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

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Henderson-Hasselbalch Equation

De pH van een gebufferde oplossing die een geconjugeerd zuur-basenpaar bevat, kan worden berekend met behulp van de Henderson-Hasselbalch-vergelijking als alternatief voor een ICE-tabel. De Henderson-Hasselbalch-vergelijking is afgeleid van de evenwichtsconstante-uitdrukking voor Ka.Deze uitdrukking kan worden herschikt om de concentratie van hydronium-ionen te bepalen. Als de negatieve log van beide zijden wordt genomen, kunnen de negatieve logaritme van de hydronium-ionenconcentratie en de negatieve logaritme van de zuurconstante worden vervangen door respectievelijk de pH en de pKa.Dit levert een vergelijking op waarbij de pH van een buffer kan worden berekend door de pKa en de log van de evenwichtsconcentraties van een geconjugeerde base over zijn zwakke zuur toe te voegen. Deze evenwichtswaarden kunnen worden vervangen door de beginconcentraties als de verandering in de hydronium-ionenconcentratie, x, kleiner is dan de 5%van de beginconcentraties van zowel het zwakke zuur als de geconjugeerde base. De Henderson-Hasselbalch-vergelijking toont ook de verhouding van base tot zuur die nodig is om een buffer bij een specifieke pH te bereiden.Evenzo kan de pH van een oplossing die een zwakke base en zijn geconjugeerd zuur bevat, worden bepaald met behulp van deze vergelijking door de pKa van het geconjugeerde zuur uit de pKb te berekenen met behulp van de formule:pKa plus pKb is gelijk aan veertien. De pH van een buffer die 0, 15 molair mierenzuur en 0, 18 molair natriumformiaat bevat, kan worden bepaald met behulp van de Henderson-Hasselbalch-vergelijking of de Ka voor mierenzuur en de ICE-tabel. De vergelijking van Henderson-Hasselbalch is echter een snellere methode om de pH te berekenen wanneer een reactie een geconjugeerd zuur-basenpaar omvat en de verandering in de hydroniumconcentratie klein is.De pKa wordt bepaald door de negatieve logaritme van de Ka voor mierenzuur te nemen, die gelijk is aan 3, 75. Wanneer de beginconcentraties van mierenzuur en formiaat in de vergelijking worden gestopt, is de pH-waarde voor de oplossing gelijk aan 3, 83. Deze pH-waarde kan worden gebruikt om de hydronium-ionenconcentratie te bepalen, 1, 5 10⁻⁴.Aangezien deze waarde minder is dan 5%van 0, 15 molair mierenzuur, zijn de benaderingen die nodig zijn om de Henderson-Hasselbalch-vergelijking te gebruiken geldig.

henderson-hasselbalch-vergelijking

De ionisatieconstante uitdrukking voor een oplossing van een zwak zuur kan worden geschreven als: <img alt="Eq1" src="/files/ftp_upload/11410/11410_Equation_1.png" style="text-align: center; height: 90px;"> Herschikken om de opbrengsten van [H3O+] op te lossen: <img alt="Eq2" src="/files/ftp_upload/11410/11410_Equation_2.png" style="text-align: center; height: 90px;"> Het nemen van de negatieve logaritme van beide zijden van deze vergelijking geeft: <img alt="Eq3" src="/files/ftp_upload/11410/11410_Equation_3.png" style="text-align: center; height: 90px;"> die geschreven kan worden als <img alt="Eq4" src="/files/ftp_upload/11410/11410_Equation_4.png" style="text-align: center; height: 90px;"> waarbij pKa het negatief is van de logaritme van de ionisatieconstante van het zwakke zuur (pKa = −log Ka). Deze vergelijking relateert de pH, de ionisatieconstante van een zwak zuur en de concentraties van het zwakke geconjugeerde zuur-basepaar in een gebufferde oplossing. Wetenschappers gebruiken deze uitdrukking, de Henderson-Hasselbalch-vergelijking genoemd, vaak om de pH van bufferoplossingen te berekenen. Het is belangrijk op te merken dat de aanname ‘x is klein’ geldig moet zijn om deze vergelijking te kunnen gebruiken. Lawrence Joseph Henderson en Karl Albert Hasselbalch Lawrence Joseph Henderson (1878–1942) was een Amerikaanse arts, biochemicus en fysioloog, om maar een paar van zijn vele bezigheden te noemen. Hij behaalde een medische graad aan Harvard en studeerde vervolgens twee jaar in Straatsburg, destijds een deel van Duitsland, voordat hij terugkeerde om een docentpositie aan te nemen aan Harvard. Uiteindelijk werd hij professor aan Harvard en werkte daar zijn hele leven. Hij ontdekte dat het zuur-base-evenwicht in menselijk bloed wordt gereguleerd door een buffersysteem dat wordt gevormd door de opgeloste koolstofdioxide in het bloed. Hij schreef in 1908 een vergelijking om het koolzuur-carbonaatbuffersysteem in het bloed te beschrijven. Henderson had een brede kennis; Naast zijn belangrijke onderzoek naar de fysiologie van bloed schreef hij ook over de aanpassingen van organismen en hun aanpassing aan hun omgeving, over sociologie en over universitair onderwijs. Hij richtte ook het Fatigue Laboratory op aan de Harvard Business School, dat de menselijke fysiologie onderzocht met een specifieke focus op werk in de industrie, lichaamsbeweging en voeding. In 1916 deelde Karl Albert Hasselbalch (1874–1962), een Deense arts en scheikundige, het auteurschap in een artikel uit 1904 met Christian Bohr waarin het Bohr-effect werd beschreven, waaruit bleek dat het vermogen van hemoglobine in het bloed om zich met zuurstof te binden omgekeerd omgekeerd was. gerelateerd aan de zuurgraad van het bloed en de concentratie van kooldioxide. De pH-schaal werd in 1909 geïntroduceerd door een andere Deen, Sørensen, en in 1912 publiceerde Hasselbalch metingen van de pH van bloed. In 1916 drukte Hasselbalch de vergelijking van Henderson uit in logaritmische termen, consistent met de logaritmische pH-schaal, en zo werd de Henderson-Hasselbalch-vergelijking geboren. Deze tekst is aangepast van<a href="https://openstax.org/books/chemistry-2e/pages/14-6-buffers"> Openstax, Chemistry 2e, Sectie 14.6: Buffers</a>.

Henderson-Hasselbalch-vergelijking

The ionization-constant expression for a solution of a weak acid can be written as:

Rearranging to solve for [H3O+] yields:

Taking the negative ...

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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

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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,...

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

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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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