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

Il pH di una soluzione tamponata contenente una coppia coniugata acido-base può essere calcolato usando l'equazione di Henderson-Hasselbalch, in alternativa ad una tabella ICE. L'equazione di Henderson-Hasselbalch è derivata dall'espressione della costante di equilibrio per Ka.Questa espressione può essere riarrangiata per determinare la concentrazione di ioni idronio. Se viene considerato il log negativo di entrambi i lati, il log negativo della concentrazione di ioni idronio e il log negativo della costante di dissociazione acida possono essere sostituiti, rispettivamente, dal pH e dal pKa.

Questo produce un'equazione in cui il pH di un tampone può essere calcolato aggiungendo il pKa e il log delle concentrazioni di equilibrio di una base coniugata al suo acido debole. Questi valori di equilibrio, possono essere sostituiti dalle concentrazioni iniziali, se la variazione della concentrazione di ioni idronio, x, è inferiore al 5 percento delle concentrazioni iniziali, sia dell'acido debole, che della base coniugata. L'equazione di Henderson-Hasselbalch mostra anche il rapporto fra base e acido necessario per preparare un tampone ad un pH specifico.

Allo stesso modo, il pH di una soluzione contenente una base debole ed il suo acido coniugato può essere determinato usando questa equazione, calcolando il pKa dell'acido coniugato dal pKb usando la formula:pKa più pKb è uguale a quattordici. Il pH di un tampone contenente 0, 15 acido formico molare e 0, 18 formiato di sodio molare, può essere determinato utilizzando l'equazione di Henderson-Hasselbalch o il valore della Ka per l'acido formico e la tabella ICE. Tuttavia, l'equazione di Henderson-Hasselbalch è un metodo più rapido per calcolare il pH quando una reazione coinvolge una coppia coniugata acido-base e la variazione della concentrazione di idronio è piccola.

Il pKa è determinato prendendo il logaritmo negativo della Ka per l'acido formico, che è uguale a 3, 75. Quando le concentrazioni iniziali di acido formico e formiato sono inserite nell'equazione, il valore del pH per la soluzione è uguale a 3, 83. Questo valore di pH può essere usato per determinare la concentrazione di ioni idronio, 1, 5 10⁻⁴.

Poiché questo valore è inferiore al 5 percento di 0, 15 acido formico molare, le approssimazioni necessarie per utilizzare l'equazione di Henderson-Hasselbalch sono valide.

De Levie, Robert. "L'equazione di Henderson-Hasselbalch: la sua storia e i suoi limiti." Journal of Chemical Education 80, n. 2 (2003): 146. <a href="https://pubs.acs.org/doi/pdf/10.1021/ed080p146">https://pubs.acs.org/doi/pdf/10.1021/ed080p146.</a>

equazione di henderson-hasselbalch

L'espressione della costante di ionizzazione per una soluzione di un acido debole può essere scritta come:

<img alt="Eq1" src="/files/ftp_upload/11410/11410_Equation_1.png" style="text-align: center; height: 90px;" />

Riorganizzando per risolvere [H3O+] si ottiene:

<img alt="Eq2" src="/files/ftp_upload/11410/11410_Equation_2.png" style="text-align: center; height: 90px;" />

Prendendo il logaritmo negativo di entrambi i lati di questa equazione si ottiene:

<img alt="Eq3" src="/files/ftp_upload/11410/11410_Equation_3.png" style="text-align: center; height: 90px;" />

che può essere scritto come:

<img alt="Eq4" src="/files/ftp_upload/11410/11410_Equation_4.png" style="text-align: center; height: 90px;" />

dove pK_a è il negativo del logaritmo della costante di ionizzazione dell'acido debole (pK_a = −log K_a). Questa equazione mette in relazione il pH, la costante di ionizzazione di un acido debole e le concentrazioni della coppia acido-base coniugata debole in una soluzione buffer. Gli scienziati usano spesso questa espressione, chiamata equazione di Henderson-Hasselbalch, per calcolare il pH delle soluzioni buffer. È importante notare che il presupposto “x è piccolo” dev’essere valido per utilizzare questa equazione.

Lawrence Joseph Henderson e Karl Albert Hasselbalch

Lawrence Joseph Henderson (1878-1942) è stato un medico, biochimico e fisiologo americano, per citare solo alcune delle sue numerose attività. Ha conseguito una laurea in medicina ad Harvard e poi ha trascorso 2 anni a studiare a Strasburgo, allora parte della Germania, prima di tornare a prendere una posizione di docente ad Harvard. Alla fine divenne professore ad Harvard e lavorò lì per tutta la vita. Scoprì che l'equilibrio acido-base nel sangue umano è regolato da un sistema buffer formato dall'anidride carbonica disciolta nel sangue. Nel 1908 scrisse un'equazione per descrivere il sistema buffer acido carbonico-carbonato nel sangue. Henderson era ampiamente informato; oltre alle sue importanti ricerche sulla fisiologia del sangue, scrisse anche sugli adattamenti degli organismi e sul loro adattamento all'ambiente, sulla sociologia e sull'istruzione universitaria. Fondò anche il Fatigue Laboratory presso la Harvard Business School, che esaminò la fisiologia umana con un focus specifico sul lavoro nell'industria, nell'esercizio fisico e nella nutrizione.

Nel 1916, Karl Albert Hasselbalch (1874-1962), un medico e chimico danese, condivise la paternità di un articolo con Christian Bohr nel 1904 che descriveva l'effetto Bohr, il quale dimostrava che la capacità dell'emoglobina nel sangue di legarsi con l'ossigeno era inversamente proporzionale all’acidità del sangue e alla concentrazione di anidride carbonica. La scala del pH fu introdotta nel 1909 da un altro danese, Sørensen, e nel 1912 Hasselbalch pubblicò le misurazioni del pH del sangue. Nel 1916, Hasselbalch espresse l’equazione di Henderson in termini logaritmici, coerenti con la scala logaritmica del pH, e così nacque l’equazione di Henderson-Hasselbalch.

Questo testo è adattato da<a href="https://openstax.org/books/chemistry-2e/pages/14-6-buffers"> Openstax, Chemistry 2e, Section 14.6: Buffers</a>.

Equazione di Henderson-Hasselbalch

L'espressione costante di ionizzazione per una soluzione di un acido debole può essere scritta come:

Riarrangiamento per risolvere i rendimenti [H3O+]:

Prendendo il negativo ...

Education

Didattica

JoVE Core

Chimica

Acid-base and Solubility Equilibria

Equilibri acido-base e di solubilità

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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

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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

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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...

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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

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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

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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

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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: Chimica illustra concetti chiave di chimica attraverso video animazioni concise e di immediata comprensione. Inoltre, i video della sezione "scienziati in azione" mostrano procedure metodologiche realizzate da ricercatori provenienti dai migliori laboratori internazionali.

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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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