Name: predicting precipitation with ksp
Uploaded: 2020-09-24T15:06:51.000Z
Duration: 3 min 7 s
Channel: JoVE

K12 Standards

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

9-12

Chemistry

Interactions Of Matter

Chemical reactions

Solubility Equilibria

塩化ナトリウムは、大量の塩化物が水に溶けるため可溶性と見なされますが、塩化鉛を水に加えると、少量しか溶解せず、残りは不溶性のままです。
溶解していない固体は、溶液中の鉛イオンと塩化物イオンと共存します。固体の塩化鉛の一部は溶解し続けますが、溶液中のイオンの一部は再結合して沈殿物を形成します。
溶解速度が沈殿速度と等しい場合、溶解度平衡が確立されます。
平衡定数は、塩化鉛が1つの鉛イオンと2つの塩化物イオンに解離する溶解反応に応じたイオンの平衡濃度から計算できます。
したがって、平衡定数は、鉛イオンのモル濃度に塩化物イオンのモル濃度の2乗を掛けたものによって与えられます。固体塩化鉛の濃度は一定のままであるため、計算から除外されます。
この平衡定数は溶解度積と呼ばれ、Kspで表されます。25°Cでは、塩化鉛のKspは10-5×1.17です。
Kspの値は、化合物が溶解して飽和水溶液を形成できる程度を表します。ある温度では、化合物のKspは一定です。
モル溶解度として知られるモル/リットルの化合物の溶解度は、飽和溶液中の溶解固体の濃度を表すためによく使用されます。化合物の溶解度は、溶液のpHや他のイオンが存在するかどうかなどの要因によって異なります。
化合物のモル溶解度xは、ICEテーブルを使用してそのKspから計算できます。
溶液中の鉛イオンと塩化物イオンの初期濃度はゼロです。
平衡状態では、鉛イオンのモル濃度はxで表されますが、塩化物イオンのモル濃度は2xです。
平衡表現に代入すると、塩化鉛の溶解度積はx×2×2に等しく、4×3に等しくなります。
塩化鉛のKspは10-5×1.17であるため、xは10-2モル×1.43と解かれます。
塩化鉛やフッ化カルシウムなど、同じ解離化学量論を持つ化合物では、各化合物の1モルが3モルの溶存イオンを生成する場合、それぞれのKsp値を直接使用して、それらの相対的な溶解度を比較できます。

<ol>
	<li>クリフォード、AF「溶解度生成物定数の予測1」 Journal of the American Chemical Society 79、no. 20 (1957):5404-5407。</li>
	<li>ヒル、アーサーE.「溶解性製品の不安定性」 Journal of the American Chemical Society 32、no. 10(1910):1186-1193。</li>
	<li>レイノルズ、ジョンP.「Ksp実験:水酸化バリウムの溶解度生成物」 Journal of Chemical Education 52、no. 8(1975):521。</li>
</ol>

溶解平衡

溶解平衡とは、溶質の溶解と析出が同じ割合で起こる状態のことです。この平衡は、虫歯から水の浄化に至るまで、多くの自然現象や技術的プロセスの基礎となっています。そのため、化合物の溶解度に影響を与える要因を理解することは、これらのプロセスを効果的に管理するために不可欠です。このセクションでは、これまでに紹介した平衡の概念と考え方を、溶解と沈殿を伴うシステムに適用します。
 溶解度積
 物質の溶解度は、本質的にゼロ（溶けない、またはほとんど溶けない）から無限大（完全に混ざり合う）まで変化します。有限の溶解度を持つ溶質は、その溶解度を超える量を溶媒に加えると飽和溶液となり、飽和溶液と過剰な未溶解の溶質の不均一な混合物を生じます。例えば、塩化銀の飽和溶液とは、以下のような平衡が成立している状態のことです。
 <img alt="Eq1" src="/files/ftp_upload/11417/11417_Equation_1.png" style="text-align: center; height: 50px;" />
 この溶液では、過剰な固体のAgClが溶解・解離して水和したAg+とCl–イオンを生成し、これらの水和イオンが結合して固体のAgClを形成して沈殿するのと同じ速度で溶解・解離します。塩化銀は疎水性の塩であるため、水溶液中の溶存イオンの平衡濃度は比較的低いです。
 このような溶解平衡の平衡定数は、溶解度積とKspと呼ばれ、この場合は
 <img alt="Eq2" src="/files/ftp_upload/11417/11417_Equation_2.png" style="text-align: center; height: 50px;" />
 平衡定数の式には気体と溶質のみが含まれるため、Kspには溶解していないAgClの項が含まれていないことに注意する必要があります。
 Kspと溶解度
 わずかに溶解するイオン性化合物のKspは、例えば、溶解過程が解離と溶媒和だけであれば、測定された溶解度と単純に関連している可能性があります。例えば、
 <img alt="Eq3" src="/files/ftp_upload/11417/11417_Equation_3.png" style="text-align: center; height: 50px;" />
 このような場合は、既知の溶解度からKspの値を導き出すことができ、逆もまたしかりです。この種の計算は、飽和溶液1リットルあたりの溶解した溶質の物質量として測定される、化合物’のモル溶解度を用いて行うのが最も便利です。
 Predicting Precipitation
 固体の炭酸カルシウムとその溶解したイオンの間の平衡を表す式は、次の通りです。
 <img alt="Eq4" src="/files/ftp_upload/11417/11417_Equation_4.png" style="text-align: center; height: 50px;" />
 この平衡は、水に炭酸カルシウムを飽和させてできた溶液だけでなく、Ca2+とCO32–イオンを含むあらゆる水溶液で成立します。例えば、可溶性化合物である炭酸ナトリウムと硝酸カルシウムの水溶液を混合することを考えてみましょう。混合溶液中のカルシウムイオンと炭酸イオンの濃度から得られる反応商Qが溶解度積Kspを超えなければ、沈殿は生じません。もし、イオン濃度が溶解度積よりも大きい反応商をもたらすならば、沈殿が発生し、平衡が成立するまでそれらの濃度を下げる（Q=Ksp）。沈殿を予測するためにQとKspを比較することは、平衡に関する箇所で最初に紹介した、反応の方向性を予測するための一般的なアプローチの一例です。溶解平衡の具体的なケースについては、以下の通りです。
 Q < Ksp: 反応は順方向に進む（溶液は飽和しない、沈殿は観察されない）
 Q > Ksp: 反応は逆方向に進む（溶液が過飽和状態になり、沈殿が発生する）
 上記の文章は以下から引用しました。<a href="https://openstax.org/books/chemistry-2e/pages/15-1-precipitation-and-dissolution">Openstax, Chemistry 2e, Section 15.1: Precipitation and Dissolution.</a>

溶解度平衡は、溶質種の溶解と沈殿が等しい速度で発生するときに確立されます。これらの均衡は多くの根底にあります...

Education

JoVE Core

化学

Acid-base and Solubility Equilibria

酸塩基および溶解度平衡

KEY TERMS AND CONCEPTS

主要用語と概念

predicting precipitation with ksp

Solubility equilibria explain how a dissolved ionic compound and its solid form can exist in balance. In a saturated solution, the solute dissolves and the ions precipitate at equal rates. These ideas matter in real settings such as tooth decay and water purification, where compound solubility affects the outcome.

A substance with finite solubility can form a saturated solution when more solute is added than the solvent can dissolve. The result is a heterogeneous mixture of the saturated solution and excess solid. Silver chloride is a classic example. In that equilibrium, solid AgCl dissolves into Ag+ and Cl− ions, and those ions also combine to form solid AgCl. For sparingly soluble salts like this, the dissolved ion concentration stays low.

The equilibrium constant for a solubility equilibrium is called the solubility product constant, or Ksp. Only gases and dissolved solutes appear in equilibrium expressions, so the undissolved solid is not included. For slightly soluble ionic compounds, Ksp can be related to measured solubility when dissolution involves only dissociation and solvation. In those cases, molar solubility is useful. It is the number of moles of dissolved solute in one liter of saturated solution.

Ksp also helps predict whether a precipitate will form. The equilibrium between solid calcium carbonate and its dissolved ions can exist in any aqueous solution that contains Ca2+ and CO32− ions. That is true even if the solution did not start with calcium carbonate as a solid. For example, when aqueous sodium carbonate and calcium nitrate are mixed, the ion concentrations determine the outcome.

The reaction quotient, Q, is compared with Ksp to test for precipitation. If Q does not exceed Ksp, no precipitation occurs. If Q is greater than Ksp, precipitation occurs and lowers the ion concentrations until equilibrium is reached again, when Q equals Ksp. In this way, Q and Ksp show whether a solution is unsaturated, saturated, or supersaturated.

Predicting Precipitation with Ksp

common ion effect

Common Ion Effect on Solubility

The common ion effect reduces the solubility of an ionic compound in a solution that already contains one of its ions. In aqueous solutions, this means less of the solid dissolves than it would in pure water. The effect follows the law of mass action and can be explained with Le Châtelier’s principle. Silver iodide shows this equilibrium clearly. When silver(I) ions or iodide ions are added, the dissolution equilibrium shifts left. More AgI precipitates, and the concentrations of dissolved Ag+...

buffers

Buffer Solutions and pH Stability

Buffer solutions are mixtures that help keep pH steady. A buffer contains an appreciable amount of a weak conjugate acid-base pair. It resists a change in pH when small amounts of a strong acid or a strong base are added. One common buffer uses a weak acid and its salt. Acetic acid and sodium acetate form this type of system, written as CH3COOH(aq) + CH3COONa(aq). Another buffer uses a weak base and its salt. A solution of ammonia and ammonium chloride, NH3(aq) + NH4Cl(aq), is an example. The...

calculating ph changes in a buffer solution

calculating-ph-changes-in-a-buffer-solution

Buffer pH After Acid or Base Addition

A buffer solution can resist sudden pH changes when a strong acid or strong base is added. It does not stop the pH from changing completely. The shift is usually small, as long as the addition stays within the buffer’s capacity. To find the new pH, first determine how the added acid or base changes the amounts of the buffer components. A buffer contains a weak acid and its conjugate base, or the reverse pair. These amounts are found with stoichiometric calculations, which track how much of...

buffer effectiveness

Buffer Capacity and pH Stability

Buffer solutions help keep pH fairly constant, but they do not work forever. Their resistance to pH change depends on having enough of a weak acid and its conjugate base, or a weak base and its conjugate acid, in the mixture. When too much strong acid or strong base is added, one part of the buffer pair is used up and the buffer action becomes weaker. Buffer capacity describes how much acid or base can be added to a fixed volume of buffer before the pH changes noticeably, usually by about one...

titration calculations: strong acid - strong base

titration-calculations-strong-acid-strong-base

pH at Key Points in Acid-Base Titration

pH at key points in a strong acid and strong base titration can be calculated from the amounts of acid and base present. The example uses 25.00 mL of 0.100 M HCl, a strong acid, and 0.100 M NaOH, a strong base. The pH changes as base is added, and each stage follows a different calculation. At 0 mL of titrant, the pH comes from the ionization of HCl. Because HCl is a strong acid, its ionization is complete. The hydronium ion molarity is 0.100 M, and the pH is found from that value. At 12.50...

titration calculations: weak acid - strong base

titration-calculations-weak-acid-strong-base

pH at Key Points in a Weak Acid Titration

pH at key points in a weak acid titration can be calculated for an acetic acid solution as sodium hydroxide is added. The example uses 25.00 mL of 0.100 M CH3CO2H titrated with 0.100 M NaOH. The reaction is shown as the weak acid reacts with the strong base. The initial pH is found from the acetic acid solution using the usual ICE approach. ICE means initial, change, and equilibrium, and it is a common way to set up equilibrium problems. The solution pH is calculated before any titrant is...

indicators

Acid-Base Color Changes

Acid-base indicators show color changes that help identify the pH of a solution. These are often weak organic acids or weak organic bases, and they respond to changes in hydronium ion concentration in dilute aqueous solution. Phenolphthalein is one example. It is colorless when the hydronium ion concentration is greater than 5.0 × 10^-9 M, which means the pH is below 8.3. In more basic solutions, where the hydronium ion concentration is lower, it turns red or pink. Methyl orange shows how an...

titration of a polyprotic acid

Polyprotic Acid Equivalence Points

Polyprotic acids have more than one ionizable hydrogen, so they lose protons in steps during titration. When the acid dissociation constants for those protons are far enough apart, the titration curve shows a separate equivalence point for each hydrogen that can ionize. Diprotic acids have two ionizable hydrogens and produce two equivalence points. Triprotic acids have three ionizable hydrogens and produce three equivalence points. Carbonic acid, H2CO3, is a weak diprotic acid. Carbonic acid...

solubility equilibria

Solubility equilibria explain how a dissolved ionic compound and its solid form can exist in balance. In a saturated solution, the solute dissolves and the ions precipitate at equal rates. These ideas matter in real settings such as tooth decay and water purification, where compound solubility affects the outcome. A substance with finite solubility can form a saturated solution when more solute is added than the solvent can dissolve. The result is a heterogeneous mixture of the saturated...

factors affecting solubility

Common Ion Effects on Solubility

The common ion effect lowers the solubility of an ionic compound in water when the solution already contains one of the ions made by that compound. It follows the law of mass action and can be explained with Le Châtelier’s principle. When a common ion is added, the dissolution equilibrium shifts toward the solid, so less of the salt stays dissolved. Silver iodide shows this effect clearly. If silver ions or iodide ions are added to a solution of AgI, the equilibrium shifts left and more AgI...

formation of complex ions

Ligands and Complex Ion Stability

Complex ions form when a central atom, often a transition metal cation, binds to ligands. Ligands are ions or molecules around the metal ion. They can be neutral molecules such as H2O or NH3, or ions such as CN− or OH−. In many cases, the ligands act as Lewis bases by donating a pair of electrons to the central atom. These reactions are part of coordination chemistry, which studies coordination complexes. When a metal ion reacts with one or more ligands to form a complex, the equilibrium...

precipitation of ions

Solubility Limits and Selective Precipitation

Solubility limits and selective precipitation explain when ions form a solid in water. The key idea is the balance between an insoluble compound and its dissolved ions. In aqueous solutions that contain calcium ions and carbonate ions, this equilibrium can exist even if the solution was not made by saturating water with calcium carbonate. When two soluble salts are mixed, such as sodium carbonate and calcium nitrate, the ion concentrations determine whether a precipitate forms. If the reaction...

qualitative analysis

Cation Identification by Precipitation Tests

Cation identification by precipitation tests uses selective reactions to find metal ions in a mixture. In qualitative analysis, different reagents are added step by step. Each reaction can produce a characteristic precipitate for a specific group of cations. Other steps, such as changing pH, heating the mixture to dissolve a precipitate again, or adding reagents that form complex ions, help separate ions within the same group. Group IV cations such as Ba2+, Ca2+, and Mg2+ are identified...

henderson-hasselbalch equation

Buffer pH with the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation helps relate buffer pH to the weak acid in the solution. It comes from the ionization-constant expression for a weak acid. By rearranging that expression to solve for hydronium ion concentration, [H3O+], and then taking the negative logarithm of both sides, the equation can be written in terms of pH. In this form, pKa is defined as the negative logarithm of the weak acid ionization constant, or pKa = −log Ka. The equation shows the connection between pH, pKa,...

acid-base titration curves

Tracking pH During Acid-Base Titration

Acid-base titration uses pH changes to track how a solution responds as titrant is added. A titration curve is a graph of a solution property versus the amount of added titrant. In acid-base titrations, pH is the main property to follow because it changes in a predictable way with the solution makeup and helps show the endpoint. This pattern can be seen with a strong acid and strong base, a strong acid and weak base, or a strong base and weak acid. For example, 25.00 mL of 0.100 M HCl titrated...

key terms and concepts

Learn how Ksp, molar solubility, and the reaction quotient Q help predict when a saturated solution forms or when a precipitate will appear.

Predicting Precipitation with Ksp | JoVE K12

chemistry

JoVE Core 化学は、簡潔で理解しやすいアニメーションビデオレッスンを使用して、一般的な化学の概念を生き生きとしたものにします。さらに、活動する科学者のビデオでは、現在世界中の実験室で行われている古典的そして独創的な研究・実験をお見せします。

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Chemical reactions
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• Acids/bases

Content elaboration: In the Physical Science course, coefficients were used to balance simple equations. Other representations, including Lewis structures and three-dimensional models, were also used and manipulated to demonstrate the conservation of matter in chemical reactions. In this course, more complex reactions will be studied, classified and represented with balanced chemical equations and three-dimensional models. Classifying reactions into types can be a helpful organizational tool for recognizing patterns of what may happen when two substances are mixed. Teachers should be aware that the common reaction classifications that are often used in high school chemistry courses may lead to misconceptions because they are not based on the actual chemistry, but on surface features that can be similar from one system to another (e.g., exchanging partners), even though the underlying chemistry is not the same. However, these classifications may be useful in making predictions about what happens when two substances are mixed. Some general types of chemical reactions are oxidation/reduction, synthesis, decomposition, single replacement, double replacement (including precipitation reactions and some acid-base neutralizations) and combustion reactions. Some reactions can fit into more than one category. For example, a single replacement reaction can also be classified as an oxidation/reduction reaction. Identification of reactions involving oxidation and reduction as well as indicating what substance is being oxidized and what is being reduced are appropriate in this course. However, balancing complex oxidation/reduction reactions is reserved for more advanced study. Organic molecules release energy when undergoing combustion reactions and are used to meet the energy needs of society (e.g., oil, gasoline, natural gas) and to provide the energy needs of biological organisms (e.g., cellular respiration). When a reaction between two ionic compounds in aqueous solution results in the formation of a precipitate or molecular compound, the reaction often occurs because the new ionic or covalent bonds are stronger than the original ion-dipole interactions of the ions in solution. Laboratory experiences (3-D or virtual) with different types of chemical reactions should be provided. Reactions occur when reacting particles collide in an appropriate orientation and with sufficient energy. The rate of a chemical reaction is the change in the amount of the reactants or products in a specific period of time. Increasing the probability or effectiveness of the collisions between the particles increases the rate of the reaction. Therefore, changing the concentration of the reactants, changing the temperature or the pressure of gaseous reactants, or using a catalyst, can change the reaction rate. Likewise, the collision theory can be applied to dissolving solids in a liquid solvent and can be used to explain why reactions are more likely to occur between reactants in the aqueous or gaseous state than between solids. The rate at which a substance dissolves should not be confused with the amount of solute that can dissolve in a given amount of solvent (solubility). Mathematical treatment of reaction rates is reserved for more advanced study. Computer simulations can help visualize reactions from the perspective of the kinetic-molecular theory. In middle school, the differences between potential and kinetic energy and the particle nature of thermal energy were introduced. For chemical systems, potential energy is in the form of chemical energy and kinetic energy is in the form of thermal energy. The total amount of chemical energy and/or thermal energy in a system is impossible to measure. However, the energy change of a system can be calculated from measurements (mass and change in temperature) from calorimetry experiments in the laboratory. Conservation of energy is an important component of calorimetry equations. Thermal energy is the energy of a system due to the movement of its particles. The thermal energy of an object depends upon the temperature and chemical composition. Some materials require little energy to change their temperature and other materials require a great deal to change their temperature by the same amount. Specific heat is a measure of how much energy is needed to change the temperature of a specific mass of material a specific amount. Specific heat values can be used to calculate the thermal energy change, the temperature (initial, final or change in) or mass of a material in calorimetry. Water has a particularly high specific heat capacity, which is important in regulating Earth's temperature. As studied in middle school, chemical energy is the potential energy associated with chemical systems. Chemical reactions involve valence electrons forming bonds to yield more stable products with lower energies. Energy is required to break interactions and bonds between the reactant atoms and energy is released when an interaction or bond is formed between the atoms in the products. Molecules with weak bonds (e.g., ATP) are less stable and tend to react to produce more stable products, releasing energy in the process. Generally, energy is transferred out of the system (exothermic) when the products have stronger bonds than the reactants and is transferred into the system (endothermic) when the reactants have stronger bonds than the products. Predictions of the energy requirements (endothermic or exothermic) of a reaction can be made given a table of bond energies. Graphic representations can be drawn and interpreted to represent the energy changes during a reaction. The role of energy in determining the spontaneity of chemical reactions is dealt with conceptually in this course. Entropy and its influence on the spontaneity of reactions are reserved for more advanced study. All reactions are reversible to a degree and many reactions do not proceed completely toward products but appear to stop progressing before the reactants are all used up. At this point, the amounts of the reactants and the products appear to be constant and the reaction can be said to have reached dynamic equilibrium. Dynamic equilibrium means the rate of the reverse reaction is equal to the rate of the forward reaction so there is no apparent change in the reaction. If a chemical system at equilibrium is disturbed by a change in the conditions of the system (e.g., increase or decrease in the temperature, pressure on gaseous equilibrium systems, concentration of a reactant or product), then the equilibrium system will respond by shifting to a new equilibrium state, reducing the effect of the change (Le Chatelier's Principle). If products are removed as they are formed during a reaction, then the equilibrium position of the system is forced to shift to favor the products. In this way, an otherwise unfavorable reaction can be made to occur. Mathematical treatment of equilibrium reactions is reserved for advanced study. Computer simulations can help visualize the progression of a reaction to dynamic equilibrium and the continuation of both the forward and reverse reactions after equilibrium has been attained. Properties of acids and bases and the ranges of the pH scale were introduced in Physical Science. In this course, the structural features of molecules are explored to further understand acids and bases. Acids often result when hydrogen is covalently bonded to an electronegative element and is easily dissociated from the rest of the molecule to bind with water to form a hydronium ion (H3O+). The acidity of an aqueous solution can be expressed as pH, where pH can be calculated from the concentration of the hydronium ion. Bases are likely to dissociate in water to form a hydroxide ion. Acids can react with bases to form a salt and water. Such neutralization reactions can be studied quantitatively by performing titration experiments.

Predicting Precipitation with Ksp

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