Problem 107 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

Variation of molar conductance of an electrolytic solution with temperature is that it (a) increases with increase of temperature (b) decreases with increase of temperature (c) first increases then decreases (d) is not affected by temperature

Step-by-Step Solution

Answer

Molar conductance of an electrolytic solution generally increases with an increase of temperature, as the mobility of ions is enhanced at higher temperatures.

Step 1: Understanding Molar Conductance

Molar conductance is defined as the conductance of a solution containing one mole of electrolyte and measures the ease with which ions can move through the solution. It is affected by various factors, including temperature.

Step 2: Effect of Temperature on Ion Mobility

As the temperature of a solution increases, the kinetic energy of its ions also increases. This heightened mobility generally lowers the resistance to ion flow, resulting in increased molar conductance.

Step 3: Analyzing Answer Options

Option (a) corresponds to the fact that higher temperatures provide more energy to the ions, resulting in greater molar conductance. Option (b) suggests the opposite, which does not align with the known effects of temperature on ion mobility, and options (c) and (d) are inconsistent with the established temperature dependence of molar conductance.

Key Concepts

Electrolytic Solution Conductance

Conductance in an electrolytic solution refers to its ability to carry an electric current. This current is carried through the movement of ions within the solution. The extent of this conductance is quantified by molar conductance, which considers the total conductance of a solution when it contains one mole of electrolyte.

The conductance of an electrolytic solution is influenced by various factors such as the type of ions, their concentration, and the nature of the solvent. If the ions are large or are strongly hydrated, they might move slower, leading to lower conductance. In dilute solutions, ions are more spaced apart, which minimizes the interactions between them and can allow for easier movement and higher conductance.

Hence, understanding molar conductance is vital in grasping the intrinsic conducting properties of a solution, irrespective of its volume or the amount of electrolyte present.

Ion Mobility in Solution

Ion mobility is a concept that describes the speed at which ions move through a solvent under the influence of an electric field. This movement is crucial because it dictates the rate at which ions can travel from one electrode to another, and thus influences the overall conductance of the solution.

Factors affecting ion mobility include the size of the ions – with smaller ions typically moving faster – and the viscosity of the solvent. In a solvent with higher viscosity, ions experience greater resistance and, as a result, move more sluggishly. This is similar to how a person would move more slowly through a pool of honey compared to water.

Ion mobility is directly related to temperature as well. Higher temperatures lead to a decrease in viscosity and an increase in the kinetic energy of the ions, which in turn increases ion mobility and the solution's conductance.

Temperature Effects on Molar Conductance

The dependence of molar conductance on temperature is a significant aspect of electrolytic solutions. As the temperature rises, the ions gain kinetic energy and the solvent's viscosity decreases. Both of these changes allow ions to move more freely through the solution, enhancing their mobility.

Consequently, the molar conductance of a solution typically increases with an increase in temperature. This is because the overcome resistance is reduced, aligning with the option (a) from the exercise, which states that molar conductance increases with an increase in temperature. This follows from basic principles of thermodynamics and the kinetic theory of molecules, which suggest that as temperature increases, molecular motion becomes more vigorous, leading to decreased resistance to ion movement.

In summary, in the context of the exercise, one can expect an increase in molar conductance in response to a rise in temperature due to the enhanced energy and reduced resistance encountered by ions in the solution.