thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...

, a component is one of a collection of chemically independent constituents of a

system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment (systems), environment, is described by its boundaries, ...

. The number of components represents the minimum number of independent

chemical species A chemical species is a chemical substance or ensemble composed of chemically identical molecular entity, molecular entities that can explore the same set of molecular energy levels on a characteristic or delineated time scale. These energy levels ...

necessary to define the

composition Composition or Compositions may refer to: Arts and literature *Composition (dance), practice and teaching of choreography *Composition (language), in literature and rhetoric, producing a work in spoken tradition and written discourse, to include v ...

of all phases of the system. Calculating the number of components in a system is necessary when applying

Gibbs' phase rule In thermodynamics, the phase rule is a general principle governing "pVT" systems, whose thermodynamic states are completely described by the variables pressure (), volume () and temperature (), in thermodynamic equilibrium. If is the number of ...

in determination of the number of

degrees of freedom Degrees of freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a thermodynamic system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or ...

of a system. The number of components is equal to the number of distinct chemical species (constituents), minus the number of chemical reactions between them, minus the number of any constraints (like charge neutrality or balance of molar quantities).

Calculation

Suppose that a chemical system has elements and chemical species (elements or compounds). The latter are combinations of the former, and each species can be represented as a sum of elements: :

A_i = \sum_j a_E_j,

where are the integers denoting number of atoms of element in molecule . Each species is determined by a vector (a row of this matrix), but the rows are not necessarily

linearly independent In the theory of vector spaces, a set of vectors is said to be if there is a nontrivial linear combination of the vectors that equals the zero vector. If no such linear combination exists, then the vectors are said to be . These concepts are ...

. If the

rank Rank is the relative position, value, worth, complexity, power, importance, authority, level, etc. of a person or object within a ranking, such as: Level or position in a hierarchical organization * Academic rank * Diplomatic rank * Hierarchy * H ...

of the matrix is , then there are linearly independent vectors, and the remaining vectors can be obtained by adding up multiples of those vectors. The chemical species represented by those vectors are ''components'' of the system. If, for example, the species are C (in the form of

graphite Graphite () is a crystalline form of the element carbon. It consists of stacked layers of graphene. Graphite occurs naturally and is the most stable form of carbon under standard conditions. Synthetic and natural graphite are consumed on large ...

), CO₂ and CO, then :

\begin 1 & 0 \\ 1 & 2\\ 1 & 1\end\beginC \\ \\ O\end = \beginC \\ CO_2\\ CO\end.

Since CO can be expressed as CO = (1/2)C + (1/2)CO₂, it is not independent and C and CO can be chosen as the components of the system. There are two ways that the vectors can be dependent. One is that some pairs of elements always appear in the same ratio in each species. An example is a series of

polymer A polymer (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...

s that are composed of different numbers of identical units. The number of such constraints is given by . In addition, some combinations of elements may be forbidden by chemical kinetics. If the number of such constraints is , then :

C = M - Z + R'.

Equivalently, if is the number of independent reactions that can take place, then :

C = N - Z - R.

The constants are related by .

Examples

CaCO₃ - CaO - CO₂ system

This is an example of a system with several phases, which at ordinary temperatures are two solids and a gas. There are three chemical species (CaCO₃, CaO and CO₂) and one reaction: : CaCO₃ CaO + CO₂. The number of components is then 3 - 1 = 2.

Water - Hydrogen - Oxygen system

The reactions included in the calculation are only those that actually occur under the given conditions, and not those that might occur under different conditions such as higher temperature or the presence of a catalyst. For example, the dissociation of water into its elements does not occur at ordinary temperature, so a system of water, hydrogen and oxygen at 25 °C has 3 independent components.

References

{{reflist Chemical thermodynamics

Calculation

Examples

CaCO3 - CaO - CO2 system

Water - Hydrogen - Oxygen system

References

CaCO₃ - CaO - CO₂ system