1.2880e+1
S·cm²/mol
1.288000e-3
S·m²/mol
1.2880e+1
S·cm²/mol
1.288000e-3
S·m²/mol
Molar conductivity (Λm) is a key electrochemical property that measures the conducting power of all the ions produced by dissolving one mole of an electrolyte in solution. Unlike specific conductivity, molar conductivity accounts for the effect of dilution and provides insight into ion-ion interactions and dissociation behavior. The Molar Conductivity Calculator converts measured specific conductivity (κ) and molar concentration into molar conductivity in both SI and CGS units. As concentration decreases, molar conductivity generally increases because ions are farther apart and experience less interionic attraction. For strong electrolytes, molar conductivity varies linearly with the square root of concentration (Debye-Hückel-Onsager theory), while for weak electrolytes, the increase is dramatic due to enhanced dissociation. Understanding molar conductivity is essential in analytical chemistry, electrolyte characterization, and determining dissociation constants of weak acids and bases.
Molar conductivity is defined as the conductivity of a solution divided by its molar concentration:
$$\Lambda_m = \frac{\kappa}{c}$$
In SI units, κ is in S/m and c is in mol/m³, giving Λm in S·m²/mol. Since concentration is usually given in mol/L, the conversion is:
$$\Lambda_m = \frac{\kappa}{c \times 1000}$$
where κ is in S/m and c is in mol/L. The traditional CGS unit is S·cm²/mol, related by:
$$\Lambda_m \text{(S·cm²/mol)} = \Lambda_m \text{(S·m²/mol)} \times 10^4$$
For strong electrolytes, molar conductivity at infinite dilution (Λ°m) is found by extrapolating the linear plot of Λm vs √c to zero concentration using the Debye-Hückel-Onsager equation:
$$\Lambda_m = \Lambda_m^\circ - (A + B\Lambda_m^\circ)\sqrt{c}$$
For weak electrolytes, Λ°m cannot be found by extrapolation and is instead obtained from Kohlrausch's law of independent migration.
A higher molar conductivity indicates that each mole of electrolyte produces ions that conduct electricity more effectively. For strong electrolytes like NaCl or KCl, Λm decreases only slightly with increasing concentration due to interionic effects. For weak electrolytes like acetic acid, Λm increases sharply on dilution because more molecules dissociate into ions. The ratio α = Λm/Λ°m gives the degree of dissociation for weak electrolytes. Typical values at infinite dilution: KCl ≈ 149.9 S·cm²/mol, NaCl ≈ 126.5 S·cm²/mol, CH₃COOH ≈ 390.7 S·cm²/mol. If your calculated value seems unusually low, check that concentration units are consistent and that temperature is controlled.
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A 0.1 M KCl solution with κ = 1.29 S/m gives Λm = 129.0 S·cm²/mol, close to the literature value of 128.96 S·cm²/mol at 25°C.
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Dilute acetic acid (weak electrolyte) shows Λm = 16.3 S·cm²/mol, much lower than Λ°m ≈ 390.7 S·cm²/mol, indicating only ~4.2% dissociation.
Specific conductivity (κ) measures the total conductivity of a solution per unit volume. Molar conductivity (Λm) normalizes this by concentration, showing the conducting ability per mole of dissolved electrolyte. This normalization reveals how ionic interactions change with dilution.
On dilution, interionic attractions decrease (Debye-Hückel effect) for strong electrolytes, allowing ions to move more freely. For weak electrolytes, dilution also increases the degree of dissociation (Le Chatelier's principle), producing more ions per mole.
Λ°m is the molar conductivity when concentration approaches zero, where all interionic interactions vanish. For strong electrolytes, it is found by extrapolating Λm vs √c plots. For weak electrolytes, it is calculated from Kohlrausch's law using individual ionic conductivities.
Strong electrolytes show a small, linear decrease in Λm with √c (Onsager equation). Weak electrolytes show very low Λm at moderate concentrations with a dramatic increase on extreme dilution, reflecting their equilibrium between dissociated and undissociated forms.
The SI unit is S·m²/mol, but the more commonly used unit is S·cm²/mol. To convert: 1 S·m²/mol = 10,000 S·cm²/mol. Literature values are almost always reported in S·cm²/mol.
For a weak electrolyte, α = Λm/Λ°m gives the degree of dissociation. Then Ka = cα²/(1-α) for a 1:1 electrolyte. This is the basis of Ostwald's dilution law.
It predicts: Λm = Λ°m − (A + BΛ°m)√c, where A and B are constants depending on solvent properties, temperature, and ion charges. It explains the linear decrease of Λm with √c for strong electrolytes at low concentrations.
H⁺ (and OH⁻) have anomalously high conductivities due to the Grotthuss mechanism—proton hopping along hydrogen-bonded water chains. λ°(H⁺) = 349.8 S·cm²/mol, roughly 5× higher than most other ions.
No, molar conductivity is always positive since both κ and c are positive quantities. A negative result would indicate a measurement error or incorrect unit conversion.
Molar conductivity increases with temperature due to reduced viscosity and enhanced ionic mobility. The temperature coefficient is typically 1.5–2.5% per °C. All literature values should specify the temperature, usually 25°C.
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