Problem 75 - A Complete Resource Book in Chemistry for JEE Main

Question

The specific conductance of \(0.1 \mathrm{~N} \mathrm{KCl}\) solution at \(23^{\circ} \mathrm{C}\) is \(0.012 \mathrm{ohm}^{-1} \mathrm{~cm}^{-1}\). The resistance of cell containing the solution at the same temperature was found to be 55 ohm. The cell constant will be (a) \(0.142 \mathrm{~cm}^{-1}\) (b) \(0.616 \mathrm{~cm}^{-1}\) (c) \(6.16 \mathrm{~cm}^{-1}\) (d) \(616 \mathrm{~cm}^{-1}\)

Step-by-Step Solution

Answer

The calculated cell constant is \(0.66 \mathrm{~cm}^{-1}\), which doesn't match any provided option.

Step 1: Understanding the problem

We need to find the cell constant of a cell containing a solution of potassium chloride (KCl). We are given the specific conductance \( \kappa \) of the solution as \(0.012 \mathrm{ohm}^{-1} \mathrm{~cm}^{-1}\) and the resistance \( R \) as \(55 \text{ ohms} \). The formula to find the cell constant \( G^* \) is \( G^* = \kappa \times R \).

Step 2: Calculation of cell constant

Using the formula \( G^* = \kappa \times R \), we substitute the given values: \( \kappa = 0.012 \mathrm{ohm}^{-1} \mathrm{~cm}^{-1} \) and \( R = 55 \text{ ohms} \). Thus, \[ G^* = 0.012 \times 55 \].

Step 3: Solve the expression

Calculate the product \( 0.012 \times 55 \) to find the cell constant \( G^* \). This gives us \( G^* = 0.66 \mathrm{~cm}^{-1} \).

Step 4: Selection of the closest option

Check the calculated value of \( G^* \) against the provided options. The calculated \(0.66 \mathrm{~cm}^{-1}\) is closest to option (c) \(6.16 \mathrm{~cm}^{-1}\), but correct calculation reveals none of the options available match 0.66 \(\mathrm{~cm}^{-1} \).

Key Concepts

Specific Conductance

Specific conductance, symbolized as \( \kappa \), is an important measure in electrochemistry. It indicates how well a substance can conduct electricity. Specifically, it tells us how efficiently electricity can flow through a given solution.
Specific conductance is expressed in units of \( \text{ohm}^{-1} \text{cm}^{-1} \), which might seem a bit tricky at first, but it’s pretty straightforward once you get used to it. The higher the specific conductance, the better the solution can conduct electricity.
In electrochemistry, this value helps determine the quality of the electrolyte and the degree of ionization. Some factors can affect this measurement, including temperature and the concentration of ions in the solution. So, when you are working with conductance values, it’s crucial to note the conditions under which they are measured. It’s not just a number but a reflection of how the ions behave in the solution.

Cell Constant

The cell constant, represented as \( G^* \), is a unique characteristic of a conductivity cell. It’s used to relate the dimensions of the cell to its conductive capability. You can think of it as a bridge that connects resistance and specific conductance.
To calculate the cell constant, we use the formula \( G^* = \kappa \times R \), where \( \kappa \) is the specific conductance and \( R \) is the resistance measured in ohms. This equation reveals the proportional relationship between the parameters. The cell constant is expressed in \( \text{cm}^{-1} \), turning our analysis from a numerical value to a spatial one, symbolizing how the size and geometry of the cell impact measurements.
The cell constant ensures that conductivity readings are accurate and reliable, effectively standardizing measurements across different setups and ensuring consistency in experimental electrochemistry.

Resistance

Resistance is a measure of how much a material opposes the flow of electric current. It is a fundamental concept not only in electrochemistry but in all of electronics and physics.
In our context, resistance affects how we understand a solution's ability to conduct electricity. It's measured in ohms, denoted by the Greek letter omega (\( \Omega \)).
When studying electrochemistry, resistance tells us how difficult it is for electricity to move through the solution. The higher the resistance, the harder it is for the electrical flow to progress. When paired with specific conductance and the cell constant, resistance helps provide a complete picture of a cell's electrical properties. Understanding these interconnected relationships ensures that one can effectively analyze and design systems for experiments and practical applications.

Potassium Chloride (KCl) Solution

Potassium chloride, often written as KCl, is a well-known compound that’s commonly used in electrochemistry labs. It is a great choice for making solutions to test conductivity because it dissociates into its component ions easily in water, creating a conductive pathway for electricity.

• KCl solutions are used as a standard when calibrating conductivity meters. This means they help ensure that the instruments give correct readings by providing a known benchmark.
• They’re also stable and non-reactive under typical laboratory conditions, which is extremely beneficial for maintaining consistent results in experiments.

In our specific exercise, the KCl solution at 22°C has a specific conductance of \(0.012 \, \text{ohm}^{-1} \, \text{cm}^{-1}\). Since temperature can significantly affect conductivity, this is an important detail to note.
Overall, potassium chloride solutions are an essential part of understanding and working with conductivity, making them invaluable in both educational settings and industrial applications.