The molar conductivity of 0.007 M acetic acid is 20 S cm2 mol−1. What is the dissociation constant of acetic acid? Choose the correct option.
The molar conductivity of 0.007 M acetic acid is 20 S cm2 mol−1. What is the dissociation constant of acetic acid? Choose the correct option.
2.50×10−5 mol L−1
1.75×10−4 mol L−1
2.50×10−4 mol L−1
1.75×10−5 mol L−1
The Correct Option is D
Solution and Explanation
To find the dissociation constant (\(K_a\)) of acetic acid, we start by using the relationship between molar conductivity at a given concentration (\(Λ_m\)) and the limiting molar conductivity (\(Λ_m^0\)). Acetic acid is a weak electrolyte, so the expression to calculate the molar conductivity at infinite dilution (\(Λ_m^0\)) is given by:
- For acetic acid, \(Λ_m^0 = Λ_{m}^{H^+} + Λ_{m}^{CH_3COO^-}\)
However, for simplicity, we'll use the known value \(Λ_m^0\) for acetic acid, which is approximately \(390 \text{ S cm}^2 \text{ mol}^{-1}\).
Given data:
- Molar conductivity of acetic acid, \(Λ_m = 20 \text{ S cm}^2 \text{ mol}^{-1}\).
- Concentration, \(C = 0.007 \text{ M}\).
Using the formula for the degree of dissociation (\(α\)):
Substitute the values:
The dissociation constant (\(K_a\)) is calculated using the formula:
Substitute the values of \(C\) and \(α\):
Therefore, the dissociation constant of acetic acid is \(1.75 × 10^{-5} \text{ mol L}^{-1}\). This matches the correct option.
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Concepts Used:
Solutions
A solution is a homogeneous mixture of two or more components in which the particle size is smaller than 1 nm.
For example, salt and sugar is a good illustration of a solution. A solution can be categorized into several components.
Types of Solutions:
The solutions can be classified into three types:
- Solid Solutions - In these solutions, the solvent is in a Solid-state.
- Liquid Solutions- In these solutions, the solvent is in a Liquid state.
- Gaseous Solutions - In these solutions, the solvent is in a Gaseous state.
On the basis of the amount of solute dissolved in a solvent, solutions are divided into the following types:
- Unsaturated Solution- A solution in which more solute can be dissolved without raising the temperature of the solution is known as an unsaturated solution.
- Saturated Solution- A solution in which no solute can be dissolved after reaching a certain amount of temperature is known as an unsaturated saturated solution.
- Supersaturated Solution- A solution that contains more solute than the maximum amount at a certain temperature is known as a supersaturated solution.