Activity - Katsuryo

The chemical potential μ _i ^{i d} of component i in an ideal solution or perfect gas mixture is expressed as follows, where x _i is the concentration of the component i:

μ _i ^{i d} = μ ° _i + RT ln x _i

Here, R and T are the gas constant and absolute temperature, respectively, and μ ° _i is the standard chemical potential for the concentration scale used. However, in real solutions, due to intermolecular interactions, the properties deviate from those of an ideal solution, and the above equation does not hold. However, by including the effect of this deviation entirely in the concentration terms, it is possible to formally express the chemical potential μ _i for component i in real solutions as

μ _i = μ ° _i + RT ln a _i

This a _i is called the activity or activity of component i . Furthermore, the activity a _i divided by the concentration x _i is

f _i ≡ a _i / x _i
is called the activity coefficient. From this definition of the activity coefficient and the two equations above, the difference between the chemical potential of a real solution and that of an ideal solution, i.e., the excess chemical potential μ _i ^{e x} , is expressed by the following equation.

μ _i ^{e x} ≡ μ _i − μ _i ^{i d} = RT ln f _i

As can be seen from the formula, any deviation from an ideal solution is reflected in the activity coefficient, and the properties of real solutions can be clarified by analyzing the behavior of the activity coefficient. Generally, three methods of expressing concentration are used: mole fraction, mass molarity, and molar concentration. Therefore, activities and activity coefficients are defined for each concentration scale. In a sufficiently dilute solution, the activity coefficients corresponding to each concentration scale are almost the same, but as the concentration increases, there are considerable differences between them. In electrolyte solutions, solutes are ions generated by the ionization of neutral molecules. For each ion, the activity and activity coefficient can be formally defined as described above, but these quantities cannot be measured and have no thermodynamic meaning. However, in thermodynamic equations, these quantities always appear in an electrically neutral form, combining the amounts of cations and anions with each other, rather than individually. Therefore, the geometric mean is taken, and the average activity and average activity coefficient of each ion are defined and used. For example, in a solution of electrolyte A _x B _y , the average activity a _± and the average activity coefficient f _± are given by:

a _± ^{x + y} = a ₊ ^x a _- ^y , f _± ^{x + y} = f ₊ ^x f _- ^y

Here, a ₊ , a _- and f ₊ , f _- are the activities and activity coefficients of the cation and anion, respectively. The activities and activity coefficients are determined by measuring the vapor pressure, boiling point, freezing point, solubility, osmotic pressure, etc. For electrolyte solutions, they can also be determined by measuring the equilibrium voltage using a reversible battery.

Source: Morikita Publishing "Chemical Dictionary (2nd Edition)" Information about the Chemical Dictionary 2nd Edition

活動度ともいう．理想溶液あるいは完全混合気体の成分iの化学ポテンシャルμ_i^id は，その濃度を x_i とすれば，

μ_i^id ＝ μ°_i ＋ RT ln x_i

となる．ここで，RおよびTはそれぞれ気体定数および絶対温度であり，μ°_i は用いられた濃度尺度に対する標準化学ポテンシャルである．一方，現実の溶液においては，分子間相互作用のため，その性質は理想溶液からずれ，上式は成り立たない．しかし，このずれの影響をすべて濃度の項に含ませて，実在の溶液の成分iでの化学ポテンシャル μ_i に対しても形式的に

μ_i ＝ μ°_i ＋ RT ln a_i

のように書き，この a_i を成分iの活量あるいは活動度という．さらに，活量 a_i を濃度 x_i で割った量

f_i ≡ a_i/x_i
を活量係数，あるいは活動度係数という．活量係数に対するこの定義と上記の二つの式より，実在溶液の化学ポテンシャルと理想溶液のそれとの差，すなわち過剰化学ポテンシャル μ_i^ex は，次式で表される．

μ_i^ex ≡ μ_i － μ_i^id ＝ RT ln f_i

式よりわかるように，理想溶液からのずれはすべて活量係数にしわ寄せされることになり，実在溶液の性質は，活量係数の挙動の解析から明らかにできることになる．一般に，濃度の表し方としては，モル分率，質量モル濃度，モル濃度の3種類が用いられるので，各濃度尺度に対応して，それぞれの活量および活量係数が定義される．十分希薄な溶液では，それぞれの濃度尺度に対応する活量係数は，いずれもほとんど同じ値をとるが，濃度が高くなるにつれて相互にかなりの差が現れてくる．電解質溶液においては，溶質は中性分子の電離によって生成するイオンである．個々のイオンに対しては形式的には上述と同様に，その活量および活量係数を定義することができるが，これらの量は実測できず，熱力学的意味をもたない量である．しかし，これらの量は，熱力学的関係式のなかには，個々ではなく，つねにカチオンおよびアニオンの量が互いに組み合わさって電気的に中性の形で現れる．したがって，その幾何平均をとり，それぞれイオンの平均活量および平均活量係数が定義され，用いられる．たとえば，電解質 A_xB_y の溶液では，平均活量 a_± および平均活量係数 f_± は，次のように与えられる．

a_±^x＋y ＝ a_＋^xa_－^y，f_±^x＋y ＝ f_＋^xf_－^y

ここで，a_＋，a_－ および f_＋，f_－ は，それぞれカチオンおよびアニオンの活量および活量係数である．活量あるいは活量係数は蒸気圧，沸点，凝固点，溶解度，浸透圧などの測定により決定される．また，電解質溶液に対しては可逆電池を用いて，その平衡電圧の測定によっても決定できる．

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