# Ionic Activity Coefficient Calculator

How to calculate the ionic activity coefficient? This calculator can help you determine it quickly and easily. Simply enter the necessary values into the calculator to find the result.

### What is Ionic Activity Coefficient?

The ion measure checks ion effective levels in a liquid mix. It sees how ions act with each other, which can change how they act. This measure is key to predicting right how ions will act in different liquid setups. It accounts for how ions bump and stick together, not just how many there are. This helps know ion true strengths in any mix.

### How to Use the Calculator

**Ionic Activity Coefficient (γ)**: Enter the ionic activity coefficient if known, otherwise leave it blank to calculate it.**A**: Enter the value of the constant $A$.**Charge of Ion**: Input the charge of the ion.**Ionic Strength**: Enter the ionic strength of the solution.**B**: Input the value of the constant $B$.**Effective Diameter of Ion**: Enter the effective diameter of the ion.

**Example Values**

**A**: 0.5**Charge of Ion**: 1**Ionic Strength**: 0.01**B**: 0.3**Effective Diameter of Ion**: 3.5

When you fill in these values and click “Calculate,” the calculator will compute the ionic activity coefficient.

## Formula

The formula to calculate the ionic activity coefficient is:

$\gamma =1{0}^{-\frac{A\cdot {z}^{2}\cdot \sqrt{I}}{1+B\cdot d\cdot \sqrt{I}}}$

**Variables**

Variable | Description |
---|---|

$\gamma $ | Ionic Activity Coefficient |

$A$ | Constant A |

$z$ | Charge of Ion |

$I$ | Ionic Strength |

$B$ | Constant B |

$d$ | Effective Diameter of Ion |

## Calculation Examples

### Example 1

**A**: 0.509**Charge of Ion**: 2**Ionic Strength**: 0.02**B**: 0.328**Effective Diameter of Ion**: 4.0

**Calculation**:

1. Plug the values into the formula:

$\gamma =1{0}^{-\frac{0.509\cdot {2}^{2}\cdot \sqrt{0.02}}{1+0.328\cdot 4.0\cdot \sqrt{0.02}}}$

2. Calculate the numerator:

`$0.509\cdot 4\cdot \sqrt{0.02}=0.509\cdot 4\cdot 0.141=0.287$`

3. Calculate the denominator:

`$1+0.328\cdot 4.0\cdot \sqrt{0.02}=1+0.328\cdot 4.0\cdot 0.141=1.185$`

4. Divide the numerator by the denominator:

`$\frac{0.287}{1.185}=0.242$`

5. Calculate the final value:

`$\gamma =1{0}^{-0.242}\approx 0.574$`

### Example 2

**A**: 0.5**Charge of Ion**: 1**Ionic Strength**: 0.1**B**: 0.3**Effective Diameter of Ion**: 3.5

**Calculation**:

1. Plug the values into the formula:

`$\gamma =1{0}^{-\frac{0.5\cdot {1}^{2}\cdot \sqrt{0.1}}{1+0.3\cdot 3.5\cdot \sqrt{0.1}}}$`

$_{2.}$Calculate the numerator:

`$0.5\cdot 1\cdot \sqrt{0.1}=0.5\cdot 0.316=0.158$`

3. Calculate the denominator:

`$1+0.3\cdot 3.5\cdot \sqrt{0.1}=1+0.3\cdot 3.5\cdot 0.316=1.332$`