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

El pH de una solución tamponada que contiene un par ácido-base conjugado puede calcularse utilizando la ecuación de Henderson-Hasselbalch como alternativa a una tabla ICE. La ecuación de Henderson-Hasselbalch se deriva de la expresión constante de equilibrio para Ka.Esta expresión se puede reorganizar para determinar la concentración de iones de hidronio. Si se toma el logaritmo negativo de ambos lados, el logaritmo negativo de la concentración de iones de hidronio y el logaritmo negativo de la constante de disociación ácida se pueden reemplazar por el pH y el pKa, respectivamente.Esto produce una ecuación en la que el pH de un tampón se puede calcular sumando el pKa y el logaritmo de las concentraciones de equilibrio de una base conjugada sobre su ácido débil. Estos valores de equilibrio pueden reemplazarse por las concentraciones iniciales si el cambio en la concentración de iones de hidronio, x, es menor que el 5 porciento de las concentraciones iniciales tanto del ácido débil como de la base conjugada La ecuación de Henderson-Hasselbalch también muestra la relación de base a ácido necesaria para preparar un tampón a un pH específico. De manera similar, el pH de una solución que contiene una base débil y su ácido conjugado se puede determinar usando esta ecuación, calculando el pKa del ácido conjugado a partir del pKb usando la fórmula:pKa más pKb es igual a catorce.El pH de un tampón que contiene ácido fórmico 0, 15 molar y formiato de sodio 0, 18 molar se puede determinar utilizando la ecuación de Henderson-Hasselbalch o el Ka para el ácido fórmico y la tabla ICE. Sin embargo, la ecuación de Henderson-Hasselbalch es un método más rápido para calcular el pH cuando una reacción involucra un par conjugado ácido-base y el cambio en la concentración de hidronio es pequeño. El pKa se determina tomando el logaritmo negativo de Ka para el ácido fórmico, que es igual a 3, 75.Cuando las concentraciones iniciales de fórmico se introducen en la ecuación, el valor del pH de la solución es igual a 3, 83. Este valor de pH se puede utilizar para determinar la concentración de iones de hidronio, 1, 5 10⁻⁴. Como este valor es inferior al 5 de ácido fórmico 0, 15 molar, las aproximaciones necesarias para utilizar la ecuación de Henderson-Hasselbalch son válidas.

De Levie, Robert. "La ecuación de Henderson-Hasselbalch: su historia y limitaciones". Revista de Educación Química 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>

ecuación de henderson-hasselbalch

La expresión de la constante de ionización para una solución de un ácido débil puede escribirse como:
 <img alt="Eq1" src="/files/ftp_upload/11410/11410_Equation_1.png" style="text-align: center; height: 90px;" />
 Al reorganizar para resolver [H3O+] se obtiene:
 <img alt="Eq2" src="/files/ftp_upload/11410/11410_Equation_2.png" style="text-align: center; height: 90px;" />
 Al tomar el logaritmo negativo de ambos lados de esta ecuación queda
 <img alt="Eq3" src="/files/ftp_upload/11410/11410_Equation_3.png" style="text-align: center; height: 90px;" />
 que se puede escribir como
 <img alt="Eq4" src="/files/ftp_upload/11410/11410_Equation_4.png" style="text-align: center; height: 90px;" />
 Donde pKa es el negativo del logaritmo de la constante de ionización del ácido débil (pKa = −logKa). Esta ecuación relaciona el pH, la constante de ionización de un ácido débil, y las concentraciones del par ácido-base conjugado débil en una solución tamponada. Los científicos a menudo utilizan esta expresión, llamada ecuación de Henderson-Hasselbalch, para calcular el pH de las soluciones tampón. Es importante notar que la suposición “x es pequeña” debe ser válida para usar esta ecuación.
 Lawrence Joseph Henderson y Karl Albert Hasselbalch
 Lawrence Joseph Henderson (1878–1942) fue un médico, bioquímico y fisiólogo estadounidense, por nombrar sólo algunas de sus muchas actividades. Obtuvo un título médico en Harvard y luego pasó 2 años estudiando en Estrasburgo, para entonces parte de Alemania, antes de regresar a tomar un puesto de instructor en Harvard. Finalmente se convirtió en profesor de Harvard y trabajó allí toda su vida. Descubrió que el equilibrio ácido-base en la sangre humana está regulado por un sistema de amortiguación formado por el dióxido de carbono disuelto en la sangre. Escribió una ecuación en 1908 para describir el sistema de tampón ácido carbónico-carbonato en sangre. Henderson tenía amplios conocimientos; además de su importante investigación sobre la fisiología de la sangre, también escribió sobre las adaptaciones de los organismos y su acoplamiento con el entorno, sobre sociología y sobre la educación universitaria. También fundó el Fatigue Laboratory en la Harvard Business School, el cual examinó la fisiología humana con un enfoque de trabajo específico en la industria, el ejercicio y la nutrición.
 En 1916, Karl Albert Hasselbalch (1874–1962), un médico y químico danés, compartió la autoría en un artículo con Christian Bohr en 1904 que describía el efecto Bohr, lo que mostró que la capacidad de la hemoglobina en la sangre para unirse con el oxígeno estaba inversamente relacionada con la acidez de la sangre y la concentración de dióxido de carbono. La escala de pH fue introducida en 1909 por otro danés, Sørensen, y en 1912, Hasselbalch publicó mediciones del pH sanguíneo. En 1916, Hasselbalch expresó la ecuación de Henderson en términos logarítmicos, consistente con la escala logarítmica del pH, y así nació la ecuación de Henderson-Hasselbalch.
 Este texto es adaptado de<a href="https://openstax.org/books/chemistry-2e/pages/14-6-buffers"> Openstax, Química 2e, Sección 14.6: Amortiguadores</a>.

Ecuación de Henderson-Hasselbalch

La expresión de la constante de ionización para una solución de un ácido débil se puede escribir como:

Reorganizando para resolver los rendimientos de [H3O+]:

Tomando el negativo ...

Education

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JoVE Core

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Acid-base and Solubility Equilibria

Equilibrios de solubilidad y ácido-base

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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

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...

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solubility equilibria

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...

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

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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 Química da vida a los conceptos de química general mediante lecciones de vídeo basadas en animaciones, concisas y fáciles de entender. Además, en los vídeos de científicos en acción, se muestran experimentos de investigación clásicos y originales realizados en laboratorios de todo el mundo.

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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. 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.

Buffer pH with the Henderson-Hasselbalch Equation

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