Can I solve for different variables?

Yes! This calculator supports reverse solving. You can solve for: Constant (A), Charge number of ion (z), Activity coefficient (f), Ionic strength (I).

Activity coefficient

Solve activity coefficient relationships quickly using core chemistry formulas.

Formula shown3 inputs definedUpdated Nov 2025By Automated Chemistry GeneratorFree, no sign-up

Quick Summary

Use this when you need:

Estimate mean ionic activity coefficients for dilute electrolyte solutions
See how increasing ionic strength suppresses γ for multivalent ions
Sanity-check laboratory measurements of γ against Debye–Hückel predictions

You’ll need:Charge number of ion (z), Activity coefficient (f), Ionic strength (I)

You’ll get:Constant (A)

How this is calculated

Formula:

log10(γ) = -A * z^2 * sqrt(I)

In plain language:

The Debye–Hückel limiting law states that the base-10 logarithm of the activity coefficient equals -A z^2 √I, so providing A, ionic strength I, and ion charge z gives γ directly.

The formula is always visible so you can verify the math and explain your numbers to anyone who asks.

What these terms mean

Constant (A)

Constant (A) used in the calculation.

Charge number of ion (z)

Charge number of ion (z) used in the calculation.

Activity coefficient (f)

Activity coefficient (f) used in the calculation.

Ionic strength (I)

Ionic strength (I) used in the calculation.

When to use this calculator

Estimate mean ionic activity coefficients for dilute electrolyte solutions
See how increasing ionic strength suppresses γ for multivalent ions
Sanity-check laboratory measurements of γ against Debye–Hückel predictions

Last updated: November 19, 2025

Activity coefficient calculator explained

This calculator lets you quickly estimate ionic activity coefficients using the Debye-Huckel limiting law. Enter the solvent constant $A$ , the ion charge number {charge}, and the ionic strength {ionic_strength}; the tool computes $\\log_{10}\\gamma$ and the corresponding activity coefficient {coefficient} so you can benchmark lab measurements or design electrolyte solutions.

Use it when you need to know how strongly non-ideal behavior suppresses thermodynamic activities in dilute solutions, especially for comparing mono- and multivalent ions during speciation studies or electrochemical design work.

How the conversion works

For dilute electrolytes the limiting law states:

\\log_{10} \\gamma = -A z^2 \\sqrt{I}

where $A$ depends on temperature and solvent dielectric constant (0.509 for water at 25 deg C), $z$ is the ionic charge number, and $I = \\tfrac12 \\sum c_i z_i^2$ is the ionic strength in mol/L. Solving for $\\gamma$ is therefore:

\\gamma = 10^{-A z^2 \\sqrt{I}}

The calculator keeps the logarithm base consistent and handles very small numbers without rounding errors.

Units and conversions

Quantity	Symbol	Units	Notes
Solvent constant	$A$	dimensionless	0.509 for water at 25 deg C, 0.491 at 18 deg C.
Charge number	$z$	unitless integer	Use the algebraic value (+2 for Ca $^{2+}$ , -1 for Cl $^-$ ).
Ionic strength	$I$	mol/L	$I = 0.5 \\sum c_i z_i^2$ .
Activity coefficient	$\\gamma$	dimensionless	Applies to mean ionic activity for electrolytes.

Worked examples

Monovalent electrolyte check
$A = 0.509$ , $z = 1$ , $I = 0.010$ mol/L.

\\log_{10} \\gamma = -0.509 \\times 1^2 \\times \\sqrt{0.010} = -0.0509

so $\\gamma = 10^{-0.0509} = 0.889$ . Activities are therefore 11% lower than concentrations.

Calcium ion in moderately ionic water
$A = 0.509$ , $z = 2$ , $I = 0.050$ mol/L.

\\log_{10} \\gamma = -0.509 \\times 4 \\times \\sqrt{0.050} = -0.455

giving $\\gamma = 10^{-0.455} = 0.351$ . The calculator reports this instantly and highlights how divalent ions depart from ideality sharply.

Tips and pitfalls

Debye-Huckel limiting law holds reliably only for $I \\lesssim 0.1$ mol/L; switch to extended models for higher ionic strength.
Always specify whether you need individual ionic coefficients or the mean ionic coefficient for salts.
Update $A$ if temperature deviates significantly from 25 deg C or if the solvent is not water.
Use measured ionic strength from conductivity or detailed composition instead of guessing to avoid compounding errors.

References and further reading

Frequently Asked Questions

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Calculator info

Version:: v1.0.0
Last reviewed:: Nov 15, 2025
Sensitivity:: low
References:: 1

Last updated: November 19, 2025

Activity coefficient calculator explained

How the conversion works

For dilute electrolytes the limiting law states:

\\log_{10} \\gamma = -A z^2 \\sqrt{I}

\\gamma = 10^{-A z^2 \\sqrt{I}}

The calculator keeps the logarithm base consistent and handles very small numbers without rounding errors.

Units and conversions

Quantity	Symbol	Units	Notes
Solvent constant	$A$	dimensionless	0.509 for water at 25 deg C, 0.491 at 18 deg C.
Charge number	$z$	unitless integer	Use the algebraic value (+2 for Ca $^{2+}$ , -1 for Cl $^-$ ).
Ionic strength	$I$	mol/L	$I = 0.5 \\sum c_i z_i^2$ .
Activity coefficient	$\\gamma$	dimensionless	Applies to mean ionic activity for electrolytes.

Worked examples

Monovalent electrolyte check
$A = 0.509$ , $z = 1$ , $I = 0.010$ mol/L.

\\log_{10} \\gamma = -0.509 \\times 1^2 \\times \\sqrt{0.010} = -0.0509

so $\\gamma = 10^{-0.0509} = 0.889$ . Activities are therefore 11% lower than concentrations.

Calcium ion in moderately ionic water
$A = 0.509$ , $z = 2$ , $I = 0.050$ mol/L.

\\log_{10} \\gamma = -0.509 \\times 4 \\times \\sqrt{0.050} = -0.455

giving $\\gamma = 10^{-0.455} = 0.351$ . The calculator reports this instantly and highlights how divalent ions depart from ideality sharply.

Tips and pitfalls

Debye-Huckel limiting law holds reliably only for $I \\lesssim 0.1$ mol/L; switch to extended models for higher ionic strength.
Always specify whether you need individual ionic coefficients or the mean ionic coefficient for salts.
Update $A$ if temperature deviates significantly from 25 deg C or if the solvent is not water.
Use measured ionic strength from conductivity or detailed composition instead of guessing to avoid compounding errors.

Quick Summary

Calculator Tool

How this is calculated

What these terms mean

Constant (A)

Charge number of ion (z)

Activity coefficient (f)

Ionic strength (I)

When to use this calculator

Activity coefficient calculator explained

How the conversion works

Units and conversions

Worked examples

Tips and pitfalls

References and further reading

Frequently Asked Questions

Related Calculators

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Was this calculator helpful?

Found an error?

Calculator info

Activity coefficient calculator explained

How the conversion works

Units and conversions

Worked examples

Tips and pitfalls

References and further reading

Frequently Asked Questions

Related Calculators

Enzyme activity

pKa

Beer-Lambert law

Molarity

Mole

Neutralization

Was this calculator helpful?

Found an error?

Calculator info