Molar Conductivity Calculator
Calculate the molar conductivity (Λm) of an electrolyte solution from its measured conductivity κ and molar concentration c. Enter both values with their units and get results in S·cm²/mol and S·m²/mol.
Molar Conductivity from Conductivity and Concentration
Molar Conductivity
Where:
- \(\Lambda_m\) — molar conductivity (S·cm²/mol or S·m²/mol)
- \(\kappa\) — specific conductivity (conductivity) of the solution (S/cm)
- \(c\) — molar concentration of the electrolyte (mol/L)
When \(\kappa\) is expressed in S/cm and \(c\) in mol/L, the practical form of the formula is \(\Lambda_m = 1000\,\kappa / c\), giving \(\Lambda_m\) directly in S·cm²/mol. The factor 1000 accounts for the conversion between mol/L and mol/cm³.
Molar Conductivity – Calculation Example
Example: a 0.01 mol/L potassium chloride solution has a measured conductivity of 1.413 mS/cm at 25 °C. What is its molar conductivity?
\[ \kappa = 1.413 \text{ mS/cm} = 1.413 \times 10^{-3} \text{ S/cm} \]
\[ \Lambda_m = \frac{1000 \times 1.413 \times 10^{-3}}{0.01} = 141.3 \text{ S·cm}^2\text{/mol} \]
\[ \Lambda_m = \frac{141.3}{10^4} = 0.014130 \text{ S·m}^2\text{/mol} \]
Result: the molar conductivity is 141.3 S·cm²/mol (0.01413 S·m²/mol), a typical value for KCl at this concentration.
How to Use the Molar Conductivity Calculator
- Enter the measured Solution Conductivity (κ) in the first field — the reading of your conductivity meter.
- Select the unit of the conductivity reading (µS/cm, mS/cm, S/cm or S/m) from the dropdown next to it.
- Enter the Molar Concentration (c) of the electrolyte in the second field.
- Select the concentration unit (mol/L, mmol/L or mol/m³) from the dropdown next to it.
- Read the Molar Conductivity in S·cm²/mol and the Molar Conductivity (SI) in S·m²/mol, together with the step-by-step calculation details.
What Is Molar Conductivity?
Molar conductivity \(\Lambda_m\) (also called molar conductance) is the conductivity of an electrolyte solution normalised to one mole of dissolved electrolyte. The raw conductivity \(\kappa\) measured by a conductivity meter depends on how much salt is dissolved, so a concentrated solution of a poorly conducting electrolyte and a dilute solution of a good one can give the same meter reading. Dividing \(\kappa\) by the molar concentration \(c\) removes this ambiguity and tells you how effectively one mole of the substance carries electric current.
The customary unit is S·cm²/mol, which is what most chemistry textbooks and reference tables use. The SI unit is S·m²/mol, and the conversion is simple: 1 S·m²/mol = 10⁴ S·cm²/mol. The calculator displays both so you can match whatever your course or publication expects.
Molar conductivity is most useful for studying strong and weak electrolytes. For strong electrolytes (NaCl, KCl, HCl), \(\Lambda_m\) decreases only slightly with increasing concentration because ions remain fully dissociated and interionic attractions merely slow them down; the variation follows Kohlrausch's law \(\Lambda_m = \Lambda_m^\circ - K\sqrt{c}\). For weak electrolytes (acetic acid, ammonia), \(\Lambda_m\) falls sharply with concentration because the degree of dissociation \(\alpha\) decreases. The ratio \(\Lambda_m / \Lambda_m^\circ\) approximates \(\alpha\), which is the basis for determining dissociation constants — and by extension solubility products of sparingly soluble salts — from conductivity measurements.
For orientation: at 25 °C the limiting molar conductivities \(\Lambda_m^\circ\) of common strong electrolytes fall roughly between 100 and 430 S·cm²/mol (KCl ≈ 149.9; ½ H₂SO₄ ≈ 426). A result far outside this range usually signals a unit error rather than unusual chemistry.
Assumptions, Limitations and Practical Tips
- Conductivity must be specific conductance. The value you enter should already be corrected for the cell constant — i.e. what a calibrated conductivity meter displays, not the raw conductance.
- Concentration refers to the formula unit. If the solution is labelled in terms of a fraction of the formula (e.g. ½ H₂SO₄), enter the concentration consistently with that definition, as reference tables do.
- Temperature matters. Conductivity of aqueous solutions increases by roughly 2% per °C. Both \(\kappa\) and \(c\) should refer to the same temperature — 25 °C is the standard reference.
- Check unit mix-ups. The most common errors are entering µS/cm instead of mS/cm, or mmol/L instead of mol/L. The calculator warns you when the result is implausibly large (>500 S·cm²/mol) or small (<5 S·cm²/mol).
- Background conductivity. In very dilute solutions, dissolved CO₂ and solvent impurities contribute to \(\kappa\) and inflate \(\Lambda_m\); subtract the conductivity of the pure solvent if you work at micromolar concentrations.
- The calculator only computes \(\Lambda_m = \kappa/c\). To extrapolate to infinite dilution \(\Lambda_m^\circ\) for a strong electrolyte, measure \(\Lambda_m\) at several concentrations and fit against \(\sqrt{c}\).
Typical Limiting Molar Conductivities at 25 °C
| Electrolyte | \(\Lambda_m^\circ\) (S·cm²/mol) |
|---|---|
| KCl | 149.9 |
| NaCl | 126.5 |
| HCl | 426.2 |
| ½ H₂SO₄ | 426 |
| CH₃COOH (weak) | 390.7 |
| NH₃·H₂O (weak) | 271 |
These values apply at infinite dilution; at finite concentrations the measured \(\Lambda_m\) is somewhat lower. If you also analyse water samples, conductivity-based checks pair naturally with our water hardness calculator.
Frequently Asked Questions
Why is there a factor of 1000 in the molar conductivity formula?
The factor 1000 converts liters to cubic centimeters. Conductivity \(\kappa\) is measured per cm, while concentration \(c\) is given per liter. Since 1 L = 1000 cm³, the formula becomes \(\Lambda_m = 1000\,\kappa / c\), which yields the result directly in the customary unit S·cm²/mol. If you convert \(c\) to mol/cm³ yourself, you can simply divide \(\kappa\) by \(c\) without the factor.
How do I convert molar conductivity between S·cm²/mol and S·m²/mol?
Divide S·cm²/mol by 10⁴ to get S·m²/mol, or multiply S·m²/mol by 10⁴ to get S·cm²/mol. For example, 141.3 S·cm²/mol equals 0.01413 S·m²/mol. The factor comes from area units: 1 m² = 10⁴ cm². Textbooks and reference tables overwhelmingly use S·cm²/mol, while SI-oriented publications prefer S·m²/mol — the calculator shows both.
What is a normal value of molar conductivity?
At 25 °C, limiting molar conductivities of common strong electrolytes lie between about 100 and 430 S·cm²/mol: NaCl ≈ 126.5, KCl ≈ 149.9, HCl ≈ 426. Weak electrolytes such as acetic acid reach ≈ 390 only at infinite dilution and show much lower values at practical concentrations. If your result is below 5 or above 500 S·cm²/mol, a unit error is far more likely than unusual chemistry.
How do I calculate molar conductivity by hand?
First convert the conductivity to S/cm and the concentration to mol/L. Then multiply the conductivity by 1000 and divide by the concentration: \(\Lambda_m = 1000\,\kappa / c\). For instance, with \(\kappa = 1.413\) mS/cm and \(c = 0.01\) mol/L: \(\Lambda_m = 1000 \times 0.001413 / 0.01 = 141.3\) S·cm²/mol. Always double-check whether your meter reads µS/cm or mS/cm before converting.
Can I use molar conductivity to find the degree of dissociation of a weak electrolyte?
Yes. The ratio \(\alpha \approx \Lambda_m / \Lambda_m^\circ\) estimates the degree of dissociation, where \(\Lambda_m^\circ\) is the limiting molar conductivity at infinite dilution. Because weak electrolytes like acetic acid dissociate only partially, \(\Lambda_m\) falls sharply with increasing concentration. Combining \(\alpha\) with the ostwald dilution law \(K_a = c\alpha^2/(1-\alpha)\) lets you determine the dissociation constant from conductivity measurements.
What is the difference between molar conductivity and equivalent conductivity?
Molar conductivity normalizes per mole of formula units, while the older equivalent conductivity normalizes per mole of charge (equivalent). For a 1:1 electrolyte like KCl the two are identical; for H₂SO₄ they differ by a factor of 2. Modern IUPAC convention discourages equivalents, which is why the calculator asks for concentration in mol/L. If you compare against older literature values labeled 'equivalent conductance', check how the formula unit was defined.
Why does my result change when I dilute the solution?
Molar conductivity depends on concentration. For strong electrolytes it rises slightly on dilution because interionic attractions weaken, following Kohlrausch's law \(\Lambda_m = \Lambda_m^\circ - K\sqrt{c}\). For weak electrolytes it rises strongly because dilution increases the degree of dissociation. There is no single 'correct' value for a substance — always report the concentration (and temperature) along with \(\Lambda_m\), or extrapolate to \(\Lambda_m^\circ\).