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

ניתן לחשב את ה-pH של תמיסת עם הבופר, המכילה זוג חומצה-בסיס מצומדים, באמצעות משוואת הנדרסון-האסלבאך כחלופה לטבלת ICE. משוואת הנדרסון-האסלבאך נגזרת מביטוי קבוע שיווי המשקל עבור Ka.ניתן לסדר מחדש את הביטוי כדי למצוא את ריכוז יוני ההידרוניום. אם ניקח את הלוגריתם השלילי של שני הצדדים, הלוגריתם השלילי של ריכוז יוני ההידרוניום והלוגריתם השלילי של קבוע פירוק החומצה ניתנים להחלפה עם pH ו-pKa, בהתאמה.כך נוצרת משוואה בה ניתן לחשב את ה-pH של בופר על ידי הוספת ה-pKa והלוג של ריכוזי שיווי המשקל של בסיס מצומד חלקי חומצתו החלשה. ערכי שיווי משקל אלה ניתנים להחלפה בריכוזים ההתחלתיים, אם השינוי בריכוז יוני ההידרוניום, x, קטן מ-5%מהריכוזים ההתחלתיים של החומצה החלשה ושל הבסיס המצומד. משוואת הנדרסון-האסלבאך מראה גם את יחס החומצה-בסיס הנדרש להכנת בופר ב-pH ספציפי.בדומה לכך, ניתן למצוא את ה-pH של תמיסה המכילה בסיס חלש ואת החומצה המצומדת שלו, באמצעות משוואה זו, על-ידי חישוב ה-pKa של החומצה המצומדת לו מה-pKb באמצעות הנוסחה:pKa ועוד pKb שווה ל-14. ניתן למצוא את ה-pH של בופר המכיל חומצה פורמית 0.15 מולר ונתרן פורמאט 0.18 מולר, באמצעות משוואת הנדרסון-האסלבאך או דרך ה-Ka של החומצה הפורמית וטבלת ICE. אך משוואת הנדרסון-האסלבאך היא שיטה מהירה יותר לחישוב ה-pH כאשר בתגובה מעורבים זוג חומצה בסיס מצומדים, והשינוי בריכוז ההידרוניום הוא קטן.כדי למצוא את ה-pKa, לוקחים את הלוגריתם השלילי של ה-Ka של חומצה פורמית, השווה ל-3.75. כשמכניסים את ריכוזי ההתחלה של חומצה פורמית ופורמאט אל תוך המשוואה, ה-pH של התמיסה שווה ל-3.83. בערך ה-pH ניתן להשתמש כדי לקבוע את ריכוז יון ההידרוניום, 1.5 כפול 10 בחזקת מינוס 4.כיוון שערך זה קטן מ-5%מחומצה פורמית 0.15 מולר, הקירובים, הנדרשים על מנת להשתמש במשוואת הנדרסון-האסלבאך, הם תקפים.

דה לוי, רוברט. "משוואת הנדרסון-האסלבלך: ההיסטוריה והמגבלות שלה". כתב עת לחינוך כימי 80, מס '2 (2003): 146. <a href="https://pubs.acs.org/doi/pdf/10.1021/ed080p146">https://pubs.acs.org/doi/pdf/10.1021/ed080p146.</a>

משוואת הנדרסון-האסלבאך

<div style="direction:rtl">ניתן לכתוב את הביטוי קבוע היינון לתמיסה של חומצה חלשה כך: <img alt="Eq1" src="/files/ftp_upload/11410/11410_Equation_1.png" style="text-align: center; height: 90px;"> ארגון מחדש כדי לפתור עבור-[H3O+] מניב: <img alt="Eq2" src="/files/ftp_upload/11410/11410_Equation_2.png" style="text-align: center; height: 90px;"> לקיחת הלוגריתם השלילי של שני הצדדים של המשוואה הזו נותן: <img alt="Eq3" src="/files/ftp_upload/11410/11410_Equation_3.png" style="text-align: center; height: 90px;"> שאפשר לכתוב בתור: <img alt="Eq4" src="/files/ftp_upload/11410/11410_Equation_4.png" style="text-align: center; height: 90px;"> כאשר pKa הוא השלילי של הלוגריתם של קבוע היינון של החומצה החלשה (pKa = −log Ka). משוואה זו מקשרת בין ה-pH, קבוע היינון של חומצה חלשה, לבין הריכוזים של זוג החומצה-בסיסים המצומדים החלשים בתמיסה מבוקרת. מדענים משתמשים לעתים קרובות בביטוי זה, הנקרא משוואת הנדרסון-האסלבאך, כדי לחשב את ה-pH של תמיסות בופר. חשוב לציין שהנחת "x קטן" חייבת להיות תקפה כדי להשתמש במשוואה זו. לורנס ג'וזף הנדרסון וקרל אלברט האסלבאך לורנס ג'וזף הנדרסון (1878–1942) היה רופא, ביוכימאי ופיזיולוגי אמריקאי, אם למנות רק כמה מעיסוקיו הרבים. הוא השיג תואר ברפואה מהרווארד ולאחר מכן בילה שנתיים בלימודים בשטרסבורג, אז חלק מגרמניה, לפני שחזר לתפקיד המרצה בהרווארד. בסופו של דבר הוא הפך לפרופסור בהרווארד ועבד שם כל חייו. הוא גילה שמאזן חומצה-בסיס בדם אנושי מווסת על ידי מערכת בופר שנוצרת על ידי הפחמן הדו-חמצני המומס בדם. הוא כתב משוואה בשנת 1908 כדי לתאר את מערכת הבופר של חומצה פחמנית-קרבונטית בדם. הנדרסון היה בעל ידע נרחב; בנוסף למחקר החשוב שלו על הפיזיולוגיה של הדם, הוא כתב גם על ההסתגלות של אורגניזמים והתאמתם לסביבתם, על סוציולוגיה ועל חינוך אוניברסיטאי. הוא גם ייסד את מעבדת העייפות בבית הספר לעסקים של הרווארד, שבדקה את הפיזיולוגיה של האדם תוך התמקדות ספציפית בעבודה, תעשייה, פעילות גופנית ותזונה. בשנת 1916, קרל אלברט האסלבאך (1874–1962), רופא וכימאי דני, שותף במאמר עם כריסטיאן בוהר ב-1904 שתיאר את אפקט בוהר, שהראה כי יכולת ההמוגלובין בדם להיקשר עם חמצן הייתה קשורה בהפוך לחומציות הדם ולריכוז הפחמן הדו חמצני. סולם ה-pH הוצג ב-1909 על ידי דני אחר, סורנסן, ובשנת 1912 פרסם האסלבאך מדידות של ה-pH של הדם. בשנת 1916, האסלבאך ביטא את המשוואה של הנדרסון במונחים לוגריתמיים, בהתאם לסולם הלוגריתמי של pH, וכך נולדה משוואת הנדרסון-האסלבאך. טקסט זה מותאם מ<a href="https://openstax.org/books/chemistry-2e/pages/14-6-buffers"> Openstax, Chemistry 2e, Section 14.6: Buffers</a>.</div>

ניתן לכתוב את הביטוי קבוע היינון לתמיסה של חומצה חלשה כך:

סידור מחדש לפתרון תפוקות [H3O+]:

לוקח את השלילי ...

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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

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

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titration calculations: strong acid - strong base

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titration calculations: weak acid - strong base

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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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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

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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

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

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JoVE Core Chemistry brings general chemistry concepts to life using concise and easy-to-understand animated video lessons. Plus, in the scientist-in-action videos, we demonstrate classical and original research experiments performed in today's laboratories worldwide.

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Mixtures of Acids

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le-chatelier-s-principle-changing-temperature

Le Chatelier's Principle: Changing Temperature

Consistent with the law of mass action, an equilibrium stressed by a change in concentration will shift to re-establish equilibrium without any change in ...

Ions as Acids and Bases

Salts with Acidic Ions
Salts are ionic compounds composed of cations and anions, either of which may be capable of undergoing an acid or base ionization ...

Bronsted-Lowry Acids and Bases

The acid-base reaction class has been studied for quite some time. In 1680, Robert Boyle reported traits of acid solutions that included their ability to ...

Determining the pH of Salt Solutions

The pH of a salt solution is determined by its component anions and cations. Salts that contain pH-neutral anions and the hydronium ion-producing cations ...

acidbase-strengths-and-dissociation-constants

Acid/Base Strengths and Dissociation Constants

The relative strength of an acid or base is the extent to which it ionizes when dissolved in water. If the ionization reaction is essentially complete, ...

Polyprotic Acids

Acids are classified by the number of protons per molecule that they can give up in a reaction. Acids such as HCl, HNO3, and HCN that contain one ...

Water: A Bronsted-Lowry Acid and Base

The reaction between a Br&#248;nsted-Lowry acid and water is called acid ionization. For example, when hydrogen fluoride dissolves in water and ionizes, ...

Chemical reactions
• Types of reactions
• Kinetics
• Energy
• Equilibrium
• Acids/bases

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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