2.4. Conductance of Electrolytic Solutions

The electrical resistance is represented by the symbol ‘R’ and it is measured in ohm (Ω), which in terms of SI base units is equal to (kg m²)/(s³ A²). The electrical resistance of any object is directly proportional to its length, l, and inversely proportional to its area of cross section, A. That is,

R ∝ l or R = ρ (l/A)

Electrical resistance (R) is a measure of how much an object opposes the flow of electric current. It depends on two geometric factors: the length of the conductor and the cross-sectional area of the conductor. The longer the conductor, the greater the resistance, because electrons have to travel a longer distance, facing more collisions. In contrast, a larger cross-sectional area allows more electrons to move through simultaneously, reducing resistance. The resistivity (ρ, rho) is a material property that indicates how strongly a material resists the flow of current.

Think of water flowing through a pipe. If the pipe is long and narrow (high resistance), water will struggle to flow through it compared to a short, wide pipe (low resistance). The same principle applies to electrical conductors.

The inverse of resistance, R, is called conductance, G, and we have the relation:

G = 1/R = k (where k is conductivity). The SI unit of conductance is siemens, represented by the symbol ‘S’ and is equal to ohm–1 (also known as mho) or W–1. The inverse of resistivity, called conductivity (specific conductance) is represented by the symbol, k (kappa). The SI units of conductivity are S m–1.

Conductance (G) is the ability of a material to allow the flow of electric current. While resistance opposes current, conductance indicates how easily electricity can pass through a material. Conductivity (k) measures how well a specific material allows electricity to flow through it. Higher conductivity means electrons can move freely, leading to lower resistance.

Imagine a highway. If the highway is wide and has no toll booths (high conductance), cars (electrons) can flow freely. But if it's a narrow, congested road with toll booths (high resistance), cars will move slowly.

However, for measuring the resistance of an ionic solution, we face challenges; first, DC changes the composition of the solution. The first difficulty is resolved by using an alternating current (AC) source of power. The second problem is solved by using a specially designed vessel called conductivity cell.

Measuring the conductivity of ionic solutions can be tricky because applying direct current can alter the chemical makeup of the solution. To bypass this issue, alternating current (AC) is used, which doesn't change the solution's composition. A conductivity cell is a device specifically designed to measure how well a solution conducts electricity, using these principles.

Think of measuring the flow of a river. Using DC is like trying to measure the flow while constantly throwing rocks in the river (which changes it). Using AC is like measuring while ensuring the rocks are taken out after measuring, preventing any change.

The conductivity of electrolytic (ionic) solutions depends on: (i) The nature of the electrolyte added (ii) Size of the ions produced and their solvation (iii) The nature of the solvent and its viscosity (iv) Concentration of the electrolyte (v) Temperature (it increases with the increase of temperature).

Several factors influence the conductivity of ionic solutions. For example, the type of electrolyte affects how many ions are produced, which is vital because more ions typically mean better conductivity. The size of the ions and how they interact with the solvent also play a role—larger ions might move slower. Additionally, as temperature increases, ion mobility improves, leading to higher conductivity.

Think of conductivity as a water slide. A more slippery surface (like a good solvent) helps water (ions) flow faster. In contrast, if the slide is rough (like a viscous solvent), water will flow slower. More people (higher concentration) on the slide also means faster flow.

--