Variation of Molar Conductivity with Concentration and Dilution
Molar conductivity quantifies how effectively an electrolyte solution conducts an electric current for one mole of solute. For JEE, understanding molar conductivity helps connect electrochemistry theory to practical ion movement in solutions. It is a core metric for comparing strong and weak electrolytes and is vital for solving numerical questions and analyzing ion dissociation behaviour during dilution.
In electrochemistry, molar conductivity bridges the gap between observable solution conductance and the nature of the dissolved chemical species. Unlike simple conductance (G) or solution conductivity (κ), molar conductivity (Λm) specifically measures the ability of all the ions produced by dissolving one mole of substance to carry current. This is why key areas in JEE Main focus on definitions, units, formulae, dependence on concentration, and the concept of infinite dilution.
Definition and Significance of Molar Conductivity
Molar conductivity (Λm) is defined as the conductance of all the ions produced from one mole of electrolyte dissolved in a solution. It indicates the total conducting power of ions from one mole, normalized to its concentration. This property is central to understanding ion dissociation, solution behaviour, and is a favourite in conceptual and calculation-based JEE questions.
Molar Conductivity Formula, Symbols, and Units
The formula for molar conductivity is:
| Symbol | Formula | Unit (SI) |
|---|---|---|
| Λm (Molar Conductivity) | Λm = κ / c | S m2 mol-1 |
| (κ = specific conductivity in S m-1; c = molarity in mol m-3) |
Λm increases as concentration decreases because each ion has more space to move, reducing interionic interactions. For clarity:
- κ (kappa) is specific conductivity (S m-1).
- c is concentration in molarity (mol m-3 or mol L-1).
- The common alternative unit is S cm2 mol-1 for laboratory data.
If using molarity in mol L-1 and conductivity in S cm-1: Λm (S cm2 mol-1) = (1000 × κ) / c.
Conductivity, Molar Conductivity, and Conductance: Key Differences
Distinguishing these terms is crucial for quick MCQ resolution and avoiding calculation mistakes. The comparison below focuses on their meaning, units, and context:
| Property | Definition | Unit (SI) |
|---|---|---|
| Conductance (G) | Reciprocal of resistance; overall ability to conduct current between two electrodes | siemens (S) |
| Specific Conductivity (κ) | Conductance of unit volume (1 m3) of solution between opposite faces of unit cube | S m-1 |
| Molar Conductivity (Λm) | Conductance of all the ions produced by 1 mole of electrolyte in solution | S m2 mol-1 |
Remember: Conductance is the measured value for a specific setup, conductivity relates to solution properties, and molar conductivity allows comparisons per mole of solute—a key requirement for analytical use in JEE.
Variation of Molar Conductivity with Concentration (Dilution Effect)
Molar conductivity always increases as a solution is diluted. This is due to a decrease in ion-ion interactions and increased ion mobility as the concentration of solute decreases. The behaviour is markedly different for strong and weak electrolytes:
- For strong electrolytes: Λm increases slightly with dilution; ions are almost fully dissociated at all concentrations.
- For weak electrolytes: Λm increases sharply on dilution; significant ionization occurs only as water is added.
Graphically, the Λm vs. √c curve is almost linear for strong electrolytes, but curved for weak electrolytes.
Molar Conductivity at Infinite Dilution and Kohlrausch’s Law
At infinite dilution (c → 0), the value of molar conductivity becomes highest and is denoted by Λm0 (“limiting molar conductivity”). At this point, each ion acts independently. For JEE, remember:
- Λm0 is used in degree of dissociation and ionic strength calculations.
- Kohlrausch’s Law: For any electrolyte, Λm0 = λ0+ + λ0-, where λ0+ and λ0- are limiting molar conductivities of cation and anion.
For example, for NaCl, Λm0(NaCl) = λ0Na+ + λ0Cl-. For weak electrolytes, Kohlrausch’s law enables you to calculate limiting values by summing contributions from ions observed in strong electrolyte solutions containing the same ions.
Table: Typical Molar Conductivities at Infinite Dilution (25°C)
| Electrolyte/Ion | Λm0 (S cm2 mol-1) |
|---|---|
| H+ (aq) | 349.8 |
| OH- (aq) | 198.5 |
| Na+ (aq) | 50.1 |
| Cl- (aq) | 76.3 |
| KCl | 149.9 |
| CH3COOH | 390.7 |
These values are essential for calculating degree of dissociation, determining strengths of acids and bases, and for checking your numericals. Always use the unit S cm2 mol-1 unless JEE specifically asks for SI units.
Solved Example: Molar Conductivity Calculation (JEE Style)
A solution of KCl has κ = 0.047 S cm-1 and c = 0.60 mol L-1 at 25°C. Find Λm.
- Formula: Λm = (1000 × κ) / c
- Λm = (1000 × 0.047) / 0.60 = 78.33 S cm2 mol-1
Final result: Λm for this KCl solution = 78.33 S cm2 mol-1.
Common Pitfalls and Quick Tips for JEE
- Never confuse molar conductivity (Λm) with equivalent conductivity; for JEE, always specify the basis: “per mole” vs “per equivalent”.
- Λm increases with dilution, but conductivity (κ) decreases as ion concentration per volume drops.
- Use correct units: SI is S m2 mol-1; in practice, S cm2 mol-1 is common for exam tables and questions.
- Among all ions, H+ has the highest molar conductivity at 25°C due to its unique proton transfer mechanism (“Grotthuss mechanism”).
- Kohlrausch’s law applies at infinite dilution only, not at higher concentrations.
- In numericals, always confirm κ and c are in compatible units before applying formulae.
For more on these distinctions, see the specialized page Electrolytic Conductance, Molar Conductance and Specific Conductance from Vedantu. Also, link Redox Reactions and Electrochemistry for practice with related JEE questions.
Practice Application: JEE Quick Numericals
- Given Λm (NaCl) at infinite dilution = 126.5 S cm2 mol-1. κ = 0.00127 S cm-1 at c = 0.01 mol L-1. Find degree of dissociation α.
- If Λm (acetic acid) at c = 0.01 mol L-1 is 39 S cm2 mol-1 and Λm0 = 390.7 S cm2 mol-1, calculate α at this dilution.
- Why does Λm (KCl) change very little on dilution, but Λm (CH3COOH) increases rapidly?
By mastering these calculations and properties, JEE aspirants develop both a theoretical and problem-solving edge in electrochemistry.
Explore advanced conductance topics in Nernst Equation and connect foundational knowledge in Solutions. For structured revision, Vedantu offers many JEE-specialized mock tests and revision notes on Chemistry.
Molar conductivity remains a lynchpin in JEE Main electrochemistry. Knowing its definition, relationship with dilution, calculation using lab data, and its limits at infinite dilution is essential for securing full marks in related questions. For further exam-oriented preparation, refer to real JEE mock tests and work through solution sets linked above.
FAQs on Molar Conductivity in Chemistry: Concepts, Formulas, and Applications
1. What is molar conductivity?
Molar conductivity is the measure of the ability of all ions from 1 mole of an electrolyte to conduct electricity in a solution.
Key points:
- It is represented by the symbol Λm.
- The unit of molar conductivity is S cm2 mol-1 (Siemens cm2 per mole).
- It plays a crucial role in understanding electrolytic solutions and is widely used in JEE, NEET, and board chemistry exams.
2. How does molar conductivity change with concentration?
Molar conductivity increases as the concentration of the electrolyte decreases (on dilution).
Summary of effects:
- For strong electrolytes: Molar conductivity increases slightly on dilution and reaches a limiting value at infinite dilution.
- For weak electrolytes: Molar conductivity increases sharply on dilution and approaches its maximum at infinite dilution.
- This is because ions experience less inter-ionic attraction and have higher mobility when the solution is diluted.
3. What is the difference between molar conductivity and conductance?
Molar conductivity is the conductance of all ions produced by 1 mole of an electrolyte, while conductance refers to the ability of a specific solution or material to conduct electric current.
Major distinctions:
- Conductance (G): Measured in Siemens (S), refers to the overall current a solution conducts.
- Molar Conductivity (Λm): Expressed as S cm2 mol-1, normalizes conductance per mole of electrolyte.
- Molar conductivity compares efficiency across different concentrations and electrolytes, whereas conductance does not account for the amount of substance.
4. What is the unit and symbol for molar conductivity?
Molar conductivity is denoted by the symbol Λm and its unit is Siemens centimeter squared per mole (S cm2 mol-1).
Symbols and trivia:
- Λm (Greek Lambda sub m) is used universally.
- Older literature may refer to molar conductance, but the modern term is molar conductivity.
5. Why is molar conductivity higher at infinite dilution?
At infinite dilution, molar conductivity (Λm0) is highest because ionic interactions are minimal and each ion moves freely.
Key insights:
- Ions have maximum mobility and are furthest apart, minimizing resistance.
- This value is also used to distinguish strong and weak electrolytes by comparing their behaviour as concentration approaches zero.
6. What is the formula for molar conductivity?
The formula for molar conductivity is:
Λm = κ / c
Where:
- Λm = Molar conductivity
- κ (kappa) = Specific conductivity or conductance (S cm-1)
- c = Molarity of the solution (mol L-1)
7. What are k and c in molar conductivity?
In the formula Λm = κ / c:
- k (κ): Represents the specific conductivity or conductance of the solution, measured in S cm-1.
- c: Denotes the concentration of the electrolyte in molarity (mol L-1).
8. Is molar conductance and molar conductivity same?
Yes, molar conductance and molar conductivity refer to the same concept, measuring the conductance provided by the ions from 1 mole of electrolyte in solution.
Details:
- The modern and IUPAC-preferred term is molar conductivity (Λm).
- Older textbooks or questions may use molar conductance interchangeably.
9. How can you distinguish strong and weak electrolytes using molar conductivity?
Strong and weak electrolytes differ in how their molar conductivity varies with dilution:
- Strong electrolytes: Molar conductivity increases gradually with dilution and reaches a limiting value at infinite dilution, as ions are almost fully dissociated.
- Weak electrolytes: Molar conductivity increases sharply with dilution, since more ions are produced as dissociation increases.
- This trend can be observed graphically and is commonly tested in exams.
10. Can two solutions with the same conductivity have different molar conductivities?
Yes, two solutions can have the same specific conductivity but different molar conductivities because molar conductivity accounts for the amount of substance per unit volume.
For instance:
- Solutions with the same κ but different concentrations will yield different Λm values after calculation.
- This is why the same conductivity does not mean equal efficiency per mole of electrolyte.
11. What type of questions are likely in JEE or board exams regarding molar conductivity?
Commonly asked questions in JEE, NEET, and board exams about molar conductivity include:
- Numerical calculations of Λm using the formula.
- Graphical questions about variation with dilution.
- Comparing strong and weak electrolytes through molar conductivity trends.
- Explaining concepts like limiting molar conductivity and its calculation via Kohlrausch's Law.
- Application-based reasoning and common misconception correction.
