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

Der pH-Wert einer gepufferten Lösung, die ein konjugiertes Säure-Base-Paar enthält, kann unter Verwendung der Henderson-Hasselbalch-Gleichung als Alternative zu einer ICE-Tabelle berechnet werden.
Die Henderson-Hasselbalch-Gleichung wird aus dem Gleichgewichtskonstantenausdruck für Ka abgeleitet.
Dieser Ausdruck kann umgestellt werden, um die Hydroniumionenkonzentration zu bestimmen. Nimmt man den negativen Logarithmus beider Seiten, so können der negative Logarithmus der Hydroniumionenkonzentration und der negative Logarithmus der Säuredissoziationskonstante durch den pH-Wert bzw. den pKa ersetzt werden.
Daraus ergibt sich eine Gleichung, in der der pH-Wert eines Puffers berechnet werden kann, indem das pKa und der Logarithmus der Gleichgewichtskonzentrationen einer konjugierten Base über ihrer schwachen Säure addiert werden.
Diese Gleichgewichtswerte können durch die Anfangskonzentrationen ersetzt werden, wenn die Änderung der Hydroniumionenkonzentration x kleiner als die 5 % der Anfangskonzentrationen sowohl der schwachen Säure als auch der konjugierten Base ist.
Die Henderson-Hasselbalch-Gleichung zeigt auch das Verhältnis von Base zu Säure, das zur Herstellung eines Puffers bei einem bestimmten pH-Wert erforderlich ist.
In ähnlicher Weise kann der pH-Wert einer Lösung, die eine schwache Base und ihre konjugierte Säure enthält, mit dieser Gleichung bestimmt werden, indem das pKa der konjugierten Säure aus dem pKb berechnet wird, wobei die Formel verwendet wird: pKa plus pKb ist gleich vierzehn.
Der pH-Wert eines Puffers, der 0,15 molare Ameisensäure und 0,18 molare Natriumformiat enthält, kann entweder mit der Henderson-Hasselbalch-Gleichung oder dem Ka für Ameisensäure und der ICE-Tabelle bestimmt werden. Die Henderson-Hasselbalch-Gleichung ist jedoch eine schnellere Methode zur Berechnung des pH-Werts, wenn an einer Reaktion ein konjugiertes Säure-Base-Paar beteiligt ist und die Änderung der Hydroniumkonzentration gering ist.
Der pKa wird bestimmt, indem der negative Logarithmus von Ka für Ameisensäure genommen wird, der 3,75 entspricht.
Wenn die Anfangskonzentrationen von Ameisensäure und Formiat in die Gleichung eingefügt werden, beträgt der pH-Wert für die Lösung 3,83.
Dieser pH-Wert kann zur Bestimmung der Hydroniumionenkonzentration von 1,5 × 10−4 verwendet werden. Da dieser Wert weniger als 5 % von 0,15 molare Ameisensäure beträgt, gelten die Näherungen, die zur Verwendung der Henderson-Hasselbalch-Gleichung erforderlich sind.

De Levie, Robert. "Die Henderson-Hasselbalch-Gleichung: ihre Geschichte und ihre Grenzen." Journal of Chemical Education 80, Nr. 2 (2003): 146. <a href="https://pubs.acs.org/doi/pdf/10.1021/ed080p146">https://pubs.acs.org/doi/pdf/10.1021/ed080p146.</a>

henderson-hasselbalch-gleichung

Der Ausdruck für die Ionisationskonstante für eine Lösung einer schwachen Säure kann wie folgt geschrieben werden: <img alt="Eq1" src="/files/ftp_upload/11410/11410_Equation_1.png" style="text-align: center; height: 90px;"> Neuordnung zur Lösung nach [H3O+] ergibt: <img alt="Eq2" src="/files/ftp_upload/11410/11410_Equation_2.png" style="text-align: center; height: 90px;"> Die Bildung des negativen Logarithmus beider Seiten dieser Gleichung ergibt <img alt="Eq3" src="/files/ftp_upload/11410/11410_Equation_3.png" style="text-align: center; height: 90px;"> was geschrieben werden kann als <img alt="Eq4" src="/files/ftp_upload/11410/11410_Equation_4.png" style="text-align: center; height: 90px;"> wobei pKa das Negativ des Logarithmus der Ionisationskonstante der schwachen Säure ist (pKa = −log Ka). Diese Gleichung setzt den pH-Wert, die Ionisierungskonstante einer schwachen Säure und die Konzentrationen des schwachen konjugierten Säure-Base-Paares in einer gepufferten Lösung in Beziehung. Wissenschaftler verwenden diesen Ausdruck, die sogenannte Henderson-Hasselbalch-Gleichung, häufig, um den pH-Wert von Pufferlösungen zu berechnen. Es ist wichtig zu beachten, dass die Annahme „x ist klein“ gültig sein muss, um diese Gleichung verwenden zu können. Lawrence Joseph Henderson und Karl Albert Hasselbalch Lawrence Joseph Henderson (1878–1942) war ein amerikanischer Arzt, Biochemiker und Physiologe, um nur einige seiner vielfältigen Interessen zu nennen. Er schloss sein Medizinstudium an der Harvard-Universität ab und studierte dann zwei Jahre lang in Straßburg, damals ein Teil Deutschlands, bevor er zurückkehrte, um eine Dozentenstelle an der Harvard-Universität anzunehmen. Schließlich wurde er Professor in Harvard und arbeitete dort sein ganzes Leben lang. Er entdeckte, dass das Säure-Basen-Gleichgewicht im menschlichen Blut durch ein Puffersystem reguliert wird, das durch das im Blut gelöste Kohlendioxid gebildet wird. Er verfasste 1908 eine Gleichung zur Beschreibung des Kohlensäure-Karbonat-Puffersystems im Blut. Henderson verfügte über umfassende Kenntnisse; Zusätzlich zu seinen wichtigen Forschungen zur Physiologie des Blutes schrieb er auch über die Anpassungen von Organismen und ihre Anpassung an ihre Umwelt, über Soziologie und über die Hochschulbildung. Er gründete außerdem das Fatigue Laboratory an der Harvard Business School, das die menschliche Physiologie mit besonderem Schwerpunkt auf Arbeit in der Industrie, Bewegung und Ernährung untersuchte. Im Jahr 1916 teilte Karl Albert Hasselbalch (1874–1962), ein dänischer Arzt und Chemiker, zusammen mit Christian Bohr die Autorschaft einer Arbeit aus dem Jahr 1904, in der er den Bohr-Effekt beschrieb, der zeigte, dass die Fähigkeit von Hämoglobin im Blut, sich an Sauerstoff zu binden, umgekehrt war hängt mit dem Säuregehalt des Blutes und der Kohlendioxidkonzentration zusammen. Die pH-Skala wurde 1909 von einem anderen Dänen, Sørensen, eingeführt, und 1912 veröffentlichte Hasselbalch Messungen des pH-Werts von Blut. Im Jahr 1916 drückte Hasselbalch die Henderson-Gleichung logarithmisch aus, was mit der logarithmischen Skala des pH-Werts übereinstimmte, und so war die Henderson-Hasselbalch-Gleichung geboren. Dieser Text wurde angepasst von<a href="https://openstax.org/books/chemistry-2e/pages/14-6-buffers"> Openstax, Chemistry 2e, Section 14.6: Buffers</a>.

Henderson-Hasselbalch-Gleichung

Der Ausdruck der Ionisationskonstante für die Lösung einer schwachen Säure kann wie folgt geschrieben werden:

Die Neuanordnung zur Auflösung von [H3O+] ergibt:

Das Negative nehmen ...

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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

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,...

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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 Chemie erweckt allgemeine Konzepte der Chemie durch kompakte und leicht verständliche animierte Videolektionen zum Leben. Außerdem zeigen wir in den Videos Wissenschaftler in Aktion bei klassischen und neuartigen Forschungsexperimenten, wie sie heutzutage in Laboren weltweit durchgeführt wurden.

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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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