medium difficulty7 min

Conductivity and Molar Conductivity

Conductivity is the conductance of an electrolyte solution of unit length and unit cross-sectional area, while molar conductivity is the conductance due to all ions produced by one mole of electrolyte in solution.

In one line: Kappa counts ions in a volume; Lambda m counts the conducting power of one mole.

Practice This Concept

Understand it

Conductivity depends on the number of ions per unit volume and their mobility.
On dilution, conductivity usually decreases because the number of ions per unit volume decreases.
Molar conductivity generally increases on dilution because ions move more freely and, for weak electrolytes, ionisation increases.
Kohlrausch's law states that at infinite dilution, each ion contributes independently to the molar conductivity of the electrolyte.

Example

If conductivity kappa = 0.012 S cm-1 and concentration c = 0.10 mol L-1, molar conductivity Lambda m = kappa x 1000 / c = 0.012 × 1000 / 0.10 = 120 S cm2 mol-1.

Rule to remember

Key formula: Lambda m = kappa x 1000 / c when kappa is in S cm-1 and c is in mol L-1.

Unit of kappa: S cm-1 or S m-1.

Unit of Lambda m: S cm2 mol-1 or S m2 mol-1.

Kohlrausch's law: Lambda degree m of electrolyte equals the sum of limiting ionic molar conductivities of its ions with stoichiometric coefficients.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

1For NaCl, if kappa = 1.26 × 10-2 S cm-1 and c = 0.10 mol L-1, Lambda m = (1.26 × 10-2 × 1000)/0.10 = 126 S cm2 mol-1.
2The answer should have molar conductivity units, not conductivity units.

Method you can reuse

1Identify whether the question asks for kappa, conductance, cell constant, or Lambda m.
2Convert concentration to the unit required by the formula.
3Substitute with the correct 1000 factor if using mol L-1 and S cm-1.
4For Kohlrausch's law, write ions with coefficients and add their limiting ionic contributions.

Visual tip

Useful visuals include a conductivity cell labelled with electrodes, electrolyte, cell constant, and conductance meter, plus a graph of molar conductivity versus square root of concentration for strong and weak electrolytes.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why does molar conductivity increase on dilution?

Think first, then show answer

It increases because interionic attractions decrease and ions move more freely; for weak electrolytes, dilution also increases degree of ionisation.

Common wrong answer

A common wrong answer is reporting 0.12 S cm2 mol-1 instead of 120 S cm2 mol-1 because the 1000 conversion factor was omitted.

Don't mix this up

Students often use Lambda m = kappa/c without adjusting units when concentration is given in mol L-1. The factor 1000 is needed when kappa is in S cm-1 and c is in mol L-1.

Exam tip

Always check the units of kappa and concentration before substitution. Most numerical errors in this topic are unit-conversion errors.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Questions commonly ask calculation of molar conductivity, comparison of strong and weak electrolyte graphs, application of Kohlrausch's law to weak electrolytes, or explanation of dilution effects.

1
Enough for 1 mark
Conductivity is the conductance of an electrolyte solution of unit length and unit cross-sectional area, while molar conductivity is the conductance due to all ions produced by one mole of electrolyte in solution.
2
Add for 2 marks
Example: If conductivity kappa = 0.012 S cm-1 and concentration c = 0.10 mol L-1, molar conductivity Lambda m = kappa x 1000 / c = 0.012 × 1000 / 0.10 = 120 S cm2 mol-1.
3
Add for 3 marks
Conductivity depends on the number of ions per unit volume and their mobility.

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