Name: buffer ph with the henderson-hasselbalch equation
Uploaded: 2020-09-24T15:06:51.000Z
Duration: 2 min 48 s
Channel: JoVE

K12 Standards

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Ohio’s Learning Standards and Model Curriculum

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Chemistry

Interactions Of Matter

Chemical reactions

Henderson-Hasselbalch Equation

共役酸-塩基対を含む緩衝溶液のpHは、ICEテーブルの代替としてヘンダーソン・ハッセルバルヒ方程式を使用して計算できます。
ヘンダーソン・ハッセルバルヒ方程式は、Ka の平衡定数式から導出されます。
この発現は、ヒドロニウムイオン濃度を決定するために再配置できます。両側の負の対数を取ると、ヒドロニウムイオン濃度の負の対数と酸解離定数の負の対数を、それぞれpHとpKaに置き換えることができます。
これにより、バッファーのpHは、pKaとその弱酸の上に共役塩基の平衡濃度の対数を加算することで計算できる方程式が得られます。
これらの平衡値は、ヒドロニウムイオン濃度xの変化が弱酸と共役塩基の両方の初期濃度の5%未満である場合、初期濃度に置き換えることができます。
ヘンダーソン・ハッセルバルチの式は、特定のpHでバッファーを調製するために必要な塩基と酸の比率も示しています。
同様に、弱塩基とその共役酸を含む溶液のpHは、この式を使用して、pKbから共役酸のpKaを計算することにより決定できます:pKaとpKbは14に等しくなります。
0.15モルのギ酸と0.18モルのギ酸ナトリウムを含む緩衝液のpHは、ヘンダーソン・ハッセルバルフの式、またはギ酸のKAとICEテーブルを使用して決定できます。ただし、ヘンダーソン・ハッセルバルヒ方程式は、反応に共役酸-塩基対が関与し、ヒドロニウム濃度の変化が小さい場合にpHを計算するためのより迅速な方法です。
pKaは、ギ酸のKaの負の対数を取ることによって決定され、これは3.75に等しくなります。
ギ酸とギ酸の初期濃度を式に当てはめると、溶液のpH値は3.83に等しくなります。
このpH値を使用して、ヒドロニウムイオン濃度(1.5 × 10-4)を決定できます。この値は0.15モルギ酸の5%未満であるため、ヘンダーソン・ハッセルバルフ方程式を使用するために必要な近似は有効です。

「ヘンダーソン・ハッセルバルフ方程式:その歴史と限界」 Journal of Chemical Education 80, no. 2 (2003): 146. <a href="https://pubs.acs.org/doi/pdf/10.1021/ed080p146">https://pubs.acs.org/doi/pdf/10.1021/ed080p146.</a>

ヘンダーソン-ハッセルバルヒ式

弱酸性溶液のイオン化式は次のように書くことができます。
 <img alt="Eq1" src="/files/ftp_upload/11410/11410_Equation_1.png" style="text-align: center; height: 90px;" />
 Rearranging to solve for [H3O+] yields:
 <img alt="Eq2" src="/files/ftp_upload/11410/11410_Equation_2.png" style="text-align: center; height: 90px;" />
 Taking the negative logarithm of both sides of this equation gives
 <img alt="Eq3" src="/files/ftp_upload/11410/11410_Equation_3.png" style="text-align: center; height: 90px;" />
 which can be written as
 <img alt="Eq4" src="/files/ftp_upload/11410/11410_Equation_4.png" style="text-align: center; height: 90px;" />
 ここでpKaは弱酸における酸解離定数の対数の負の値である（pKa = −log Ka）。この式は、pH、弱酸の酸解離定数、および緩衝液中の弱共役酸・弱共役塩基対の濃度を関係づけています。科学者たちは、緩衝液のpHを計算するのに、ヘンダーソン-ハッセルバルヒ式と呼ばれるこの式をよく利用します。この式は “x が小さい”の仮定のもとで成立します。
 ローレンス・ジョセフ・ヘンダーソンとカール・アルバート・ハッセルバルヒ
 ローレンス・ジョセフ・ヘンダーソン(1878–1942)は、アメリカの医師、生化学者、生理学者であり、様々な分野で成果を残しました。ハーバード大学で医学の学位を取得した後、当時ドイツの一部であったストラスブールに2年間留学し、その後ハーバード大学の講師に就任しました。その後、ハーバード大学の教授となり、生涯研究を続けた。彼は、人間の血液の酸塩基平衡が、血液中に溶け込んでいる二酸化炭素によって形成される緩衝系によって調整されていることを発見しました。1908年には、血液中の炭酸-炭酸塩緩衝系を表す方程式を書いています。ヘンダーソンは幅広い知識を持っていました。血液の生理学に関する重要な研究に加えて、生物の適応や環境への適合、社会学や大学教育についても執筆しています。また、ハーバード・ビジネス・スクールに「疲労研究所」を設立し、産業界での労働、運動、栄養に焦点を当てた人間の生理学を研究していました。
 1916年、デンマークの医師・化学者であるカール・アルバート・ハッセルバルヒ（1874–1962）は、1904年にクリスチャン・ボーアと共著で、血液中のヘモグロビンが酸素と結合する能力は、血液の酸性度と二酸化炭素の濃度に反比例するというBohr効果を記述した論文を発表しました。1909年には、同じくデンマーク人のセーレンセンがpHスケールを導入し、1912年にはハッセルバルヒが血液のpHの測定値を発表しました。1916年、ハッセルバルヒはヘンダーソンの式を対数で表し、pHの対数目盛と一致させ、ヘンダーソン-ハッセルバルヒ式を誕生させました。
 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/14-6-buffers"> Openstax, Chemistry 2e, Section 14.6: Buffers</a>.

弱酸溶液のイオン化定数の発現は、次のように書くことができます。

[H3O+] を解くために並べ替えると、次のようになります。

ネガティブなことを言うと...

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

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, and the concentrations of a weak conjugate acid-base pair in a buffered solution. Scientists often use this relationship to calculate the pH of buffer solutions.

A key condition is that the “x is small” assumption must be valid before the equation is used. If that assumption does not hold, the result may not be reliable. The equation is a practical shortcut, but it depends on the chemistry of the weak acid system.

The equation is named for Lawrence Joseph Henderson and Karl Albert Hasselbalch. Henderson was an American physician, biochemist, and physiologist who studied the carbonic acid-carbonate buffer system in blood and wrote an equation for it in 1908. He also worked on organisms and their environment, sociology, university education, and the Fatigue Laboratory at Harvard Business School, which studied human physiology in industry, exercise, and nutrition.

Hasselbalch was a Danish physician and chemist who helped connect this idea to the pH scale. The pH scale was introduced in 1909 by Sørensen, and Hasselbalch later published measurements of blood pH in 1912. In 1916, he rewrote Henderson’s equation in logarithmic form, which matched the logarithmic pH scale. That is how the Henderson-Hasselbalch equation was born.

Buffer pH with the Henderson-Hasselbalch Equation

buffer-ph-with-the-henderson-hasselbalch-equation

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+...

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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...

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Buffer Capacity and pH Stability

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titration calculations: strong acid - strong base

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pH at Key Points in Acid-Base Titration

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titration calculations: weak acid - strong base

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pH at Key Points in a Weak Acid Titration

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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,...

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key terms and concepts

Learn how the Henderson-Hasselbalch equation links buffer pH, pKa, and weak acid-base pair concentrations, and why the small-x assumption matters.

Buffer pH with the Henderson-Hasselbalch Equation | 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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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. 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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.

Buffer pH with the Henderson-Hasselbalch Equation

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