Degree of dissociation, when molar conductivity of X at its concentration C is 24.14 and its limiting molar conductivity is 48.28 will be:
0.5
Calculating Degree of Dissociation from Molar Conductivity
The degree of dissociation ($\alpha$) of an electrolyte tells us what fraction of the total electrolyte molecules have dissociated into ions in a solution at a given concentration. For weak electrolytes, the degree of dissociation changes with concentration.
We can determine the degree of dissociation using the molar conductivity of the solution at a given concentration ($\Lambda_m$) and the limiting molar conductivity ($\Lambda_m^0$). The limiting molar conductivity is the molar conductivity when the concentration approaches zero, which represents complete dissociation for weak electrolytes.
The relationship is given by the formula:
\(\alpha = \frac{\Lambda_m}{\Lambda_m^0}\)
In this problem, we are given:
- Molar conductivity of X at concentration C, \(\Lambda_m = 24.14\)
- Limiting molar conductivity of X, \(\Lambda_m^0 = 48.28\)
Now, we can substitute these values into the formula to find the degree of dissociation:
\(\alpha = \frac{24.14}{48.28}\)
Let's perform the calculation:
\(\alpha = 0.5\)
So, the degree of dissociation of X at concentration C is 0.5.
Revision Table: Key Concepts
| Concept | Definition/Formula | Unit |
|---|---|---|
| Molar Conductivity (\(\Lambda_m\)) | Conductivity of a solution containing one mole of electrolyte, placed between electrodes one unit distance apart with unit area of cross-section. | S cm2 mol-1 or S m2 mol-1 |
| Limiting Molar Conductivity (\(\Lambda_m^0\)) | Molar conductivity at infinite dilution (concentration approaches zero). Represents complete dissociation for weak electrolytes. | S cm2 mol-1 or S m2 mol-1 |
| Degree of Dissociation (\(\alpha\)) | Fraction of total electrolyte that has dissociated into ions. | Dimensionless |
Additional Information on Degree of Dissociation
The degree of dissociation is a crucial concept, especially for understanding the behavior of weak electrolytes. Here are some additional points:
- For strong electrolytes, dissociation is considered complete at all concentrations, so the degree of dissociation is effectively 1.
- For weak electrolytes, the degree of dissociation increases as the concentration decreases (or dilution increases). It reaches its maximum value (approaching 1) at infinite dilution, which is why we use the limiting molar conductivity to represent complete dissociation.
- The value of the degree of dissociation helps in calculating the concentration of ions in a solution of a weak electrolyte, which in turn is needed to calculate equilibrium constants like the acid dissociation constant (Ka) or base dissociation constant (Kb).
- Oswald's Dilution Law relates the degree of dissociation of a weak electrolyte to its dissociation constant and concentration.
Important Questions from p-block Elements
Second most abundant element in alloy misch metal is:
Match List-I with List-II:
List-I List-II (A) Gel (I) Hair cream (B) Foam (II) Dust (C) Emulsion (III) Cheese (D) Aerosol (IV) Whipped cream Choose the correct answer from the options given below:
Rate of a reaction changes from 2.48 × 10⁻³ mol⁻¹ sec⁻¹ to 4.96 × 10⁻³ mol⁻¹ sec⁻¹ when concentration of reactant is changed from 0.6 M to 2.4 M respectively, the order of reaction is:
A divalent ion of 'V' (Atomic no. 23) in aqueous solution is:
Which of the following sols are correctly matched with their corresponding charges?
(A) Cr(OH)₃ sol : negatively charged sol
(B) TiO₂ sol : positively charged sol
(C) CdS sol : positively charged sol
(D) Gum : negatively charged sol
(E) Silver sol : positively charged sol
Choose the correct answer from the options given below:
