# Ionic Strength Calculator

Created by Komal Rafay
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Dec 30, 2022

Our ionic strength calculator is here to help you calculate the ionic strength of a solution. All you need is the concentrations of the ions in the solution and their charge number.

Some of you might be wondering what ionic strength is and why do you need to calculate it. At the same time, others of you may be excited to find out how to calculate the ionic strength of a solution or a buffer with a helpful equation.

We have something for every curious one of you, from ionic strength calculation formulas to examples and how to calculate ionic strength from molarity. You will find all your answers here!

## Ionic strength calculator

Our ionic strength calculator is an efficient tool for all you chemists and chemistry geeks out there. As the name indicates, it calculates the ionic strength of a solution by using the concentration of ions and their charge numbers.

The study of ionic strength is helpful in many different studies, from understanding of electrolysis of different solutions to Debye-Huckel theory (a theory that explains the behavior of electrolytes where it played a significant role).

Our calculator can help you after only a few simple inputs using the built-in ionic strength equation. You only have to input the concentration of all the ions present in the solution along with their charges, and you will get the ionic strength of your solution under study as your result.

## What is ionic strength?

Ionic strength is the concentration of ions in a solution.

Ionic compounds tend to dissociate and split into ions upon dissolving in water. Ionic strength is one of the most important properties of an electrolytic solution.

The unit of ionic strength is mol/L of solution (mole per litre) or mol/kg of solvent (mole per kilogram). The unit depends on whether you used the molarity formula or molality formula to calculate the ionic concentration.

## Ionic strength calculation formula

The ionic strength of a solution is dependant on the ionic concentration and charge on the ions. The ionic strength calculation formula is written as follows:

$\small \text{I} = \frac 1 2 \sum(\text{c}_\text{i} \cdot \text{z}_{\text{i}}^2)$

where:

• $\small \text{I}$ - Ionic strength;

• $\small\sum$ - Sum of values;

• $\small\text{c}_\text{i}$ - Concentration of ions; and

• $\small\text{z}_\text{i}^2$ - Charges of ions squared.

## How to calculate the ionic strength of a solution?

Indeed, by now, you should understand that the ionic strength of a solution is the concentration of ions in that solution. It can be found from the ionic strength equation.

Now comes the matter of how to calculate the ionic strength of a solution?

The two most important things you need are the concentration of ions and their charge numbers. Then it would be best if you used the ionic strength formula mentioned above:

1. Calculate the power of the charge numbers.
2. Multiply the squared charge numbers by the ionic concentration.
3. Add up all the products of the ionic concentration and charge numbers.
4. Divide the sum value by 2.
5. The result is the ionic strength of the solution as mol/kg of solute or mol/L of solution.

If you're having trouble with finding the name of your ionic compound, our chemical name calculator will help you.

## Ionic strength calculation example

The ionic strength of a solution is an important property and is studied for various reasons. For a greater understanding, let's look at an ionic strength calculation example and a few other things that are important to know about the ionic strength of a solution:

1. Calculate ionic strength from molarity
• In a circumstance where you do not have the concentration of ions, but instead you have the molarity or molality, you need to multiply the number of each particular atom in the molecule by the molarity or molality. This will give you the ionic concentration.

• For instance, you have a 0.02 molar ZnCl2 solution. There is one zinc atom and two chlorine atoms in this situation.

• The ionic concentrations will be:

$\small \text{c}_\text{i}(\text{Zn}) = 0.02 * 1 = 0.02 \text{ mol/L}$
$\text{c}_\text{i}(\text{Cl}_2) = 0.02 * 2 = 0.04 \text{ mol/L}$
1. Ionic strength calculation example
• Let's calculate the ionic strength of a 1 molar, ZnCl2, and Na2SO4 solution.

• First, you will have to calculate the concentrations of the ions using the value of molarity and, as mentioned above, the formula of ci.

$\footnotesize \text{c}_\text{i}(\text{element}) \!=\! \frac{\text{molarity}}{\text{molality}}\! \cdot\! \text{species quantity}$
$\footnotesize \text{c}_\text{i}(\text{Zn}) = 1 * 1 = 1 \text{ mol/L} \\ \text{c}_\text{i}(\text{Cl}_2) = 1 * 2 = 2 \text{ mol/L} \\ \text{c}_\text{i}(\text{Na}_2) = 1 * 2 = 2 \text{ mol/L} \\ \text{c}_\text{i}(\text{SO}_4) = 2 * 1 = 2 \text{ mol/L}$
• Next, verify the charge of ions:
$\footnotesize \text{z}_\text{i}(\text{Zn}^+) = +2 \\ \text{z}_\text{i}(\text{Cl}_2^-) = -1 \\ \text{z}_\text{i}(\text{Na}_2^+) = +1 \\ \text{z}_\text{i}(\text{SO}_4^-) = -2$
• Place all the values into the formula:
$\footnotesize \text{I} = \frac 1 2 \sum(\text{c}_\text{i} \cdot \text{z}_{\text{i}}^2)$
$\footnotesize \text{I} = \frac 1 2 ([ 1 \cdot (+2)^2 + 2 \cdot (-1)^2] + [2 \cdot (+1)^2 + 1 \cdot (-2)^2])$
$\footnotesize \text{I} = \frac 1 2 ([ 1 \cdot 4 + 2 \cdot 1] + [2 \cdot 1 + 1 \cdot 4])$
$\footnotesize \text{I} = \frac 1 2 ([ 4 + 2] + [2 + 4])$
$\footnotesize \text{I} = \frac 1 2 (6+ 6)$
$\footnotesize \text{I} = \frac 1 2 \cdot 12$
$\footnotesize \bold{\text{I} = 6.0 \text{ mol/L}}$
1. Calculate ionic strength of a buffer

A buffer is a solution that maintains its pH by neutralizing small amounts of acids or bases. It is used in solutions where maintaining the pH during a reaction is crucial. The formula to calculate the ionic strength of a buffer is the same as that of a simple solution:

$\small \text{I} = \frac 1 2 \sum(\text{c}_\text{i} \cdot \text{z}_{\text{i}}^2)$

## Why is ionic strength calculated?

The ionic strength of a solution plays a crucial role in many other concepts in chemistry. The noteworthy studies are given below:

• Debye-Huckel theory

This theory explains the unusual behavior of electrolytes. In this theory, the activity coefficients of ions are calculated based on diluted solutions with predetermined ionic strength.

• The theory of double-layer

The double-layer theory explains that two charged layers surround an object when the object is introduced to a charged fluid. This theory holds for aqueous solutions with ionic strengths closer to water.

• Electrokinetic and electroacoustic phenomena

Electrokinetic and electroacoustic phenomena occur when ultrasound waves are transferred through an ionic solution of a known and controlled ionic strength.

• Stability constant determination

A stability constant is the equilibrium constant for a complex in solution. This measure is how we calculate the concentration of a complex in an ionic solution. Its value depends on specific electrolytes and their specific ionic strengths.

Some other relevant calculators that you can study later are the molecular weight calculator or the atomic mass calculator.

## FAQ

### How do I calculate the ionic strength of a buffer?

A buffer is a type of solution, and its ionic strength is calculated the same way as for a solution.

To calculate the ionic strength of a buffer you may use the following formula:

I = 1/2 × ∑(ci × zi2)

where:

• I - Ionic strength;

• - Sum of values;

• ci - Concentration of ions; and

• zi2 - Charges of ions squared.

### What is the ionic strength of ZnCl₂ if its ionic concentrations are 1.2 and 2.2 mol/L for Zn and Cl, respectively?

The ionic strength of ZnCl2 is 3.5 mol/L or mol/kg (depending on how the ionic concentration was obtained) if the ionic concentration of zinc and chloride is 1.2 and 2.2, respectively.

The formula to calculate ionic strength of a solution is:

I = 1/2 × ∑(ci × zi2)

where:

• I - Ionic strength;

• - Sum of values;

• ci - Concentration of ions; and

• zi2 - Charges of ions squared.

The charges on the ions are:

zi(Zn+) = +2

zi(Cl-) = -1

And the ionic concentrations are:

ci(Zn) = 1.2 mol/L

ci(Cl) = 2.2 mol/L

### How do I calculate ionic strength if molarity is given instead of ion concentration?

If you do not have the concentration of ions, but instead you have the molarity or molality, you need to get the ionic concentration first. To do this, multiply the number of ions of each atom/ion by the molarity or morality.

ci(element) = molarity/molality × species quantity

You then place the ionic concentrations in the ionic strength formula like you normally would:

I = 1/2 × ∑(ci × zi2)

where:

• I - Ionic strength;

• - Sum of values;

• ci - Concentration of ions; and

• zi2 - Charges of ions squared.

### How to calculate ionic strength of 0.2 M (molar) Na₂HPO₄?

To find the ionic strength of 0.2 M Na2HPO4, follow the below instruction:

1. When a solution of Na2HPO4 (di-sodium phosphate or sodium hydrogen phosphate) is formed, it consists of two sodium ions (Na+) and one hydrogen phosphate ion (HPO4-), which gives us the charge numbers as zi(Na+) = +2 and zi(HPO4-) = -1.

2. There are two sodium ions and one phosphate ion. Using the formula of ionic concentrations from molarity/molality:

ci(element) = molarity/molality × species quantity

ci(Na) = 0.2 × 2 = 0.4 mol/L

ci(HPO4) = 0.2 × 1 = 0.2 mol/L

3. Finally, use the formula for ionic strength:

I = 1/2 × ∑(ci × zi2)

to get:

I = 0.9 mol/L

The ionic concentration of Na2HPO4 is 0.9 mol/L.

### How to calculate the ionic strength of a KCl solution?

To find the ionic strength of a KCl solution:

1. Let's consider the ionic concentration of potassium and chlorine in potassium chloride (KCl) to both be one molar.

2. When dissociated, it produces one potassium (K+) and one chloride (Cl-) ion.
So, the ionic concentrations are:

ci(K) = 1 × 1 = 1 mol/L

ci(Cl) = 1 × 1 = 1 mol/L

and charges are:

zi(K+) = +1

zi(Cl-) = -1.

3. Using the ionic strength formula for ion strength:

I = 1/2 × ∑(ci × zi2)

we get:

I = 1 mol/L

So, the ionic concentration of our KCl is 1 mol/L.

Komal Rafay
You may enter values for up to 10 ions:
Ionic concentration of 1st ion
Charge number of 1st ion
Ionic concentration of 2nd ion
Charge number of 2nd ion
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