Name: buffer ph with the henderson-hasselbalch equation
Uploaded: 2020-09-24T15:06:51.000Z
Duration: 2 min 48 s
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Ohio’s Learning Standards and Model Curriculum

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Chemistry

Interactions Of Matter

Chemical reactions

Henderson-Hasselbalch Equation

含有共轭酸碱对的 缓冲溶液的 pH 值可以 使用亨德森-哈塞尔巴尔赫方程来计算，作为 ICE 表的一种替代方法。亨德森-哈塞尔巴尔赫方程 由 Ka 的平衡常数表达式导出。这个表达式可以重新排列 以确定水合氢离子的浓度。如果取两边的负对数，水合氢离子浓度的负对数 和酸离解常数的负对数 可分别用 pH 和 pKa 代替。这就产生了一个方程，其中 缓冲液的 pH 值可以通过加上 pKa 和 共轭碱与其弱酸的平衡浓度之比 的对数来计算。如果氢离子浓度的变化，x 小于弱酸和共轭碱的 初始浓度的 5%则可以用初始浓度 代替这些平衡值。亨德森-哈塞尔巴尔赫方程 还显示了在特定的 pH 值下 制备缓冲液所需的酸碱比。类似地，含有弱碱及其共轭酸的 溶液的 pH 值可以 用这个方程来确定，通过使用以下公式 由 pKb 来计算共轭酸的 pKa pKa 加 pKb 等于 14。含有 0.15M 甲酸和 0.18M 甲酸钠的 缓冲液的 pH 值可以 使用亨德森-哈塞尔巴尔赫方程 或甲酸的 Ka 和 ICE 表来确定。然而，当一个反应涉及共轭酸碱对并且 水合氢离子浓度的变化很小时，亨德森-哈塞尔巴尔赫方程是计算 pH 值的 一种更快的方法。通过取甲酸的 Ka 的负对数 来确定 pKa，等于 3.75。当甲酸和甲酸盐的初始浓度 插入方程中时，溶液的 pH 值 等于 3.83。该 pH 值可用于确定水合氢离子 浓度，即为 1.5×10⁻⁴。由于该值小于 0.15 M 甲酸的 5%因此使用亨德森-哈塞尔巴尔赫方程所需的近似 是有效的。

De Levie， Robert. "Henderson-Hasselbalch 方程:其历史和局限性。"化学教育杂志 80，第 2 期（2003 年）:146。<a href="https://pubs.acs.org/doi/pdf/10.1021/ed080p146">https://pubs.acs.org/doi/pdf/10.1021/ed080p146。</a>

亨德森-哈塞尔巴尔赫方程（henderson-hasselbalch equation）

弱酸的溶液的电离常数表达式可以写为： 
 <img alt="Eq1" src="/files/ftp_upload/11410/11410_Equation_1.png" style="text-align: center; height: 90px;" />
 重新安排以解决 [H3O+] 的产量： 
 <img alt="Eq2" src="/files/ftp_upload/11410/11410_Equation_2.png" style="text-align: center; height: 90px;" />
 使用该方程两侧的负对数 给出 
 <img alt="Eq3" src="/files/ftp_upload/11410/11410_Equation_3.png" style="text-align: center; height: 90px;" />
 可作为写入 
 <img alt="Eq4" src="/files/ftp_upload/11410/11410_Equation_4.png" style="text-align: center; height: 90px;" />
 其中 pka 是弱酸电离常数对数的负 (pka = −log ka)。 该方程将 pH 值，弱酸的电离常数以及缓冲溶液中弱共轭酸碱对的浓度关联起来。 科学家经常使用这种称为 亨德森-哈塞尔巴尔赫方程（Henderson-Hasselbalch Equation） 的表达来计算缓冲溶液的 pH 值。 请注意，“ x is small ”假设必须有效才能使用此方程。 
 劳伦斯 · 约瑟夫 · 亨德森和 卡尔·阿尔伯特·哈塞​​尔巴尔（Karl Albert Hasselbalch） 
 劳伦斯 · 约瑟夫 · 亨德森 (1878 – 1942 年 ) 是美国生物化学家和生理学家医师，仅列举他的几项追求。 他获得了哈佛大学的医学学位，然后在斯特拉斯堡学习了两年，后来又进入了德国，然后回到哈佛大学担任讲师。 他最终成为了哈佛的教授，一生都在那里工作。 他发现人类血液中的 酸-碱 平衡由溶解血液中的二氧化碳形成的缓冲液系统调节。 1908 年，他写了一篇方程，描述血液中的碳酸二酯缓冲液系统。 亨德森知识渊博；除了他关于血液生理学的重要研究之外，他还撰写了有关生物体适应及其与环境的适应，社会学和大学教育的文章。 他还在哈佛大学商学院创办了疲劳实验室，该实验室专门研究人体生理学，重点关注工业，运动和营养方面的工作。 
 1916 年，丹麦医师和化学家 卡尔·阿尔伯特·哈塞​​尔巴尔（Karl Albert Hasselbalch） (1874 – 1962 年) 在 1904 年与 克里斯蒂安·玻尔（Christian Bohr） 分享了一份描述玻尔效应的文件， 这表明血液中的血红蛋白与氧气结合的能力与血液的酸度和二氧化碳的浓度成反比。 pH值 于 1909 年由另一名丹麦人 索伦森（Sørensen） 推出， 1912 年，哈塞尔巴尔赫发布了血液 pH 值的测量结果。 1916 年，哈塞尔巴尔赫以对数表示亨德森的方程，与 pH 的对数刻度一致，因此 亨德森-哈塞尔巴尔赫方程（Henderson-Hasselbalch Equation） 诞生了。 
 本文改编自<a href="https://openstax.org/books/chemistry-2e/pages/14-6-buffers"> Openstax, 化学 2e, 第14.6节：缓冲液</a>。

亨德森-哈塞尔巴尔赫方程（Henderson-Hasselbalch Equation）

弱酸溶液的电离常数表达式可写为：

重排以求解 [H3O+] 得：

取负对数……

Education

教育

JoVE Core

化学

Acid-base and Solubility Equilibria

酸碱与溶解平衡

KEY TERMS AND CONCEPTS

关键术语与概念

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+...

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

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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...

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Acid-Base Color Changes

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Polyprotic Acid Equivalence Points

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Predicting Precipitation with Ksp

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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...

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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

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 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 化学通过简单明了且通俗易懂的动画视频课程，将普通化学概念带入到现实生活当中。此外，在科学家行动视频中，我们演示了在实验室中进行的经典和原始研究实验。

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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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