Ion exchange equilibrium

This refers to the state in which the ion exchange resin is in equilibrium with the external solution. If we consider that Donnan's membrane equilibrium exists between the resin phase and the external solution phase, the exchange equilibrium equation between ions of the same sign (for example, A and B) can be obtained as follows:

Here, γ is the activity coefficient, the bar is the resin phase, z is the ionic valence, V is the partial molar volume, and π is the swelling pressure. K _A ^B is expressed by the following formula and is called the selectivity coefficient.

Here, c is the concentration. Also, S _A ^B in the following formula is called the separation factor.

The separation coefficient of differently charged ions changes significantly depending on the concentration. In dilute solutions, the selectivity of multivalent ions is high ( S _A ^B is large). If we consider that the amount of ion A to be separated is small compared to the amount of ion B to be exchanged, as in liquid chromatography, the distribution coefficient is expressed by the following formula:

Since / c _B is considered to be constant, the selectivity can be expressed by K _d (A). In recent liquid chromatography, the mass distribution ratio (capacity factor) shown in the following formula is used instead of the distribution coefficient.

Here, Q represents the amount of ions. The selectivity in cation exchange is

Ba ²⁺ > Ca ²⁺ > Mg ²⁺ > K ⁺ > Na ⁺ ,
The selectivity in anion exchange is

NO ₃ ^- > Cl ^- > HCO ₃ ^- > F ^-
The selectivity for H ⁺ is extremely low with strongly acidic resins and is highest with weakly acidic resins. The selectivity ^for OH- is also extremely low with strongly basic resins and highest with weakly basic resins.

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

イオン交換樹脂が外部溶液と平衡にある状態をいう．樹脂相と外部溶液相との間にドナンの膜平衡が成り立つと考えると，同符号イオン間(たとえばA，B間)の交換平衡式が次式で得られる．

ここに，γは活量係数，のバーは樹脂相，zはイオン価，Vは部分モル容積，πは膨潤圧である．K_A^B は次式で示され選択係数という．

ここに，cは濃度である．また次式で示される S_A^B は分離係数という．

異価イオンの分離係数は濃度によっていちじるしく変化し，希薄溶液のとき，多価イオンの選択性が大(S_A^B が大)となる．液体クロマトグラフィーのように分離すべきイオンAが交換するイオンBに対して微量と考えると，次式で示す分配係数

は，/c_Bが一定とみられるので，K_d(A)によって選択性を表しうる．最近の液体クロマトグラフィーでは，分配係数のかわりに次式で示す質量分配比(キャパシティーファクター)

が用いられる．ここに，Qはイオンの量を示す．陽イオン交換における選択性は

Ba^2＋ ＞ Ca^2＋ ＞ Mg^2＋ ＞ K^＋ ＞ Na^＋，
陰イオン交換における選択性は

NO₃^－ ＞ Cl^－ ＞ HCO₃^－ ＞ F^－
である．H^＋ の選択性は強酸性樹脂ではきわめて小で，逆に弱酸性樹脂はもっとも大である．OH^－ の選択性も強塩基性樹脂ではきわめて小で，弱塩基性樹脂ではもっとも大である．

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