Problem 14 - Chemistry in 30 days

Question

The equivalent conductances of \(\mathrm{NaCl}, \mathrm{HCl}\) and \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COONa}\) at infinite dilution are \(126.45\), \(426.16\) and \(91 \mathrm{ohm}^{-1} \mathrm{~cm}^{2}\). The eq. conductance of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOH}\) is (a) \(201.28 \mathrm{ohm}^{-1} \mathrm{~cm}^{2}\) b) \(390.71 \mathrm{ohm} \mathrm{cm}^{2}\) (c) \(698.28\) ohm \(\mathrm{cm}^{2}\) d) \(540.48 \mathrm{ohm} \mathrm{cm}^{2}\)

Step-by-Step Solution

Answer

\(\Lambda^0_{\text{C}_2\mathrm{H}_5\mathrm{COOH}} = 201.28 \, \mathrm{ohm}^{-1} \, \mathrm{cm}^2\).

Step 1: Identify Key Values

Determine the given values of equivalent conductances for each compound at infinite dilution.- \( \Lambda^0_{\text{NaCl}} = 126.45 \, \mathrm{ohm}^{-1} \, \mathrm{cm}^2 \)- \( \Lambda^0_{\text{HCl}} = 426.16 \, \mathrm{ohm}^{-1} \, \mathrm{cm}^2 \)- \( \Lambda^0_{\text{C}_2\mathrm{H}_5\mathrm{COONa}} = 91 \, \mathrm{ohm}^{-1} \, \mathrm{cm}^2 \).

Key Concepts

Infinite Dilution

Infinite dilution refers to a hypothetical condition where an electrolyte is dissolved in a solvent to such an extent that any further increase in solvent does not produce any significant change in the properties of the electrolyte. This concept is important because it allows us to study the intrinsic properties of ionic compounds without the interference of intermolecular interactions. At this extreme dilution, the ions are so far apart that they do not affect each other's movement, making it easier to determine their individual contributions to conductance.
Understanding infinite dilution helps in calculating the maximum conductance an electrolyte can achieve. For instance, at infinite dilution, we can determine the sum of the ionic conductivities of all the ions present in a solution. This is a key step to calculate or predict the conductance of weak electrolytes or for comparing the strengths of different electrolytes when they are fully dissociated.

Electrolyte Conductivity

Electrolyte conductivity refers to the ability of an electrolyte solution to conduct electricity. This ability is mediated through the movement of ions in the solution, as they are the charge carriers responsible for conducting electric current. The conductivity of an electrolyte depends on:

• The concentration of ions.
• The nature of the ions (size and charge).
• Temperature and the viscosity of the solution.

A higher concentration of ions typically leads to higher conductivity, but the dynamics change as the solution becomes more concentrated, due to ion pairing and other interactions. Conductivity measurements are often used to assess the purity of water and the strength of acids and bases.
In practice, conductivity is measured in units of siemens per meter (S/m) in the SI system, but frequently, ohm^-1 cm² is used when dealing with equivalent conductance. Understanding how electrolyte conductivity changes with concentration allows chemists to deduce information about ion speciation and structure in any given solution.

Ionic Molar Conductivity

Ionic molar conductivity is a measure of how well an individual ion conducts electricity in solution. It is calculated at infinite dilution, where the ions are free from interaction with each other, representing their maximal conductance ability. Molar conductivity \(\Lambda_m\) is related to concentration \(c\) and measured as:\[ \Lambda_m = \frac{\kappa}{c} \]where \(\kappa\) is the conductivity of the solution. As concentration approaches zero (infinite dilution), molar conductivity reaches a constant value, which is characteristic for each ion in a given solvent.
Each ion's contribution to conductivity at infinite dilution is additive, allowing chemists to utilize Kohlrausch's Law of Independent Migration of Ions. This principle states that the molar conductivity of an electrolyte at infinite dilution can be expressed as the sum of the molar conductivities of its constituent ions.
By measuring or calculating \ Lambda_m\ at various concentrations and plotting it against concentration, researchers can gain insight into ion pairing and dissociation behavior in solutions.