Electric Conductance and Electrolysis

Classification of Water-Soluble Substances

• Water-soluble substances are categorized into two primary groups based on their ability to conduct electricity in solution: electrolytes and nonelectrolytes.

• Electrolytes:
      * These are electrovalent substances that form ions when dissolved in a solution.
      * The presence of these ions allows the solution to conduct an electric current.
      * Crucially, an electrolyte always undergoes chemical decomposition when an electric current passes through its solution.
      * Examples of electrolytes include:
          * Sodium chloride ($NaCl$)
          * Copper (II) sulphate ($CuSO_4$)
          * Potassium nitrate ($KNO_3$)

• Nonelectrolytes:
      * These are covalent substances that furnish neutral molecules rather than ions in solution.
      * Because they do not produce ions, their water-solutions do not conduct an electric current.
      * Typical examples of nonelectrolytes include:
          * Sugar
          * Alcohol
          * Glycerol

Electrolysis and the Electrolytic Cell

• Definition of Electrolysis: The phenomenon of the decomposition of an electrolyte by passing an electric current through its solution is termed Electrolysis. The term is derived from "lyo," meaning breaking.

• The Electrolytic Cell: The process of electrolysis is carried out in an apparatus known as the electrolytic cell. The components of this cell include:
      * Solution: A water-solution of an electrolyte.
      * Electrodes: Two metallic rods dipped into the solution.
      * Battery: A source of electricity to which the electrodes are connected.

• Electrode Functions:
      * Anode: The electrode connected to the positive terminal of the battery. It attracts negative ions, which are called anions.
      * Cathode: The electrode connected to the negative end of the battery. It attracts positive ions, which are called cations.

• Example: Decomposition of Hydrochloric Acid ($HCl$):
      * In solution, $HCl$ dissociates: $HCl <br>ightarrow H^{+} + Cl^{-}$
      * At Cathode (Reduction): $H^{+} + e^{-} <br>ightarrow H$. Positive hydrogen ions gain electrons to become neutral hydrogen atoms.
      * At Anode (Oxidation): $Cl^{-} <br>ightarrow Cl + e^{-}$. Negative chloride ions lose electrons to become neutral chlorine atoms.
      * Overall Reaction: The net effect is the decomposition of $HCl$ into hydrogen and chlorine gases: $2HCl <br>ightarrow H_2 + Cl_{2(g)}$.

Fundamental Electrical Units

• Coulomb: A unit of the quantity of electricity. It is defined as the amount of electricity that will deposit $0.001118 ext{ gram}$ of silver from a $15 ext{ per cent}$ solution of silver nitrate in a coulometer.

• Ampere: A unit of the rate of flow of electricity. It is defined as the current that will deposit $0.001118 ext{ gram}$ of silver in one second. Conversely, an ampere is a current of one coulomb per second.

• Ohm: A unit of electrical resistance. It is defined as the resistance offered at $0^ ext{o}C$ to a current by a column of mercury that is $106.3 ext{ cm}$ long, has a cross-sectional area of approximately $1 ext{ sq mm}$, and weighs $14.4521 ext{ grams}$.

• Volt: A unit of electromotive force (EMF). It represents the difference in electrical potential required to send a current of one ampere through a resistance of one ohm.

Faraday's Laws of Electrolysis

• First Law: The amount of a given product liberated at an electrode during electrolysis is directly proportional to the quantity of electricity ($Q$) passing through the electrolyte solution.

• Second Law: When the same quantity of electricity passes through solutions of different electrolytes, the amounts of the substances liberated at the electrodes are directly proportional to their chemical equivalents.

• The Electrical Unit Faraday ($F$): Experimental findings show that the quantity of electricity required to liberate one gram-equivalent of any substance is $96,500 ext{ coulombs}$. This specific quantity is referred to as a Faraday ($F$).

Conductance of Electrolytes

• Mechanism of Conductivity: Electrolyte solutions conduct electric currents via the movement of ions toward the electrodes. This power to conduct current is called conductivity or conductance.

• Ohm's Law in Electrolytes: Electrolytes obey Ohm's law similarly to metallic conductors. The relationship is given by:
      * $I = rac{E}{R}$
      * Where $I$ is current, $E$ is potential difference (volts), and $R$ is resistance (ohms or $ext{Ω}$).

• Resistance ($R$): The resistance of a conductor is directly proportional to its length ($l$) and inversely proportional to its cross-sectional area ($A$):
      * $R = <br>ho imes rac{l}{A}$
      * The constant of proportionality, $<br>ho$ (rho), is called resistivity or specific resistance.

• Specific Resistance: This is defined as the resistance in ohms offered by one centimetre cube of a conductor to the passage of electricity.

Specific Conductance ($ext{κ}$)

• Definition: The power of a substance to conduct electricity is the converse of resistance. Specific conductance (or specific conductivity) is the reciprocal of specific resistance.

• Functional Definition: It is defined as the conductance of one centimetre cube (cc) of a solution of an electrolyte.

• Notation and Units: Specific conductance is denoted by the Greek letter kappa ($ext{κ}$). Its units are expressed in reciprocal ohms ($ext{r.o}$), mhos, or $ext{ohm}^{-1}$.

Equivalent Conductance ($ext{Λ}$)

• Definition: Equivalent conductance is defined as the conductance of an electrolyte solution obtained by dissolving one gram-equivalent of the substance in $V ext{ cc}$ of water.

• Relationship to Specific Conductance: It is the product of the specific conductance ($ext{κ}$) and the volume ($V$) in cc containing one gram-equivalent at a given dilution:
      * $ext{Λ} = ext{κ} imes V$

• Calculations using Normality ($N$): If a solution contains $N$ gram-equivalents in $1000 ext{ cc}$, the volume containing $1 ext{ gram-equivalent}$ is $rac{1000}{N}$. Therefore:
      * $ext{Λ} = rac{ ext{κ} imes 1000}{N}$

Molar Conductance ($ext{Μ}$ or $ext{Λ}_m$)

• Definition: Molar conductivity ($ext{Μ}$) is the conductance of a volume of solution containing one mole of a dissolved substance when placed between two parallel electrodes set at a unit distance apart and large enough to contain the entire solution.

• Formula:
      * $ext{Μ} = ext{κ} imes V = rac{ ext{κ} imes 1000}{M}$
      * Where $V$ is the volume in cc containing one mole and $M$ is the molarity.

• Units of Molar Conductance: Derived as follows:
      * $ext{Units} = rac{1}{ ext{ohm}} imes rac{1}{ ext{cm}} imes rac{ ext{cm}^3}{ ext{mol}} = ext{ohm}^{-1} ext{ cm}^2 ext{ mol}^{-1}$

Strong and Weak Electrolytes

• Strong Electrolytes:
      * These substances result in solutions where almost all molecules are ionized.
      * They are excellent conductors and maintain high equivalent conductance values even at low concentrations.
      * Categories:
          1. Strong Acids: $HCl$, $H_2SO_4$, $HNO_3$, $HClO_4$, $HBr$, and $HI$.
          2. Strong Bases: $NaOH$, $KOH$, $Ca(OH)_2$, $Mg(OH)_2$, etc.
          3. Salts: Virtually all salts (e.g., $NaCl$, $KCl$) are strong electrolytes.

• Weak Electrolytes:
      * These substances result in solutions where only a small fraction of solute molecules are ionized.
      * They have low equivalent conductance values.
      * Categories:
          1. Weak Acids: Organic acids such as acetic acid, oxalic acid, and sulphurous acid ($H_2SO_3$).
          2. Weak Bases: Most organic bases, such as alkyl amines ($C_2H_5NH_2$).
          3. Salts: A rare few, such as mercury (II) chloride ($HgCl_2$) and lead (II) acetate.

Variation of Equivalent Conductance with Concentration

• General Behavior: Equivalent conductance ($ext{Λ}$) does not vary linearly with concentration ($C$). The relationship is typically studied by plotting $ext{Λ}$ against $ext{√}C$.

• Strong Electrolytes:
      * They are completely ionized at all concentrations.
      * The increase in $ext{Λ}$ upon dilution is not due to an increase in the number of ions.
      * Instead, it is due to a decrease in the forces of attraction between ions of opposite charges as they move further apart in dilute solutions.
      * At high concentrations, "ionic interference" occurs: opposite ions attract each other more strongly, slowing their speed toward electrodes.
      * As dilution increases, speed increases until $ext{Λ}$ reaches a limiting value ($ext{Λ}_0$).

• Weak Electrolytes:
      * They possess low ionic concentrations; therefore, interionic forces are usually negligible.
      * The increase in $ext{Λ}$ with dilution is primarily caused by an increase in the number of current-carrier species.
      * This means the degree of ionisation ($ext{α}$) increases as the solution becomes more dilute.