Chemical Activity

The chemical activity of a species corresponds to the concentration activates this species. Indeed, within a solution the interactions of an electrostatic nature between the various species reduce their potential of reactivity. It is thus necessary to correct the term of concentration by a coefficient lower than the unit, called coefficient of activity, $\backslash \; gamma~$.
L' activity, noted $a~$, intervenes in the definition of the chemical Potentiel.

The chemical potential $\backslash \; mu\_i~$ of a species I is the derivative partial of the free Enthalpie (or free energy of Gibbs) of the system compared to the Quantité of matter $n\_i~$: it is a molar size partial which corresponds here to the molar free enthalpy, $g\_i~$ of the component I .

$\backslash \; mu\_i\; (T,\; p)\; =\; g\_i\; (T,\; p)\; =\; \backslash \; left\; (\backslash \; frac\; \{\backslash \; partial\; G\}\; \{\backslash \; partial\; n\_i\}\; \backslash \; right)\; \_\; \{T,\; p,\; n\_\; \{J\; \backslash \; neq\; I\}\}\; ~$

This chemical potential depends on the Température T , on the Pression p and on the activity a_i according to the formula:

$\backslash \; mu\_i\; (T,\; p)\; =\; \backslash \; mu\_i^0\; (T)\; +\; R\; \backslash \; cdot\; T\; \backslash \; cdot\; \backslash \; ln\; (a\_i)$

where $R~$ is the constant of the Perfect gas S and $\backslash \; mu\_i^0\; (T)\; ~$ is the value of $\backslash \; mu\_i\; (T)\; ~$ under the standard conditions of pressure.

Case of a compound in a mixture gas

The activity is expressed in the form:

$a\_i\; =\; \backslash \; gamma\_i\; \backslash \; cdot\; \backslash \; frac\; \{p\_i\}\; \{p^0\}\; =\; \backslash \; gamma\_i\; \backslash \; cdot\; x\_i\; \backslash \; cdot\; \backslash \; frac\; \{p\_\; \{early\}\}\; \{p^0\}\; =\; \backslash \; frac\; \{f\_i\}\; \{p^0\}\; ~$

where $\backslash \; gamma\_i~$ is the coefficient of activity (, without dimension) of the species I ; $x\_i~$ the molar Fraction of composed in the gas mixture; $p\_i~$ the Pressure partial of the gas I and $p\_\; \{early\}\; ~$ total pressure of the mixture expressed in bar.

The $f\_i\; quantity\; =\; \backslash \; gamma\_i\; \backslash \; cdot\; p\_i~$ with the dimension of a Pressure and is named fugacity .

$p^0~$ is the standard pressure. By convention, it is equal to 1 bar.

One has then:

$\backslash \; mu\_i\; (T,\; p)\; =\; \backslash \; mu\_i^0\; (T)\; +\; R\; \backslash \; cdot\; T\; \backslash \; cdot\; \backslash \; ln\; \backslash \; left\; (\backslash \; gamma\_i\; \backslash \; cdot\; x\_i\; \backslash \; cdot\; \backslash \; frac\; \{p\_\; \{early\}\}\; \{p^0\}\; \backslash \; right)\; =\; \backslash \; mu\_i^0\; (T)\; +\; R\; \backslash \; cdot\; T\; \backslash \; cdot\; \backslash \; ln\; \backslash \; left\; (\backslash \; frac\; \{f\_i\}\; \{p^0\}\; \backslash \; right)\; ~$

Note:

For a perfect gas, the coefficient of activity $\backslash \; gamma~$ is equal to 1.

Case of a compound in a solution Liquid

The activity is expressed in the form:

$a\_i\; =\; \backslash \; gamma\_i\; \backslash \; frac\; \{C\_i\}\; \{C^0\}$

where $\backslash \; gamma\_i~$ is the coefficient of activity of the species I , $C\_i~$ its concentration in the solution, expressed in mol·L^-1. The term $C^0~$ (concentration of reference), is equal, by convention, to 1 mol·L^-1. One has then:

$\backslash \; mu\_i\; (T,\; p)\; =\; \backslash \; mu\_i^0\; (T)\; +\; R\; \backslash \; cdot\; T\; \backslash \; cdot\; \backslash \; ln\; \backslash \; left\; (\backslash \; gamma\_i\; \backslash \; cdot\; \backslash \; frac\; \{C\_i\}\; \{C^0\}\; \backslash \; right)$

One will note that in a liquid solution, the coefficient of activity of a Ion insulated is not measurable because it is in experiments impossible to measure the Electrochemical potential of an ion, independently of the other ions present in the solution. This is why one introduces the concept of average Coefficient of activity.

Usual approximations

One can simplify the relations above by considering that:

• For a solution:
• the Solvant is the very majority species. It can thus be comparable with a pure phase and its activity is then equal to 1.
• When the concentration of a Soluté is weak, its coefficient of activity $\backslash \; gamma~$ is close to 1. That involves that the activity becomes equal to the report/ratio of its concentration on the concentration of reference:
  $a\_i\; \backslash simeq\; \backslash frac\{C\_i\}\{C^0\}$
  .
• For a mixture of Gas: the activity is equal to the report/ratio of the Pression partial of gas on the standard pressure, as long as this pressure keeps low values what involves that $\backslash \; gamma~$ is close to 1;
  $a\_i\; \backslash \; simeq\; \backslash \; frac\; \{p\_i\}\; \{p^0\}$
  
• For a pure Substance the activity is equal to 1.

The chemical activity intervenes in the expression of the Constante of balance.

See Too

Related articles

• Constant of balance
• chemical pH
• Balance

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