CUET UG Chemistry Booster Test – 2 Measurement and Applications of Conductivity

According to NCERT, the cell constant of a conductivity cell is generally determined using standard potassium chloride (KCl) solutions whose conductivity (κ) is accurately known. The conductivity of a solution is related to the cell constant (G*) and resistance (R) by: Rearranging: Thus, after measuring the resistance of the KCl solution and using the known conductivity value, the cell constant can be calculated accurately. Direct measurement of electrode distance and area is difficult due to the irregular nature of platinized platinum electrodes. Therefore, calibration with KCl solution is preferred. The calculated cell constant is then used for conductivity measurements of unknown solutions.

The cell constant is theoretically given by: where l is the distance between electrodes and A is their area of cross-section. Although this equation appears simple, NCERT points out that direct determination of l and A is inconvenient and unreliable. The reason is that conductivity cells use platinized platinum electrodes. These electrodes are coated with platinum black, producing a rough and irregular surface. Consequently, the actual effective area of the electrodes cannot be measured accurately. Similarly, determining the exact separation between electrode surfaces is difficult. Because of these practical limitations, the cell constant is determined experimentally using standard KCl solutions of known conductivity rather than by direct geometric measurement.

In a Wheatstone bridge, balance is achieved when no current flows through the detector. Under this condition, the ratio of resistances in one arm equals the ratio in the other arm. Statement 1 is correct because zero detector current indicates balance. Statement 2 is incorrect because direct current causes polarization and electrochemical changes in the solution. Therefore, alternating current is used. Statement 3 is correct because an audio-frequency oscillator supplies the AC current required for accurate measurements. At balance: Rearranging: Hence Statement 4 is also correct. Therefore, Statements 1, 3 and 4 are correct.

Conductance (G) measures the ease with which electric current flows through a conductor. It is defined as the reciprocal of resistance: Since resistance is measured in ohms (Ω), the unit of conductance is: The SI name for Ω⁻¹ is Siemens (S). A larger conductance corresponds to lower resistance and easier current flow. Conductance is widely used in electrochemistry because conductivity calculations are based on conductance measurements. Thus, the SI unit of conductance is Siemens (S), which is equivalent to Ω⁻¹.

Copper is an excellent metallic conductor with conductivity around S m⁻¹. Therefore, it has the highest conductivity among the given substances. A 0.1 M HCl solution is a strong electrolyte and dissociates almost completely into H⁺ and Cl⁻ ions, giving high ionic conductivity. However, its conductivity is still much lower than that of copper. Pure water contains only a very small concentration of H⁺ and OH⁻ ions produced by self-ionization. Consequently, its conductivity is very low. Teflon is an excellent insulator with extremely low conductivity, making it the poorest conductor among the options. Therefore, the decreasing order is: Copper > 0.1 M HCl(aq) > Pure Water > Teflon Corresponding to: 1 > 2 > 4 > 3

According to NCERT, resistivity (ρ) is the resistance of a conductor having unit length and unit cross-sectional area. Its SI unit is Ω m. The cell constant (G*) is defined as: and therefore has the SI unit m⁻¹. Conductivity (κ) is the reciprocal of resistivity: Thus, its SI unit is S m⁻¹. Molar conductivity (Λm) is the conductivity associated with one mole of electrolyte and has the SI unit S m² mol⁻¹. Therefore, the correct matching is: 1-b, 2-d, 3-a, 4-c.

Molar conductivity is defined as the conductance of the volume of solution containing one mole of electrolyte. It is related to conductivity by: where c is the concentration in mol L⁻¹. When a solution is diluted, conductivity decreases because the number of ions per unit volume decreases. However, the volume containing one mole of electrolyte increases substantially. This increase in volume is much greater than the decrease in conductivity. As a result, molar conductivity increases with dilution. For strong electrolytes, the increase is gradual, while for weak electrolytes it is more pronounced because dilution also increases the degree of dissociation. Therefore, the increase in molar conductivity occurs because the volume effect dominates over the decrease in conductivity.

When conductivity is expressed in S cm⁻¹ and concentration in mol L⁻¹, NCERT gives the relation: The factor 1000 converts litres into cubic centimetres because: This equation allows determination of molar conductivity directly from conductivity and concentration data. For example, if conductivity decreases upon dilution, the corresponding increase in the volume containing one mole of electrolyte may still cause molar conductivity to increase. This formula is therefore essential for solving electrochemistry numerical problems. Hence, the correct expression is:

The passage clearly states that conductivity decreases with dilution for both strong and weak electrolytes. This behavior is explained by the reduction in the number of ions present per unit volume of solution. When water is added, the ions become distributed throughout a larger volume. Although the total number of ions may remain the same, the concentration of ions in any given volume decreases. Since conductivity depends on the availability of charge carriers per unit volume, conductivity decreases. This is different from molar conductivity, which often increases upon dilution. The distinction between conductivity and molar conductivity is an important NCERT concept frequently tested in examinations. Therefore, the correct reason is the decrease in the number of current-carrying ions per unit volume.

NCERT defines conductivity as the conductance of a solution contained between two electrodes of unit area of cross-section separated by unit distance. Under these conditions, the volume of solution enclosed between the electrodes is one unit volume. This definition allows conductivity to be treated as an intrinsic property of the solution, independent of the actual dimensions of the conductivity cell. Conductivity therefore represents the conductance of a standardized unit volume of solution. The concept is fundamental in electrochemistry because it provides a basis for comparing the conducting abilities of different electrolytic solutions. Hence, conductivity is equivalent to the conductance of one unit volume of solution.

For strong electrolytes, NCERT gives the relation: This equation predicts a straight-line plot between Λm and √c. The intercept at √c = 0 gives the limiting molar conductivity (Λ°m), making Statement 1 correct. The slope of the line is equal to –A. The value of A depends on factors such as the nature of the solvent, temperature and the ionic charges present. Therefore, Statement 2 is also correct. Electrolytes belonging to the same charge type, such as 1–1 electrolytes (NaCl, KCl, etc.), have similar values of A under identical conditions, making Statement 3 correct. Statement 4 is incorrect because strong electrolytes are considered completely dissociated at infinite dilution. Hence, Statements 1, 2 and 3 are correct.

For strong electrolytes, the Debye-Hückel-Onsager equation is: This equation has the form: where: The intercept is Λ°m and the slope is –A. The constant A depends on the type of electrolyte, ionic charges, solvent and temperature. Since the slope of the graph is negative, it is represented by –A. Therefore, the negative slope of the Λm versus √c graph represents the constant A.

Weak electrolytes are only partially dissociated in solution. At any concentration, the extent of dissociation can be estimated from conductivity measurements. According to NCERT: where: Λm = molar conductivity at concentration c Λ°m = limiting molar conductivity at infinite dilution At infinite dilution, complete dissociation occurs and α approaches 1. Since Λ°m corresponds to complete ionization, the ratio Λm/Λ°m gives the fraction of electrolyte dissociated at a given concentration. This relationship is widely used in calculating dissociation constants of weak electrolytes.

Strong electrolytes show nearly complete dissociation at all concentrations. Therefore, their Λm versus √c plots are approximately straight lines. Weak electrolytes behave differently. As dilution increases, the degree of dissociation rises significantly. This produces a rapid increase in the number of ions available for conduction. Consequently, the molar conductivity increases steeply at lower concentrations. The resulting graph is curved and non-linear rather than a straight line. Because of this non-linearity, Λ°m cannot be obtained by simple extrapolation of the graph to zero concentration. Therefore, the characteristic feature of weak electrolytes is a steep upward curve at low concentrations.

Limiting molar conductivity (Λ°m) is the molar conductivity of an electrolyte at infinite dilution. Since it is a molar conductivity quantity, it has the same unit as molar conductivity. When conductivity is expressed in S cm⁻¹ and concentration in mol L⁻¹, the commonly used unit becomes: This unit indicates the conductance contribution associated with one mole of electrolyte. Limiting molar conductivity is especially important in Kohlrausch's law and in determining dissociation constants of weak electrolytes. Therefore, the standard unit of Λ°m is S cm² mol⁻¹.

According to Kohlrausch's law of independent migration of ions, each ion contributes a definite value to the limiting molar conductivity of an electrolyte at infinite dilution. In the expression: the symbols λ°Na⁺ and λ°Cl⁻ represent the limiting molar conductivities of sodium ions and chloride ions respectively. At infinite dilution, ions move independently without significant interionic interactions. Therefore, the total limiting molar conductivity of an electrolyte is obtained by adding the individual ionic contributions. These ionic conductivities are experimentally determined quantities and form the basis of Kohlrausch's law. Hence, λ°Na⁺ and λ°Cl⁻ specifically denote limiting molar conductivities of the individual ions.

The limiting molar conductivity of ions depends on their mobility in aqueous solution. Hydrogen ions and hydroxide ions exhibit exceptionally high conductivities because they move through the solution via proton-transfer mechanisms rather than simple ionic migration. Given ions: 1. OH⁻ 2. Na⁺ 3. H⁺ 4. Ca²⁺ Typical conductivity trend: Hydrogen ion has the highest limiting molar conductivity among common ions, while hydroxide ion is also exceptionally high. Sodium ion possesses lower mobility because of extensive hydration. Calcium ion, although doubly charged, has conductivity greater than sodium ion under standard conditions. Therefore, the increasing order is: Na⁺ < Ca²⁺ < OH⁻ < H⁺ Corresponding to: 2 < 4 < 1 < 3

According to Kohlrausch's law: For NaCl: For MgSO₄: For CaCl₂: For Al₂(SO₄)₃: Thus the correct matching is: 1-c, 2-d, 3-a, 4-b.

The limiting molar conductivity of acetic acid cannot be obtained directly by extrapolation because acetic acid is a weak electrolyte. Therefore, Kohlrausch's law is used. Using ionic contributions: Adding the first two equations and subtracting the third eliminates Na⁺ and Cl⁻: Hence Option D is correct.

The dissociation constant of a weak electrolyte can be determined using conductivity measurements. First, the molar conductivity at a given concentration (Λm) is measured experimentally. The limiting molar conductivity (Λ°m) is then obtained using Kohlrausch's law. The degree of dissociation is calculated as: After determining α, Ostwald's dilution law is applied: where c is the concentration of the electrolyte. Thus, determination of Ka requires knowledge of Λm, Λ°m, α and the above equation. Therefore, all four statements are correct.