Conductance of Electrolytic Solutions MCQ Quiz - Objective Question with Answer for Conductance of Electrolytic Solutions - Download Free PDF

Explanation:

Kohlrausch's law states that the equivalent conductivity of an electrolyte at infinite dilution is equal to the sum of the conductances of the anions and cations. If salt is dissolved in water, the conductivity of the solution is the sum of the conductances of the anions and cations.

\(\Lambda_{\mathrm{m}(\mathrm{HAc})}^0=\lambda_{\mathrm{H}^{+}}^0+\lambda_{\mathrm{Ac}^{-}}^0\)

Given, \(\rm \wedge^o_m\) for NaCl, HCl and NaOAc are 126.4, 425.9 and 91.0 S cm² mol^-1 

\(=\lambda_{\mathrm{H}^{+}}^0+\lambda_{\mathrm{Cl}^{-}}^0+\lambda_{\mathrm{AC}^{-}}^0+\lambda_{\mathrm{Na}^{+}}^0-\lambda_{\mathrm{Cl}^{-}}^0-\lambda_{\mathrm{Na}^{+}}^0\)

\(=\Lambda_{\mathrm{m}(\mathrm{HCl})}^{\circ}+\Lambda_{\mathrm{m}(\mathrm{NaAc})}^{\circ}-\Lambda_{\mathrm{m}(\mathrm{NaCl})}^{\circ}\)

= (425.9 + 91.0 – 126.4) S cm² mol^–1 

= 390.5 S cm2 mol–1 

The conductance of electricity by ions present in the solutions is called electrolytic or ionic conductance. The conductivity of electrolytic (ionic) solutions depends on :

(i) the nature of the electrolyte added

(ii) size of the ions produced and their solvation

(iii) the nature of the solvent and its viscosity

(iv) concentration of the electrolyte

(v) temperature (it increases with the increase of temperature)

CONCEPT:

Limiting Equivalent Conductivity

• The limiting equivalent conductivity (Λ_m⁰) of an electrolyte is the sum of the limiting ionic conductivities of the cations and anions.
• The limiting equivalent ionic conductivity (λ_i⁰) is a measure of the contribution of each ion to the conductivity of the electrolyte at infinite dilution.
• The relationship can be expressed as:

  Λm0(NaCl) = λNa+0 + λCl-0

  Λm0(KBr) = λK+0 + λBr-0

EXPLANATION:

• Given:
  • Λm0(NaCl) = 126.5 Scm2 eq-1
  • Λm0(KCl) = 150.0 Scm2 eq-1
  • Λm0(KBr) = 151.5 Scm2 eq-1
  • λBr-0 = 78 Scm2 eq-1
• To find the limiting equivalent ionic conductivity for Na+ ions (λNa+0), we need to first find λK+0:
  • Λm0(KBr) = λK+0 + λBr-0
  • 151.5 = λK+0 + 78
  • λK+0 = 151.5 - 78
  • λK+0 = 73.5 Scm2 eq-1
• Now, using Λm0(KCl):
  • Λm0(KCl) = λK+0 + λCl-0
  • 150.0 = 73.5 + λCl-0
  • λCl-0 = 150.0 - 73.5
  • λCl-0 = 76.5 Scm2 eq-1
• Finally, using Λm0(NaCl):
  • Λm0(NaCl) = λNa+0 + λCl-0
  • 126.5 = λNa+0 + 76.5
  • λNa+0 = 126.5 - 76.5
  • λNa+0 = 50 Scm2 eq-1

Therefore, the limiting equivalent ionic conductivity for Na⁺ ions is 50 Scm² eq^-1.

\( m(\text{theoretical})=\dfrac{63.5 \times 0.1 \times 7200}{96500}=0.4738g \)

\( \therefore \) % efficiency = \( \dfrac{0.3745}{0.4738} \times 100 = 79 \) %

For \(25 \times 10^{-4} \, \text{M} \, \text{NaCl}\) solution,

\(\lambda_m = \lambda_m^{\infty} - b \sqrt{C}\)

\(\lambda_m = 127 - 10^3 (25 \times 10^{-4})^{1/2}\)

\(\lambda_m = 127 - 10^3 \times 5 \times 10^{-2}\)

\(\lambda_m = 77\)

\(\lambda_m = \frac{1000 G \sigma}{M}\)

so, \(\sigma = \frac{M \lambda_m}{1000 G} = \frac{M \lambda_mR}{1000} = \frac{25 \times 10^{-4} \times 77 \times 1000}{1000} = 0.1925 \, \text{cm}^{-1}\)

Explanation:

Kohlrausch's law states that the equivalent conductivity of an electrolyte at infinite dilution is equal to the sum of the conductances of the anions and cations. If salt is dissolved in water, the conductivity of the solution is the sum of the conductances of the anions and cations.

\(\Lambda_{\mathrm{m}(\mathrm{HAc})}^0=\lambda_{\mathrm{H}^{+}}^0+\lambda_{\mathrm{Ac}^{-}}^0\)

Given, \(\rm \wedge^o_m\) for NaCl, HCl and NaOAc are 126.4, 425.9 and 91.0 S cm² mol^-1 

\(=\lambda_{\mathrm{H}^{+}}^0+\lambda_{\mathrm{Cl}^{-}}^0+\lambda_{\mathrm{AC}^{-}}^0+\lambda_{\mathrm{Na}^{+}}^0-\lambda_{\mathrm{Cl}^{-}}^0-\lambda_{\mathrm{Na}^{+}}^0\)

\(=\Lambda_{\mathrm{m}(\mathrm{HCl})}^{\circ}+\Lambda_{\mathrm{m}(\mathrm{NaAc})}^{\circ}-\Lambda_{\mathrm{m}(\mathrm{NaCl})}^{\circ}\)

= (425.9 + 91.0 – 126.4) S cm² mol^–1 

= 390.5 S cm2 mol–1 

The conductance of electricity by ions present in the solutions is called electrolytic or ionic conductance. The conductivity of electrolytic (ionic) solutions depends on :

(i) the nature of the electrolyte added

(ii) size of the ions produced and their solvation

(iii) the nature of the solvent and its viscosity

(iv) concentration of the electrolyte

(v) temperature (it increases with the increase of temperature)

Correct answer: 1 and 2)

Concept:

• Conductivity:  Electric resistance of electrolytic solution is directly proportional to its length (l) and inversely proporational to its area of cross section (A).
• Molar Conductivity : Conducting power of all the ions produced by dissolving one mole of an electrolyte between two large electrodes one centimeter apart. 
• Equivalent Conductivity: It is the conducting power of one equivalent electrolyte placed between two large electrodes one centimeter apart. 
• Limiting Molar Conductivity: The value of molar conductivity when the concentration approaches zero is known as limiting molar conductivity or molar conductivity at infinite dilution. 

Explanation:

• Conductivity is the inverse of resistivity ρ, and is represented by the formula:
• \(\kappa =\frac{1}{\rho }\)
• \(\kappa =\frac{1}{\frac{RA}{l}}\)
• \(\kappa =\frac{1}{R}.\frac{l}{A}\)
• Here the quantity l/A is called cell constant denoted by the symbol, G*.
• \(\kappa =\frac{G^{\star }}{R}\)
• Thus, options 1 and 2 are correct. 

Conclusion:

Thus, Conductivity κ , is equal to \(\rm\frac{1}{R} \ \frac{I}{A}\) and \(\rm\frac{G^*}{R} \).

Additional Information 

CONCEPT:

Molar Conductivity at Infinite Dilution (Λ⁰_m)

• Molar conductivity at infinite dilution, Λ⁰_m, is the sum of the individual ionic conductivities of the cation and the anion at infinite dilution.
• For a weak electrolyte like ammonium hydroxide (NH₄OH), the molar conductivity at infinite dilution can be calculated using the known values of other strong electrolytes and the principle of additivity of ionic conductivities.

EXPLANATION:

• We need to determine Λ⁰_m(NH₄OH) using known molar conductivities of other compounds.
• Given:
  • Λ⁰_m(NH₄Cl)
  • Λ⁰_m(NaOH)
  • Λ⁰_m(NaCl)
• Using the principle of additivity of ionic conductivities:
  • Λ⁰_m(NH₄OH) = Λ⁰_m(NH₄Cl) + Λ⁰_m(NaOH) - Λ⁰_m(NaCl)
• This equation works because:
  • Λ⁰_m(NH₄Cl) provides the ionic conductivities of NH₄⁺ and Cl^-
  • Λ⁰_m(NaOH) provides the ionic conductivities of Na⁺ and OH^-
  • Subtracting Λ⁰_m(NaCl) removes the ionic conductivities of Na⁺ and Cl^- from the sum, leaving the ionic conductivities of NH₄⁺ and OH^-

Therefore, the correct answer is option 2: Λ⁰_m(NH₄Cl) + Λ⁰_m(NaOH) - Λ⁰_m(NaCl).

CONCEPT:

Cell Constant of a Conductivity Cell

• The cell constant of a conductivity cell is a characteristic property of the cell.
• It is defined as the ratio of the distance between the electrodes (d) to the area of the electrodes (A).
• The cell constant (K) can be expressed as:

  K = d / A

EXPLANATION:

• The cell constant is a fixed value for a given conductivity cell. It does not change with:
  • Change of electrolyte
  • Change of concentration of electrolyte
  • Change of temperature of electrolyte
• Since the cell constant is determined by the physical dimensions of the cell, it remains constant for that cell.

Therefore, the correct answer is option 4: The cell constant of a conductivity cell remains constant for a cell.

CONCEPT:

Conductivity of Electrolyte Solutions

• The conductivity of an electrolyte solution is influenced by several factors, including the size of the ions, the viscosity of the solution, the degree of solvation of the ions, and the temperature of the solution.
• Smaller ions typically move more easily through the solution, leading to higher conductivity.
• A higher viscosity in the solution can impede the movement of ions, decreasing conductivity.
• Solvation of ions (interaction with solvent molecules) affects the mobility of the ions; more solvation tends to reduce mobility and thus lower conductivity.
• As temperature increases, the mobility of ions generally increases, leading to higher conductivity.

EXPLANATION:

• Statement 1: "Conductivity of solution depends upon size of ions." This is correct because the size affects the mobility of the ions.
• Statement 2: "Conductivity depends upon viscosity of solution." This is correct because higher viscosity can decrease ion mobility and therefore conductivity.
• Statement 3: "Conductivity does not depend upon solvation of ions present in solution." This statement is not correct because solvation affects ion mobility; higher solvation typically decreases conductivity.
• Statement 4: "Conductivity of solution increases with temperature." This is correct because increased temperature generally increases ion mobility and thus conductivity.

Therefore, the statement that is not correct about solutions of electrolytes is: "Conductivity does not depend upon solvation of ions present in solution."

Explanation:

Kohlrausch's law states that the equivalent conductivity of an electrolyte at infinite dilution is equal to the sum of the conductances of the anions and cations. If salt is dissolved in water, the conductivity of the solution is the sum of the conductances of the anions and cations.

\(\Lambda_{\mathrm{m}(\mathrm{HAc})}^0=\lambda_{\mathrm{H}^{+}}^0+\lambda_{\mathrm{Ac}^{-}}^0\)

Given, \(\rm \wedge^o_m\) for NaCl, HCl and NaOAc are 126.4, 425.9 and 91.0 S cm² mol^-1 

\(=\lambda_{\mathrm{H}^{+}}^0+\lambda_{\mathrm{Cl}^{-}}^0+\lambda_{\mathrm{AC}^{-}}^0+\lambda_{\mathrm{Na}^{+}}^0-\lambda_{\mathrm{Cl}^{-}}^0-\lambda_{\mathrm{Na}^{+}}^0\)

\(=\Lambda_{\mathrm{m}(\mathrm{HCl})}^{\circ}+\Lambda_{\mathrm{m}(\mathrm{NaAc})}^{\circ}-\Lambda_{\mathrm{m}(\mathrm{NaCl})}^{\circ}\)

= (425.9 + 91.0 – 126.4) S cm² mol^–1 

= 390.5 S cm2 mol–1 

The conductance of electricity by ions present in the solutions is called electrolytic or ionic conductance. The conductivity of electrolytic (ionic) solutions depends on :

(i) the nature of the electrolyte added

(ii) size of the ions produced and their solvation

(iii) the nature of the solvent and its viscosity

(iv) concentration of the electrolyte

(v) temperature (it increases with the increase of temperature)

Concept:

Conductance in electrolytes relates to how well the electrolyte solution can conduct electricity. Different types of conductance include specific conductance and equivalent conductance. Specific conductance, also called conductivity (κ), is affected by dilution and temperature.

Molar Conductance (\(\Lambda_m\)): \( \Lambda_m = \frac{\kappa \cdot 1000}{M} \)

Where:

• \(\Lambda_m\) is the molar conductance (S cm² mol⁻¹).
• \(\kappa\) is the specific conductance (conductivity) of the solution (S cm⁻¹).
• C is the molar concentration of the electrolyte solution (mol L⁻¹).
• The factor 1000 is used to convert (C) from mol L⁻¹ to mol cm⁻³.

Equivalent Conductance (\(\Lambda_{eq}\)): \(\Lambda_{eq} = \frac{\kappa \cdot 1000}{N} \)

Where:

• \(\Lambda_{eq}\) is the equivalent conductance (S cm² eq⁻¹).
• \(\kappa\) is the specific conductance (conductivity) of the solution (S cm⁻¹).
• N is the normality of the electrolyte solution (eq L⁻¹).
• The factor 1000 is used to convert (N) from eq L⁻¹ to eq cm⁻³.

Explanation:

1. Specific conductance (κ) generally decreases with dilution because the number of ions per unit volume decreases as the solution is diluted.
2. Equivalent conductance (Λ_eq) increases with dilution because ions have more space to move in a diluted solution, decreasing inter-ionic interactions and allowing better conductance per equivalent of the electrolyte.
3. The conductance of all electrolytes typically increases with temperature because higher temperatures provide more kinetic energy to the ions, facilitating better movement and higher conductance.

Conclusion:

Based on the above explanation:

1. Statement 1 is incorrect because specific conductance decreases with dilution.
2. Statement 2 is incorrect because equivalent conductance increases with dilution.
3. Statement 3 is correct because conductance generally increases with temperature for all electrolytes.

Thus, Statement 1 and 2 are incorrect.

Concept:

Kohlrausch's Law: It is  also known as the Law of Independent Migration of Ions. It states that at infinite dilution, each ion contributes a specific value to the molar conductivity of an electrolyte, regardless of the nature of the other ions present in the solution.

Kohlrausch's Law Equation:
The molar conductivity (Λ_m) of an electrolyte at infinite dilution \((Λ^0_m)\) can be expressed as the sum of the individual contributions of the anion and the cation. Mathematically, it is written as:

\(Λ^0_m=λ^0_++λ^0_−\)

Where:

• \(Λ^0_m\) is the molar conductivity at infinite dilution.
• \(λ^0_+\) is the limiting molar conductivity of the cation.
• \(λ^0_−\) is the limiting molar conductivity of the anion.

Explanation:

In a solution, the ions A⁺ and B^2- contribute to the overall conductivity of the electrolyte. As per Kohlrausch's Law, the total limiting molar conductivity is the sum of the individual conductivities of the ions, each multiplied by the stoichiometric coefficient.

For the electrolyte A₂B, this means:

\(2 \times \lambda^\infty (\text{A}^+) + 1 \times \lambda^\infty (\text{B}^{2-}) = 2 \lambda^\infty (\text{A}^+) + \lambda^\infty (\text{B}^{2-})\)

Conclusion:

Therefore, the correct expression for the limiting molar conductivity of the electrolyte A₂B is: None of these.