Question

Unit of ionic mobility is: (a) \(\mathrm{m} \mathrm{V}^{-1} \mathrm{~s}^{-1}\) (b) \(\mathrm{m}^{2} \mathrm{~V}^{-2} \mathrm{~s}^{-1}\) (c) \(\mathrm{m}^{2} \mathrm{~V}^{-1} \mathrm{~s}^{-1}\) (d) \(\mathrm{m}^{-2} \mathrm{~V} \mathrm{~s}^{-1}\)

Short answer

The unit of ionic mobility is (c) \(\mathrm{m}^{2} \mathrm{~V}^{-1} \mathrm{~s}^{-1}\).

Step-by-step solution

Understand the Concept of Ionic Mobility

Ionic mobility is defined as the speed at which an ion moves through a conductor or a semiconductor under the influence of an electric field. The speed is typically due to the movement caused by a potential difference of one volt. Therefore, ionic mobility is measured in terms of the distance covered per unit time per unit voltage.

Analyze the Units of Measurement

Since mobility is about distance covered (measured in meters), per time (measured in seconds), per voltage (measured in volts), the correct unit will combine these measurements. The unit should reflect meters squared because it's a per voltage (squared due to being in the denominator of the fraction), per time unit.

Eliminate Incorrect Options

Option (a) suggests meters per volt per second, which lacks the square of meters needed. Option (b) has meters squared per volt squared per second, which has an extra square on the voltage. Option (d) suggests meters to the power of negative two per volt per second, which doesn't conform to the definition of mobility.

Identify the Correct Option

The correct unit of ionic mobility should have meters squared per volt per second. Therefore, the correct answer is reflected in the unit that combines these measurements adequately, which is meters squared per volt per second.

Key concepts

Understanding Physical Chemistry

Physical chemistry is the branch of chemistry concentrated on the study of the physical properties and behavior of matter. It delves into understanding the forces that govern chemical reactions and phenomena, blending principles from physics and chemistry to explain how chemical systems operate. At the heart of physical chemistry lies the study of rate reactions, thermodynamics, quantum chemistry, statistical mechanics, and spectroscopy.

One particular area of interest in physical chemistry is the study of ionic mobility, which reflects how ions behave under the influence of an electric field. This concept is fundamental because it helps in understanding how electric currents are conducted in ionic substances and can be applied in technologies such as batteries, electrochemical cells, and various sensors. Therefore, comprehending ionic mobility requires a blend of concepts from physics, like electric fields, and chemistry, like the behavior of ions in solutions or other conductive materials.

Electric Field Influence on Ions

The behavior of ions in the presence of an electric field is a critical concept in physical chemistry. When an electric field is applied, ions in a solution or conductive material will experience a force that will cause them to move. This movement of ions is the basis of electrical conductivity in many materials.

Positive ions will move towards the negative electrode (cathode), while negative ions will move towards the positive electrode (anode). The speed at which these ions travel is called ionic mobility and it's an indicator of how well a certain ion can conduct electric current. Several factors can influence the mobility of ions, including the viscosity of the medium, the size and charge of the ions, and the temperature of the solution. The fundamental understanding of electric field influence on ions is essential for designing and optimizing devices that rely on ionic movement, such as fuel cells or electrophoresis apparatus.

Units of Measurement in Ionic Mobility

In any scientific endeavor, the units of measurement are vital for precision and standardization. Ionic mobility is quantified by its unit, which combines distance (meters, m), time (seconds, s), and electric potential (volts, V). The unit of ionic mobility is \(\mathrm{m}^{2}\mathrm{V}^{-1}\mathrm{s}^{-1}\), where the meter squared (\(\mathrm{m}^{2}\)) term accounts for the movement in two dimensions, the volt (\(\mathrm{V}\)) term in the denominator represents the electric potential affecting the ion's movement, and the second (\(\mathrm{s}\)) term denotes the time over which the movement occurs.

To illustrate the application of these units and the role of each dimension, consider a scenario where a single ion drifts across a medium. By knowing its mobility, we can calculate the distance it travels within a specific time under a certain electric potential. Accurate measurements are crucial in experimental physical chemistry, where ionic mobility data can help infer other fundamental properties, such as ion size, charge, and medium's resistivity. Recognizing and using the correct unit of ionic mobility is essential for students and researchers alike to effectively communicate and understand experimental results.