Buffer Ionic Strength Calculator (IEX · SEC · EMSA Condition Check)
Formula
I = 0.5 × Σ(ci × zi²)
- I: ionic strength, in mol/L (this tool accepts and reports values in mM; numerically, mM = mol/L × 1000)
- ci: molar concentration of ion i (mol/L)
- zi: charge number of ion i (integer; squaring removes the sign, so positive and negative ions both contribute positively)
Sum over all ions in solution, including counterions introduced when adjusting pH (e.g., Na⁺ brought in by NaOH addition). The formula derives from Debye–Hückel theory (Debye P, Hückel E, Phys Z, 1923, 24:185–206) and is the standard definition of ionic strength in all physical chemistry textbooks.
The z² amplification effect
Ionic strength measures the total electrostatic effect of all ions in solution. The z² term makes multivalent ions contribute nonlinearly: a divalent ion (HPO₄²⁻, Mg²⁺, SO₄²⁻, Ca²⁺) contributes 4× more ionic strength per mM than a monovalent ion (Na⁺, K⁺, Cl⁻).
The four formulations below have identical ionic strengths despite differing threefold in concentration—looking only at “salt concentration” is seriously misleading:
| Salt | Concentration (mM) | I (mM) |
|---|---|---|
| NaCl | 150 | 150 |
| MgCl₂ | 50 | 150 |
| Na₂HPO₄ | 50 | 150 |
| (NH₄)₂SO₄ | 50 | 150 |
Applicable range
The formula is accurate for fully dissociated strong electrolytes in dilute solutions (I < 0.5 mol/L). The common range in biochemical experiments (0–300 mM) falls entirely within this limit and requires no correction. Two boundary conditions to keep in mind:
- Weak-acid/weak-base buffers (Tris, HEPES, phosphate, which at a given pH are only partially in their charged form): for rigorous calculation, first use the Henderson–Hasselbalch equation to determine the concentration of each charged species, then enter each separately; for engineering accuracy, it is conservative to treat the buffer species as fully charged.
- High-concentration sulfate (I > 300 mM): Mg²⁺ and SO₄²⁻ form a small fraction of ion pairs, so the actual effective ion concentration is slightly below the calculated value; the error is typically < 5% and can be ignored.
Worked example
Individual ions after complete dissociation:
|—|—|—|—| | Na⁺ | 157（137 + 20） | 1 | 78.50 | | HPO₄²⁻ | 10 | −2 | 20.00 | | H₂PO₄⁻ | 1.8 | −1 | 0.90 |
I = 78.50 + 2.25 + 69.85 + 20.00 + 0.90 = 171.5 mM
This matches the “~170 mM PBS” figure routinely cited in chromatography literature and instrument manufacturer manuals.
Common mistakes
- Counting only NaCl and omitting phosphate: In PBS, 10 mM Na₂HPO₄ contributes 20 mM ionic strength because HPO₄²⁻ has z²=4; omitting this underestimates I by 12%.
- MgCl₂ dissociates into two Cl⁻: 50 mM MgCl₂ produces 100 mM Cl⁻ upon dissociation; its ionic strength contribution is 0.5×100×1 = 50 mM, not 0.5×50×1 = 25 mM.
- Forgetting counterions introduced during pH adjustment: Titrating HEPES to pH 7.4 with NaOH introduces several millimoles of Na⁺ per mL; this portion of ionic strength is not negligible and should be entered as a separate row.
FAQ
Why does 50 mM MgCl₂ have the same ionic strength as 150 mM NaCl?
Ionic strength is weighted by the square of the charge: MgCl₂ dissociates into Mg²⁺ (z=+2) and 2 Cl⁻ (z=−1); Mg²⁺ contributes 0.5×50×4=100 mM, and the two Cl⁻ contribute 0.5×100×1=50 mM, totaling 150 mM—at only one-third the concentration of NaCl, yet with the same ionic strength.
What ionic strength should the IEX binding buffer be set to?
Most ion-exchange protocols require the binding buffer to have I < 50 mM, ensuring the target protein carries sufficient net charge to bind the resin; elution is achieved by linearly increasing NaCl to 200–1000 mM, depending on the protein's isoelectric point and resin type.
Why is an ionic strength above 150 mM recommended for SEC runs?
When ionic strength is insufficient, surface charges on the protein interact nonspecifically with residual charged sites on the gel matrix, causing peak tailing or apparent molecular weight shifts; 150 mM NaCl (I=150 mM) is generally sufficient to suppress nonspecific electrostatic interactions for most proteins.
Should Tris or HEPES themselves be included in the ionic strength calculation?
Yes. For example, titrating 20 mM HEPES (pKa 7.55) to pH 7.4 with NaOH requires approximately 9 mM NaOH, introducing ~9 mM Na⁺ and ~9 mM HEPES⁻, contributing roughly 9 mM ionic strength. It is recommended to enter the buffer species and the Na⁺ or Cl⁻ used for pH adjustment as separate rows.
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