Number of:
Components
Phases
Factor
Result:
Degrees of freedom

# Gibbs' Phase Rule Calculator

By Filip Derma

Gibbs' phase rule calculator assists you in calculating the number of degrees of freedom for the phase rule. In the article below, you can find the explanation of what is Gibbs' phase rule, Gibb's equation and some information about how to use the calculator correctly. Scroll down to find out more!

## What is Gibbs' phase rule?

Gibbs' phase rule bases on the laws of thermodynamics and provides the theoretical principle for characterizing the chemical state of a system. It predicts the equilibrium relations of phases and is present as a function of physical conditions such as pressure and temperature. Moreover, phase rule allows creating phase diagrams to represent and interpret phase equilibria in heterogeneous systems.

The phase rule equation proposed by Josiah Willard Gibbs in 1875 (American theoretical physicist, the professor at Yale University) is expressed by the formula:

`F = C - P + factor`

where:

• "F" is the number of degrees of freedom,
• "C" is the number of components,
• "P" is the number of phases in the system.
• "Factor" (by default = 2) is an integer value in the equation that depends on the temperature and pressure of the system. If one of these variables is constant, you have to change its value to "1". If both of them are constant change the value to "0".

This equation allows computing the number of degrees of freedom (F) from the number of components (C) and the number of phases in the system (P).

## Phase rule details

Number of phases (P)

A phase is a form of matter which is homogeneous in the chemical composition and the physical properties throughout its volume. It is also a physically separable material in the system. We can distinguish:

• solid,
• liquid,
• gas,
• plasma.

Number of components (C)

C means the minimum number of chemical components required to constitute all the phases in the system. The compound cannot be a product of the chemical reaction between other components of the system.

Number of degrees of freedom (F)

F refers to the number of variables (e.g., temperature, pressure, the concentration of the component) which can be changed independently (with certain limits) without altering the state of the system (e.g., the numbers of phases and compounds).

The number of degrees of freedom increases with the increasing number of components and with the decreasing number of phases in balance.

## Gibb's equation

Let's see the application of the Gibbs' equation on the example below:

`NH₄HCO₃(s) <-> NH₃(g) + CO₂(g) + H₂0(g)`

In this system, there are 4 compounds, 1 equation and 2 conditions (third condition results from the previous two):

I. `[NH₃] = [CO₂]` II. `[CO₂] = [H₂0]` III. `[NH₃] = [H₂0]`

That gives:

`C = 4 - 1 - 2 = 1`

`P = 2`

and the number of degrees of freedom equals to:

`F = 2 + 1 - 2 = 1`

## How to use Gibbs' phase rule calculator?

1. Choose the chemical system for calculations. Let's assume that it consists of 1 component which is present in 2 phases.
2. In that system, both pressure and temperature can change.
3. Type in the relevant numbers into the calculator: the number of compounds and number of phases, the factor is equal 2 for that example.
4. Check the result in the last calculator field ☺

`F = 1 - 2 + 2 - 0 = 1`

Now you can do your calculations with Gibbs' phase rule calculator.

Filip Derma

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