Donnan Equilibrium Calculator

Balance ions across membranes with fixed charges easily. Explore ratios, potential, and osmotic pressure fast. Ideal for labs, classes, and quick consistency checks anywhere.

Inputs
Enter values and compute equilibrium
Units: mol/L, L, degC
Concentration of the impermeant species in compartment A.
Negative values represent fixed anionic charge (common in gels/proteins).
Both assume 1:1 permeant ions (e.g., NaCl-like).
How salt-only mode initializes ions
It starts with neutral salt on each side, then adds the needed counterions in A to satisfy electroneutrality with the fixed charge.
Custom initial concentrations (mol/L)
Provide permeant cation and anion concentrations for each compartment. Values should usually be charge-consistent with the fixed species for best realism.

Formula used

This calculator uses ideal Donnan equilibrium for a 1:1 electrolyte with an impermeant fixed species in compartment A.

  • Electroneutrality: A: c+A − c-A + zfCf = 0, and B: c+B = c-B.
  • Electrochemical equality: For each ion, RT ln(ci,A/ci,B) + ziFΔψ = 0.
  • Donnan relations: c+A = c+Be−α, c-A = c-Beα, where α = FΔψ/(RT).
  • Mass balance: Total permeant moles are conserved using your volumes and initial concentrations.
  • Osmotic estimate: Δπ ≈ RT(ΣCA − ΣCB), including the fixed species as an osmole in A.

Assumes ideal solutions, constant volumes, and a membrane permeable to both permeant ions.

How to use this calculator

  1. Choose an input mode: salt-only for quick setups, or custom for full control.
  2. Enter temperature, compartment volumes, and the fixed charge concentration and valence.
  3. Provide initial concentrations. Use mol/L and liters for consistent results.
  4. Press Compute. Results appear above the form under the header.
  5. Download a report using the CSV or PDF buttons in the results box.

Example data table

Example inputs and typical outputs (rounded). Try these values to validate your setup.

Case T (degC) VA (L) VB (L) Cf (mol/L) zf Salt A (mol/L) Salt B (mol/L) Δψ (mV) c+A (mol/L) c+B (mol/L)
Demo 1 25 1.0 1.0 0.05 -1 0.15 0.15 ~ -5 to -25 ~ 0.18 to 0.22 ~ 0.14 to 0.17
Demo 2 37 2.0 1.0 0.10 -2 0.10 0.15 More negative Higher Lower

Outputs depend on charge balance, volumes, and fixed-charge strength.

Related Calculators

Membrane potential calculatorGoldman equation calculatorIon channel conductancePatch clamp sealCable length constantMembrane time constantAxon conduction velocityHodgkin Huxley solverAction potential thresholdEPSP amplitude calculator

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.