Name: activity coefficient in ionic solutions
Uploaded: 2024-04-04T10:51:15.000Z
Duration: 1 min 24 s
Channel: JoVE

活動は、効果的な集中力の尺度です。これは単位がなく、種のモル濃度とその活性係数の積として表すことができます。
活性係数は、理想的な挙動からの偏差を測定する無次元の量であり、イオン強度に依存します。理想的な解決策では、活動は集中力に相当します。
イオン強度が非常に低い溶液では、イオンの活性係数はユニティに近く、挙動は基本的に理想的です。
イオン強度が増加すると、活性係数はユニティよりも小さくなり、活性が濃度よりも低い場合の理想性からの逸脱を示します。
ただし、イオン強度が非常に高い溶液では、放射能係数がユニティを超える場合があります。
興味深いことに、中性種の活性係数は、イオン強度が1リットルあたり0.1モル未満でほぼ1です。
放射能係数とイオン強度の関係は、拡張されたデバイ・ヒュッケル方程式として表されます。
ただし、イオン強度が非常に低い非常に希薄な溶液の場合、方程式は Debye–Hückel 制限則に還元されます。

熱力学: 活動係数

活性は、溶液中の種の有効濃度の尺度です。 これは、種のモル濃度とその活量係数の積として表すことができます。 活量係数は無次元量であり、溶液の総イオン強度に依存します。

活動係数は、理想的な動作からの逸脱の尺度です。 溶液のイオン強度が最小の場合、イオン種の活量係数は 1 に近くなり、活量はモル濃度とほぼ等しくなります。 このようなソリューションは、理想的なソリューションに非常に近い動作を示します。 荷電していない分子の活量係数は、0.1 mol/L 未満のすべてのイオン強度でほぼ 1 です。

溶液のイオン強度が増加すると、活量係数は減少し、活量はモル濃度よりも低くなります。 これは、種が理想的な行動から逸脱していることを示しています。 イオン強度が 0.1 mol/L を超える溶液では、活量係数が増加し、1 を超えます。

イオン強度から活量係数を計算するための有用な方程式は、拡張デバイ・ヒュッケル方程式です。この方程式は、係数をイオン強度、イオンの有効直径、および溶質のイオン電荷に関連付けます。 デバイ・ヒュッケル方程式は、イオン サイズ (水和物イオンの有効直径) に依存しています。イオン サイズは電荷やイオンの形状によって大きく変化する可能性があるため、方程式に不確実性が生じます。

この方程式は、極度に希薄な溶液やイオン強度が 0.1 mol/L 未満の極度に希薄な溶液でうまく機能します。この場合、イオン サイズの不確実性は活量係数にほとんど影響しません。 このような場合、解はほぼ理想的に動作し、デバイ・ヒュッケル方程式はデバイ・ヒュッケル制限則として知られるより単純な形式に帰着します。

活動は、効果的な集中力の尺度です。それは単位がなく、種のモル濃度とその...

Education

JoVE Core

Analytical Chemistry

分析化学

Unit 1

ユニット1

Chemical Equilibria

化学平衡

KEY TERMS AND CONCEPTS

主要用語と概念

Thermodynamics: Activity Coefficient

activity coefficient in ionic solutions

Activity coefficient in ionic solutions describes how much a species behaves like its measured concentration. Activity is the effective concentration of a solute in solution. It equals the molar concentration multiplied by the activity coefficient, which is a unitless number.

The activity coefficient depends on the total ionic strength of the solution. It shows how far a solution is from ideal behavior. When ionic strength is very low, the activity coefficient of an ionic species is close to 1, so activity is nearly the same as molar concentration. In that case, the solution behaves much like an ideal solution.

An uncharged molecule has an activity coefficient of about 1 at ionic strengths below 0.1 mol/L. As ionic strength rises, the activity coefficient of a species can decrease, and activity becomes less than the molar concentration. This shift shows greater deviation from ideal behavior. For ionic strengths above 0.1 mol/L, the activity coefficient increases and can exceed 1.

The extended Debye-Hückel equation is used to estimate activity coefficients from ionic strength. It relates the coefficient to ionic strength, the effective diameter of the ion, and the ionic charges of the solute. The equation depends on ion size, which is the effective diameter of a hydrated ion. Ion size can vary with charge and ion geometry, so it adds uncertainty to the calculation.

The Debye-Hückel equation works best in extremely dilute solutions and in solutions with ionic strength below 0.1 mol/L. In these cases, uncertainty in ion size has little effect on the activity coefficient. The solution behaves mostly ideally, and the equation reduces to the simpler Debye-Hückel Limiting Law.

Activity Coefficient in Ionic Solutions

ionic strength: overview

Ionic Strength in Salt and Acid Solutions

Ionic strength describes the total electrolyte concentration in a solution. It is a quantitative measure of how many ions are present and how strongly they contribute to the solution. The concept was introduced in 1921 by Gilbert N. Lewis and Merle Randall while they were describing the activity coefficient of strong electrolytes. To calculate ionic strength, written as I or μ, both cations and anions are included. The concentration of each ion matters, but the charge number z matters even...

ionic strength: effects on chemical equilibria

ionic-strength-effects-on-chemical-equilibria

Salt Effect on Salt Solubility

Salt effect can change the solubility of a sparingly soluble salt in water. When an inert ionic compound is added, the dissolved salt may become more soluble. A common example is potassium nitrate added to a saturated calcium sulfate solution, which increases the amount of calcium sulfate that dissolves. Le Châtelier’s principle does not explain this shift well. Instead, the change is described by the effective concentration of ions in solution. Each ion is surrounded by an ionic atmosphere,...

thermodynamics: chemical potential and activity

thermodynamics-chemical-potential-and-activity

Chemical Potential in Solution Activity

Chemical potential and activity describe how a species behaves in a solution. Activity is the effective concentration of a species. It accounts for the electrolytes near that species and depends on the ionic strength of the solution. Activity is calculated as molar concentration multiplied by the activity coefficient. This makes it a more precise way to describe a species in solution than concentration alone. The thermodynamic equilibrium constant is also defined more accurately using activity...

thermodynamics: activity coefficient

Activity coefficient in ionic solutions describes how much a species behaves like its measured concentration. Activity is the effective concentration of a solute in solution. It equals the molar concentration multiplied by the activity coefficient, which is a unitless number. The activity coefficient depends on the total ionic strength of the solution. It shows how far a solution is from ideal behavior. When ionic strength is very low, the activity coefficient of an ionic species is close to...

chemical equilibria: redefining equilibrium constant

chemical-equilibria-redefining-equilibrium-constant

Salt Effect in Equilibrium Constant Calculations

Salt effect changes how a sparingly soluble salt dissolves when an inert salt is added. The size of this effect depends on the ionic strength of the solution. Ionic strength reflects how strongly the ions in the solution interact. In solution, the activity of a species is the product of its concentration and its activity coefficient. A redefined equilibrium constant must account for these activity effects when the ionic strength is moderately high. This form is also called the thermodynamic...

factors affecting activity coefficient

How Ionic Strength Changes Activity Coefficient

The activity coefficient of an ion in water depends on ionic strength, ion charge, and ion size. The extended Debye-Hückel equation describes these effects for aqueous solutions at 25°C. These three factors are partly linked, so changes in one can influence the others. When a solution has almost zero ionic strength, the activity coefficient is close to one. That means the solution behaves almost ideally. As ionic strength rises from 0 to 0.1 mol/L, the activity coefficient usually drops.

chemical equilibria: systematic approach to equilibrium calculations

chemical-equilibria-systematic-approach-to-equilibrium-calculations

Equilibrium Calculations with Mass and Charge

Chemical equilibrium calculations become easier when they are organized around mass balance and charge balance. This approach is useful for systems with multiple equilibria, where several reactions must be considered together. It is especially helpful when finding the solubility of a sparingly soluble salt in water with a common ion present. The first step is to identify every chemical reaction in the system. Next, write the equilibrium constant expression for each reaction. These expressions...

acid&#8211;base equilibria: activity-based definition of ph

acidbase-equilibria-activity-based-definition-of-ph

How Ionic Strength Changes pH

pH depends on hydrogen ion activity, not just hydrogen ion concentration. In an ideal solution, pH is the negative logarithm of the hydrogen ion concentration. In a non-ideal solution, a more accurate pH uses hydrogen ion activity, which combines concentration with an activity coefficient. This difference matters most in very low ionic strength solutions, such as pure water. At first, the hydrogen ion activity coefficient is close to one. When an electrolyte that does not donate or accept a...

ladder diagrams: acid&#8211;base equilibria

Using Ladder Diagrams to Predict pH

Ladder diagrams help show how acid-base equilibria change with pH. They are graphical tools that make the chemistry of a system easier to read during analysis. In a ladder diagram, the vertical axis shows pH. Horizontal bars, or steps, place the pKa values in the system.

ladder diagrams: redox equilibria

Redox Potential Shifts in Ladder Diagrams

Ladder diagrams show redox equilibrium using electrochemical potential, E, as the vertical scale. They help students see how changes in concentration affect which species is most stable. The areas of predominance are set with the Nernst equation. A useful example is the Fe3+/Fe2+ half-reaction, which has a standard-state potential of +0.771 V. At potentials more positive than +0.771 V, Fe3+ predominates. At potentials more negative than +0.771 V, Fe2+ predominates. Ladder diagrams also show...

ladder diagrams: complexation equilibria

Reading Metal-Ligand Ladder Diagrams

Ladder diagrams help show equilibria in metal-ligand complexes. In these diagrams, the vertical scale shows pL, or the concentration of free ligand that has not reacted. The horizontal lines mark the log of formation constants and show which species is dominant in each region. For the Cd and ammonia system, the formation constant K1 for Cd(NH3)2+ is 3.55 × 10^2. Its log value is 2.55, so pNH3 = 2.55 is the dividing line between Cd2+ and Cd(NH3)2+ dominance. Above 2.55, Cd2+ is the predominant...

solubility equilibria: overview

How Solubility Reaches Equilibrium

Solubility equilibrium describes what happens when a sparingly soluble salt dissolves in water and then reaches a balance with the solid left over. In a saturated solution, dissolved ions and the undissolved solid are in dynamic equilibrium. The process is reversible, so this topic is also called precipitation equilibrium. This balance matters in real life. Sugar-rich foods can produce organic acids that dissolve hydroxyapatite, the mineral in tooth enamel, which can lead to tooth decay. A...

solubility equilibria: ionic product of water

solubility-equilibria-ionic-product-of-water

Water Ionization and Kw in Equilibrium

Water ionization and the ionic product of water describe how pure water reaches equilibrium. Water is a weak electrolyte, so only a small amount breaks into hydrogen ions and hydroxide ions. At a fixed temperature, the amount of undissociated water stays almost constant. Because of this, the ionic product of water is the product of the hydrogen ion concentration and the hydroxide ion concentration. It is written as K w . The square root of K w gives the concentration of each ion in pure water.

complexation equilibria: overview

Stepwise Metal-Ligand Complexation

Stepwise metal-ligand complexation forms coordination compounds when metal ions and ligands share electrons through dative, or coordinate covalent, bonds. In these reactions, the metal ion binds to one or more ligands until its coordination number is reached. This number tells how many bonds form between the metal ion and the ligands. In aqueous solution, many metal ions are already surrounded by water molecules. These species are called aqua complexes. Complexation reactions are described by...

complexation equilibria: the chelate effect

complexation-equilibria-the-chelate-effect

Chelating Ligands and Metal Complex Stability

Metal complexes form when metal atoms or cations interact with ligands in a complexation reaction. These donor-acceptor adducts are central to understanding how metal ions bind in chemistry. Ligands can bind in different ways. A monodentate ligand uses one donor site. A bidentate ligand uses two donor sites, and a polydentate ligand uses more than two. Ethylene diamine is a bidentate ligand that binds through two nitrogen donor atoms and forms a five-membered ring. Polydentate ligands can...

complexation equilibria: factors influencing stability of complexes

complexation-equilibria-factors-influencing-stability-of-complexes

Complex Ions: Metal and Ligand Stability

Complex ions form when a metal cation accepts electron pairs from ligands, which are the electron pair donors. The stability of these metal complexes depends mainly on the metal ion and on the ligands attached to it. The metal ion’s size and charge play a major role in stability. As the size of the metal ion increases, complex stability usually decreases when the valency of the metal ion and the ligands stays the same. As the charge on the metal ion increases, complex stability increases. <br...

redox equilibria: overview

Redox Electron Transfer and Half-Reactions

Redox reactions involve the transfer of electrons from one species to another. In this type of reaction, electrons are not shared between atoms. They move from the species that loses them to the species that gains them. The species that loses electrons is the reducing agent, also called the reductant. It is oxidized during the reaction. The species that gains electrons is the oxidizing agent, or oxidant, and it is reduced. Redox reactions are often written as two half-reactions. One...

titrimetric methods: types and commonly used strategies

titrimetric-methods-types-and-commonly-used-strategies

Direct, Back, and Displacement Titrations

Titrimetric methods use a standard solution to measure the amount of an analyte in chemistry. The main categories are volumetric, gravimetric, and coulometric methods. Each one reaches the endpoint in a different way. In volumetric titrations, the key measurement is the volume of a titrant with a known concentration. The titrant is added until it reacts completely with the analyte. In gravimetric titrations, the standard solution forms an insoluble precipitate with the analyte. That solid is...

classification of titrimetric analysis based on reaction types

classification-of-titrimetric-analysis-based-on-reaction-types

Four Reaction Types in Titrimetric Analysis

Titrimetric analysis measures solution volume and is also called volumetric analysis. A standard solution with a known concentration is placed in the burette and is called the titrant. The solution with an unknown concentration in the flask is the analyte, or titrand. Titrimetric analysis is grouped into four types based on the reaction between the titrant and the analyte. Acid-base titrations involve a neutralization reaction between an acid and a base. This reaction forms water molecules.

key terms and concepts

Learn how activity coefficient changes with ionic strength, why activity differs from concentration, and when the Debye-Hückel Limiting Law applies.

Activity Coefficient in Ionic Solutions | JoVE K12

JoVE Core 分析化学 は、複雑な化学原理をアニメーションで視覚化することで、SI 単位から NMR 分光法を含むトピックをよりわかりやすくします。実験を撮影した実写動画では、これらの概念が世界中の研究所でどのように応用されているかを取り上げています。

analytical chemistry

Activity Coefficient in Ionic Solutions

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