:
   • Dissociate almost completely into ions in aqueous solution.
   • Have high conductivity.
   • Examples: Strong acids (HCl, HSO), Strong bases (NaOH, KOH), and most salts (NaCl, KNO).
2. Weak Electrolytes:
   • Dissociate only partially in aqueous solution (low degree of dissociation, ).
   • An equilibrium exists between ions and unionized molecules.
   • Have low conductivity.
   • Examples: Weak acids (CHCOOH, HCN), Weak bases (NHOH).