Question

The distance between two electrodes of a cell is \(2.5 \mathrm{~cm}\) and area of each electrode is \(5 \mathrm{~cm}^{2}\). The cell constant is (a) \(0.5 \mathrm{~m}^{-1}\) (b) \(12.5 \mathrm{~cm}^{3}\) (c) \(2.0 \mathrm{~cm}\) (d) \(50 \mathrm{~m}^{-1}\)

Short answer

The correct cell constant is (d) 50 m^{-1}.

Step-by-step solution

Understand the concept of cell constant

The cell constant is defined as the ratio of the distance between electrodes (l) to the area (A) of the electrodes. It is given by the formula, cell constant (G) = l / A, where l is in meters and A is in square meters.

Convert distance and area to consistent units

First convert the given distance and area into consistent SI units. Since the distance is given in centimeters, convert it to meters by dividing by 100. Convert the area from square centimeters to square meters by dividing by 10,000 (since 1 m2 = 10,000 cm2). Distance l = 2.5 cm = 2.5 / 100 m, Area A = 5 cm2 = 5 / 10,000 m2.

Calculate the cell constant

Using the formula G = l / A, plug in the converted values: G = (2.5 cm / 100) / (5 cm2 / 10,000) = (0.025 m) / (0.0005 m2) = 50 m-1. Therefore, the correct cell constant is 50 m-1.

Key concepts

Understanding Electrochemistry

Electrochemistry is a branch of chemistry that deals with the relationship between electrical energy and chemical changes, which involves the movement of electrons from one substance to another. At the heart of electrochemical processes are electrochemical cells, which convert chemical energy into electrical energy and vice versa.

Electrochemical cells consist of two electrodes (an anode and a cathode) and an electrolyte that facilitates ion transport. The electrodes are typically connected to an external circuit, which allows electrons to flow, generating electrical current. In a typical electrochemical experiment, we might want to measure the electrical conductivity of a solution, which is where the concept of the cell constant becomes significant.

The cell constant is a crucial factor in understanding how electricity conducts through an electrochemical cell. It's not only important in theoretical chemistry but also has practical applications in determining the concentrations of solutions through techniques like conductometric titration. By mastering the significance of the cell constant, students can unlock a deeper understanding of the mechanisms of electrochemical reactions and their applications in fields like energy storage and environmental monitoring.

Conductometric Titration Principles

Conductometric titration is a type of titration in which the electrical conductivity of the solution is measured as a function of added titrant. This measured conductivity can tell us a lot about the progress of a titration without the need for a colored indicator.

When an ionic compound dissolves in water, it breaks down into charged particles called ions, which are responsible for conducting electricity in the solution. As the titration proceeds and the reaction occurs, the number and type of ions change, which affects the solution's conductivity.

In order to relate the changes in conductivity to concentration, the cell constant of the measuring apparatus must be known. The cell constant is used to convert the measured conductance to conductivity, which can then be analyzed to determine the endpoint of the titration or the concentration of ions in solution. Conductometric titration is particularly useful for reactions that do not have clear visual end points, like precipitation or neutralization of a strong acid and a strong base.

The Role of Electrode Surface Area

The surface area of electrodes is a vital aspect of electrochemical cells and can greatly affect the efficiency and rate of electrochemical reactions. The more surface area available, the more space for the electrochemical processes to occur, which can significantly increase the rate at which the reactions take place.

When discussing the cell constant, the electrode surface area directly influences its value. The cell constant represents the geometry of an electrochemical cell by relating the distance between the electrodes to their area. A larger surface area with the same distance between electrodes would result in a smaller cell constant, meaning more efficient conductivity.

In the context of the original exercise, knowing that the area is large compared to the distance between the electrodes (given the cell constant of 50 m^-1) implies that the cell is well-designed for sensitive measurements of conductivity. This understanding is crucial for students as it bridges the gap between theoretical formulae and practical applications such as designing electrochemical sensors or optimizing battery electrodes.