AkCalculators

Conductance explained — electrical conductance, specific conductivity and molar conductivity

Conductance is a fundamental electrical property that describes how easily charge flows through a material or solution. In physics and electrical engineering this is usually expressed as the electrical conductance G, the reciprocal of resistance R (G = 1/R) and measured in siemens (S). In electrochemistry and analytical chemistry the concept is extended to solutions, where specific conductivity (commonly denoted κ, kappa) and molar conductivity (Λ_m) help quantify how well ions transport charge in an electrolyte at a given concentration and temperature. This article brings together both viewpoints: basic definitions, unit conversions, the role of temperature, practical measurement considerations, and worked examples.

Electrical conductance: G = 1 / R

For a uniform conductor with resistance R, the electrical conductance G is the inverse: G = 1 / R. If R is expressed in ohms (Ω), G is in siemens (S). Conductance is additive for parallel branches, which makes it convenient in circuit analysis: total conductance of parallel resistors equals the sum of their conductances. When working with small resistances or very high conductance, precision is essential — avoid subtractive cancellation and present enough significant figures in results.

Specific conductivity (κ) of electrolytes

Specific conductivity κ (also just 'conductivity') measures a solution's ability to carry electric current per unit length and area. In practice, κ is often reported in S·cm⁻¹ or mS·cm⁻¹. Instrumentation typically measures conductance (G) of a cell with known cell constant (cell constant = l/A, length over cross-sectional area) and converts to κ via κ = G × cell_constant. For simplicity, many practical workflows use directly measured κ values from calibrated conductivity meters.

Molar conductivity Λ_m

Molar conductivity Λ_m normalizes κ by concentration to express how conductive each mole of electrolyte is. When κ is in S·cm⁻¹ and concentration C is in mol·L⁻¹, molar conductivity is computed as

Λ_m = κ × 1000 / C

The units become S·cm²·mol⁻¹ (often written S·cm²·mol⁻¹). Λ_m is particularly useful for comparing ion mobility and limiting molar conductivities at infinite dilution.

Temperature dependence

The conductivity of electrolytes generally increases with temperature because ion mobility improves and solution viscosity decreases. A simple and widely used linear approximation is

κ_T = κ₂₅ × [1 + α × (T − 25)]

Here α is the temperature coefficient (per °C), T is temperature in °C, and κ₂₅ is conductivity at 25°C. The linear model is a pragmatic correction for typical laboratory ranges; more accurate treatments use empirical tables or polynomial fits for particular electrolytes and instruments. In the combined module this calculator applies the α-correction wherever temperature is provided.

Unit handling and common pitfalls

Be careful with units when converting between κ and Λ_m. Common pitfalls include mixing S·m⁻¹ with S·cm⁻¹, or mol·m⁻³ with mol·L⁻¹. This tool accepts common unit choices and converts them internally. If you use cell conductance (G measured from a conductivity cell), remember to include the cell constant to get κ: κ = G × cell_constant.

Practical examples

Example 1 — Electrical: A resistor measures 200 Ω. The conductance is G = 1 / 200 = 0.005 S (5 mS). Use the electrical tab to convert rapidly and export results for a report.

Example 2 — Electrochemical: A conductivity meter reads κ = 1.20 mS·cm⁻¹ for an NaCl solution at 25°C and concentration C = 0.01 mol·L⁻¹. Convert units: κ = 1.20 mS·cm⁻¹ = 0.00120 S·cm⁻¹. Then Λ_m = κ × 1000 / C = 0.00120 × 1000 / 0.01 = 120 S·cm²·mol⁻¹. If temperature is 35°C and α = 0.02, κ₃₅ = 0.00120 × [1 + 0.02 × (35 − 25)] = 0.00144 S·cm⁻¹ and recalculate Λ_m accordingly.

Measurement and standards

Use calibrated conductivity cells and standard reference solutions to ensure κ accuracy. The cell constant can change slightly over time; frequent verification with standard solutions (e.g., KCl standards) is recommended. For high-precision work, temperature control and using the exact temperature compensation curve provided by the instrument are preferable to a linear α approximation.

When to use molar conductivity

Use Λ_m when studying ion mobility, comparing electrolytes, or extrapolating to infinite dilution. However, remember that at higher concentrations ion interactions (shielding, ion pairing) make Λ_m concentration-dependent and non-ideal; use activity-based corrections or detailed models in those regimes.

Final notes

This combined Conductance Calculator is designed for quick conversions and lab-friendly workflows. Use the Electrical tab for pure circuit needs, the Electrochemical tab for solution conductivity and molar conductivity computations, and Combined mode to compare and cross-check results while including temperature corrections. Export CSVs for lab notebooks and include step-by-step derivations in reports to show your working. Always state units and temperature alongside reported numbers for reproducibility.