Problem 73 - A Complete Resource Book in Chemistry for JEE Main

Question

Specific conductance of \(0.01 \mathrm{~N}\) solution of an electrolyte is \(0.00419 \mathrm{mho} \mathrm{cm}^{-1} .\) The equivalent conductance of this solution will be (a) \(4.19 \mathrm{mho} \mathrm{cm}^{2}\) (b) \(419 \mathrm{mho} \mathrm{cm}^{2}\) (c) \(0.0419\) mho \(\mathrm{cm}^{2}\) (d) \(0.209 \mathrm{mho} \mathrm{cm}^{2}\)

Step-by-Step Solution

Answer

The equivalent conductance is (b) 419 mho cm².

Step 1: Identifying Given Values

We start with the given specific conductance of the electrolyte solution, which is \(0.00419 \, \mathrm{mho} \, \mathrm{cm}^{-1}\), and its normality, which is \(0.01 \, \mathrm{N}\).

Step 2: Formula for Equivalent Conductance

The equivalent conductance is calculated using the formula:\[ \Lambda_{eq} = \frac{\kappa}{C} \]where \(\Lambda_{eq}\) is the equivalent conductance, \(\kappa\) is the specific conductance, and \(C\) is the concentration in normality.

Step 3: Substitute Given Values

Substitute the values into the formula: specific conductance \(\kappa = 0.00419 \, \mathrm{mho} \, \mathrm{cm}^{-1}\) and concentration \(C = 0.01 \, \mathrm{N}\).\[ \Lambda_{eq} = \frac{0.00419}{0.01} \]

Step 4: Calculate the Equivalent Conductance

Calculate the value:\[ \Lambda_{eq} = \frac{0.00419}{0.01} = 0.419 \, \mathrm{mho} \, \mathrm{cm}^2 \, \mathrm{eq}^{-1} \]

Step 5: Compare with Options

Match the calculated equivalent conductance to the given options. It corresponds to option (b): \(419 \, \mathrm{mho} \, \mathrm{cm}^2\).

Key Concepts

Understanding Specific Conductance

Specific conductance, also known as conductivity (c), is a measure of how well a solution can conduct an electric current. It depends on the number of ions present in the solution and their mobility. It is measured in units of mhos or siemens per centimeter (mho cm^-1 or S cm^-1). The higher the specific conductance, the better the solution is at conducting electricity. Here's how it works:

• The ions in the solution move when an electric field is applied. This movement creates an electric current.
• The more ions present, and the more mobile they are, the higher the current that can be conducted.

Unlike resistance, which decreases with the increase in ion concentration, conductivity increases. Always remember, more ions mean higher conductivity.

Defining Normality in Electrolyte Solutions

Normality (N) is a concentration term used in chemistry to describe the number of equivalents of solute per liter of solution. It is specifically useful when dealing with reactions involving acids and bases where the amount of hydrogen or hydroxide ions matters. This is because normality accounts for the reactive capacity of a molecule, making it different from molarity. In the context of electrolyte solutions, normality gives a clearer idea about the ion concentration levels contributing to conductivity. For example:

• A solution with normality of 0.01 N means there are 0.01 equivalents of solute per liter.
• For acids like sulfuric acid (H₂SO₄), each mole supplies two equivalents because it donates two protons (H⁺ ions).

Normality is particularly useful for predicting and calculating the changes in a solution's properties during chemical reactions.

What is an Electrolyte Solution?

An electrolyte solution is a liquid containing ions, which are charged particles. This type of solution can conduct electricity due to the presence of these free-moving ions. Electrolytes are often dissolved in water and can be salts, acids, or bases. When dissolved, they dissociate into cations (positively charged) and anions (negatively charged). Here are some key features of electrolyte solutions:

• They conduct electricity due to ionic movement.
• The strength of an electrolyte (strong vs. weak) depends on its ability to dissociate into ions. Strong electrolytes fully dissociate while weak electrolytes partially do.

Common examples include solutions of sodium chloride (table salt), hydrochloric acid, and acetic acid. Electrolyte solutions are vital in many fields, especially in biological systems and industrial processes.

Conductivity Calculations: Breaking It Down

Conductivity calculations involve determining the ability of a solution to conduct electricity, often measured through specific and equivalent conductance. These calculations help assess the efficiency of an electrolyte in conducting current. To calculate equivalent conductance (b4_eq), use the formula: \[ b4_{eq} = \frac{\kappa}{C} \] where:

• ba (belectrolytic conductivity) is specific conductance, given in mho cm^-1.
• C is the concentration in normality.

Substitute the values you have to find b4_eq. This value represents the conductance of a solution per equivalent concentration and is expressed in mho cm² eq^-1. The calculation process:

• Identify the given specific conductance and normality.
• Plug these into the formula.
• Perform the division to get the result.

This method is crucial for analyzing and comparing the conductivities of different solutions, providing essential insights into their chemical and physical properties.