Library / Solution chemistry, equilibria and kinetics / SCH-04
Solution chemistry, equilibria and kinetics
Ionic strength on a concentration basis
Ionic strength of a solution, half the sum of each ion’s concentration times the square of its charge number.
- Ref
- SCH-04
- Rev
- v1
- Field
- Solution chemistry, equilibria and kinetics
- Result
- I [mol/L]
Ionic strength measures the total electrical environment of the ions, I = ½ Σ cᵢ zᵢ². The squares of the charges weight multiply-charged ions strongly, so a 2+ ion counts four times as much as a 1+ ion at the same concentration. List every ion actually in solution, including the counterions of each salt. It sets the activity coefficients in the Debye–Hückel equations.
Ionic strength of a solution, half the sum of each ion’s concentration times the square of its charge number. Up to three species can be entered, and every ion, counterions included, must be listed. For 0.010 M CaCl₂ use 0.010 of Ca²⁺ and 0.020 of Cl⁻.
Calculator
- Total ion concentration, Σ c0.03 mol/L
- Net charge, Σ c z (zero when balanced)0 eq/L
- log₁₀ γ of a singly charged ion, limiting law at 25 °C−0.08816
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The ions give an ionic strength of 0.03 mol/L, against a total concentration of 0.03 mol/L.
- At this ionic strength the limiting law gives an activity coefficient of about 0.816 for a singly charged ion, so concentration-based constants are only approximate.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (mol/L) | Local step | Change in result |
|---|---|---|---|---|---|---|
| c1 Concentration of ion 1 | 0 to 1 mol/L | 0.01 | 2.01 | 2 | +10% | +6.67 % |
| c2 Concentration of ion 2 | 0 to 1 mol/L | 0.02 | 0.52 | 0.5 | +10% | +3.33 % |
| c3 Concentration of ion 3 (zero if unused) | 0 to 1 mol/L | 0.03 | 0.53 | 0.5 | +10% | 0 % |
| z2 Charge number of ion 2 | −4 to 4 | 0.02 | 0.18 | 0.16 | +1 | −33.3 % |
| z1 Charge number of ion 1 | −4 to 4 | 0.01 | 0.09 | 0.08 | +1 | +83.3 % |
| z3 Charge number of ion 3 | −4 to 4 | 0.03 | 0.03 | 0 | +1 | 0 % |
Sweep of Concentration of ion 1
| Concentration of ion 1 (mol/L) | Ionic strength (mol/L) |
|---|---|
| 0 | 0.01 |
| 0.125 | 0.26 |
| 0.25 | 0.51 |
| 0.375 | 0.76 |
| 0.5 | 1.01 |
| 0.625 | 1.26 |
| 0.75 | 1.51 |
| 0.875 | 1.76 |
| 1 | 2.01 |
Sweep one variable
Variables and how each one contributes
Ionic strength
What the equation gives you. Everything else feeds it.
Concentration of ion 1
The concentration of ion 1, in mol/L. Raises the ionic strength in direct proportion, weighted by z₁². Raising it by 10 % (to 0.011) moves the result by +6.67 %, from 0.03 to 0.032 mol/L.
Charge number of ion 1
The signed charge number of ion 1. Raises the ionic strength with the square of the charge, ignoring the sign. Raising it by 10 % (to 2.2) moves the result by +14 %, from 0.03 to 0.0342 mol/L.
Concentration of ion 2
The concentration of ion 2, in mol/L. Raises the ionic strength in direct proportion, weighted by z₂². Raising it by 10 % (to 0.022) moves the result by +3.33 %, from 0.03 to 0.031 mol/L.
Charge number of ion 2
The signed charge number of ion 2. Raises the ionic strength with the square of the charge, ignoring the sign. Raising it by 10 % (to −1.1) moves the result by +7 %, from 0.03 to 0.0321 mol/L.
Concentration of ion 3 (zero if unused)
The concentration of ion 3, in mol/L (zero if unused). Raises the ionic strength in direct proportion, weighted by z₃². Raising it by 10 % (to 0) moves the result by +0 %, from 0.03 to 0.03 mol/L.
Charge number of ion 3
The signed charge number of ion 3. Raises the ionic strength with the square of the charge, ignoring the sign (matters only if c₃ is not zero). Raising it by 10 % (to 1.1) moves the result by +0 %, from 0.03 to 0.03 mol/L.
Worked example with the values above
- Weighted terms: c₁z₁² = 0.04, c₂z₂² = 0.02, c₃z₃² = 0.
- Sum: 0.06.
- I = ½ × that = 0.03 mol/L.
Assumptions and limits
- Ideal dilute solutions, with concentrations in mol/L and masses in grams unless stated.
- Complete mixing and no evaporation or contraction on mixing unless the inputs say otherwise.
Common mistakes
- Mixing molality (per kg of solvent) with molarity (per litre of solution).
- Entering a mass percentage where a fraction between 0 and 1 is needed.
- Leaving out counterions when adding up charges.
Statistics and uncertainty
Masses and volumes are usually known to 0.1 % to 1 %, and concentrations from them carry the same relative error. Volumetric glassware tolerances add up through serial dilutions, so each extra stage widens the uncertainty.
Where it is used
- Preparing standards, stocks and dilution series in the laboratory.
- Checking charge balance and ionic strength in water analysis.
Maths you need
- Amount of substance: n = m/M, in mol
- Concentration: c = n/V, in mol/L
- Electroneutrality: total positive charge equals total negative charge