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Henderson–Hasselbalch equation

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In chemistry and biochemistry , the Henderson–Hasselbalch equation pH = p K a + log 10 ⁡ ( [ Base ] [ Acid ] ) {\displaystyle {\ce {pH}}={\ce {p}}K_{{\ce {a}}}+\log _{10}\left({\frac {[{\ce {Base}}]}{[{\ce {Acid}}]}}\right)} relates the pH of a chemical solution of a weak acid to the numerical value of the acid dissociation constant , K a , of acid and the ratio of the concentrations, [ Base ] [ Acid ] {\displaystyle {\frac {[{\ce {Base}}]}{[{\ce {Acid}}]}}} of the acid and its conjugate base in an equilibrium.

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38-568: The Henderson–Hasselbalch equation can be used to estimate the pH of a buffer solution by approximating the actual concentration ratio as the ratio of the analytical concentrations of the acid and of a salt, MA. The equation can also be applied to bases by specifying the protonated form of the base as the acid. For example, with an amine , R N H 2 {\displaystyle \mathrm {RNH_{2}} } The Henderson-Hasselbach buffer system also has many natural and biological applications. The Henderson-Hasselbalch equation

76-472: A good approximation. Assumption 3 : The salt MA is completely dissociated in solution. For example, with sodium acetate the concentration of the sodium ion, [Na] can be ignored. This is a good approximation for 1:1 electrolytes, but not for salts of ions that have a higher charge such as magnesium sulphate , MgSO 4 , that form ion pairs . Assumption 4 : The quotient of activity coefficients, Γ {\displaystyle \Gamma } ,

114-538: A mixture of ice VI and the enneahydrate MgSO 4 ·9H 2 O . The enneahydrate MgSO 4 ·9H 2 O was identified and characterized only recently, even though it seems easy to produce (by cooling a solution of MgSO 4 and sodium sulfate Na 2 SO 4 in suitable proportions). The structure is monoclinic, with unit-cell parameters at 250 K: a  = 0.675  nm , b  = 1.195 nm, c  = 1.465 nm, β = 95.1°, V = 1.177 nm with Z  = 4. The most probable space group

152-404: A quotient, Γ {\displaystyle \Gamma } , of activity coefficients γ H + γ A − γ H A {\displaystyle {\frac {\gamma _{{\ce {H+}}}\gamma _{{\ce {A^-}}}}{\gamma _{HA}}}} . In these expressions, the quantities in square brackets signify

190-546: Is P21/c. Magnesium selenate also forms an enneahydrate MgSeO 4 ·9H 2 O , but with a different crystal structure. As Mg and SO 2− 4 ions are respectively the second most abundant cation and anion present in seawater after Na and Cl , magnesium sulfates are common minerals in geological environments. Their occurrence is mostly connected with supergene processes. Some of them are also important constituents of evaporitic potassium -magnesium (K-Mg) salts deposits. Bright spots observed by

228-407: Is a chemical compound , a salt with the formula MgSO 4 , consisting of magnesium cations Mg (20.19% by mass) and sulfate anions SO 2− 4 . It is a white crystalline solid , soluble in water but not in ethanol . Magnesium sulfate is usually encountered in the form of a hydrate MgSO 4 · n H 2 O , for various values of n between 1 and 11. The most common

266-439: Is a constant under the experimental conditions covered by the calculations. The thermodynamic equilibrium constant, K ∗ {\displaystyle K^{*}} , is a product of a quotient of concentrations [ H + ] [ A − ] [ HA ] {\displaystyle {\frac {[{\ce {H+}}][{\ce {A^-}}]}{[{\ce {HA}}]}}} and

304-474: Is an association constant, K b , which is simply related to the dissociation constant of the conjugate acid, BH. The value of p K w {\displaystyle \mathrm {pK_{w}} } is ca. 14 at 25°C. This approximation can be used when the correct value is not known. Thus, the Henderson–Hasselbalch equation can be used, without modification, for bases. With homeostasis

342-436: Is environmentally friendly, it does none of the purported claims except for correcting magnesium deficiency in soils. Magnesium sulfate can even pollute water if used in excessive amounts. Magnesium sulfate was historically used as a treatment for lead poisoning prior to the development of chelation therapy , as it was hoped that any lead ingested would be precipitated out by the magnesium sulfate and subsequently purged from

380-499: Is its high solubility , which also allows the option of foliar feeding . Solutions of magnesium sulfate are also nearly pH neutral, compared with the slightly alkaline salts of magnesium as found in limestone ; therefore, the use of magnesium sulfate as a magnesium source for soil does not significantly change the soil pH . Contrary to the popular belief that magnesium sulfate is able to control pests and slugs, helps seeds germination, produce more flowers, improve nutrient uptake, and

418-463: Is liberated and the following equation may be used instead. C O 2 ( g ) {\displaystyle \mathrm {CO_{2}(g)} } represents the carbon dioxide liberated as gas. In this equation, which is widely used in biochemistry, K m {\displaystyle K^{m}} is a mixed equilibrium constant relating to both chemical and solubility equilibria. It can be expressed as where [HCO 3 ]

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456-447: Is mainly utilized in the production of lightweight insulation panels, although its poor water resistance limits its usage. Magnesium (or sodium) sulfate is also used for testing aggregates for soundness in accordance with ASTM C88 standard, when there are no service records of the material exposed to actual weathering conditions. The test is accomplished by repeated immersion in saturated solutions followed by oven drying to dehydrate

494-544: Is slowly depleted in their calcification process. In a magnesium-deficient marine aquarium, calcium and alkalinity concentrations are very difficult to control because not enough magnesium is present to stabilize these ions in the saltwater and prevent their spontaneous precipitation into calcium carbonate . Double salts containing magnesium sulfate exist. There are several known as sodium magnesium sulfates and potassium magnesium sulfates . A mixed copper -magnesium sulfate heptahydrate (Mg,Cu)SO 4 ·7H 2 O

532-434: Is stable at atmospheric pressure only below 2 °C. Above that temperature, it liquefies into a mix of solid heptahydrate and a saturated solution . It has a eutectic point with water at −3.9 °C and 17.3% (mass) of MgSO 4 . Large crystals can be obtained from solutions of the proper concentration kept at 0 °C for a few days. At pressures of about 0.9 GPa and at 240 K , meridianiite decomposes into

570-510: Is such an acid. Assumption 2 . The self-ionization of water can be ignored. This assumption is not, strictly speaking, valid with pH values close to 7, half the value of pK w , the constant for self-ionization of water . In this case the mass-balance equation for hydrogen should be extended to take account of the self-ionization of water. However, the term K w / [ H + ] {\displaystyle \mathrm {K_{w}/[H^{+}]} } can be omitted to

608-477: Is the concentration the hydrogen ion that has been added to the solution. The self-dissociation of water is ignored. A quantity in square brackets, [X], represents the concentration of the chemical substance X. It is understood that the symbol H stands for the hydrated hydronium ion. K a is an acid dissociation constant . The Henderson–Hasselbalch equation can be applied to a polybasic acid only if its consecutive p K values differ by at least 3. Phosphoric acid

646-417: Is the formulation as bath salts , especially for foot baths to soothe sore feet. Such baths have been claimed to also soothe and hasten recovery from muscle pain, soreness, or injury. Potential health effects of magnesium sulfate are reflected in medical studies on the impact of magnesium on resistant depression and as an analgesic for migraine and chronic pain . Magnesium sulfate has been studied in

684-402: Is the heptahydrate MgSO 4 ·7H 2 O , known as Epsom salt , which is a household chemical with many traditional uses, including bath salts . The main use of magnesium sulfate is in agriculture, to correct soils deficient in magnesium (an essential plant nutrient because of the role of magnesium in chlorophyll and photosynthesis ). The monohydrate is favored for this use; by

722-616: Is the molar concentration of bicarbonate in the blood plasma and P CO 2 is the partial pressure of carbon dioxide in the supernatant gas. Davenport, Horace W. (1974). The ABC of Acid-Base Chemistry: The Elements of Physiological Blood-Gas Chemistry for Medical Students and Physicians (Sixth ed.). Chicago: The University of Chicago Press. PH">pH The requested page title contains unsupported characters : ">". Return to Main Page . Magnesium sulphate Magnesium sulfate or magnesium sulphate

760-545: Is the next lower hydrate. Three next lower hydrates – pentahydrite , starkeyite , and especially sanderite – are rare. Kieserite is a monohydrate and is common among evaporitic deposits. Anhydrous magnesium sulfate was reported from some burning coal dumps . Magnesium sulfate is usually obtained directly from dry lake beds and other natural sources. It can also be prepared by reacting magnesite ( magnesium carbonate , MgCO 3 ) or magnesia ( oxide , MgO) with sulfuric acid ( H 2 SO 4 ): Another possible method

798-446: Is the primary mechanism that causes the absorption of sound in seawater at frequencies above 10  kHz ( acoustic energy is converted to thermal energy ). Lower frequencies are less absorbed by the salt, so that low frequency sound travels farther in the ocean. Boric acid and magnesium carbonate also contribute to absorption. Magnesium sulfate is used both externally (as Epsom salt) and internally. The main external use

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836-435: Is to treat seawater or magnesium-containing industrial wastes so as to precipitate magnesium hydroxide and react the precipitate with sulfuric acid . Also, magnesium sulfate heptahydrate ( epsomite , MgSO 4 ·7H 2 O ) is manufactured by dissolution of magnesium sulfate monohydrate ( kieserite , MgSO 4 ·H 2 O ) in water and subsequent crystallization of the heptahydrate. Magnesium sulfate relaxation

874-500: Is treated with anhydrous magnesium sulfate. The hydrated solid is then removed by filtration , decantation , or by distillation (if the boiling point is low enough). Other inorganic sulfate salts such as sodium sulfate and calcium sulfate may be used in the same way. Magnesium sulfate is used to prepare specific cements by the reaction between magnesium oxide and magnesium sulfate solution, which are of good binding ability and more resistance than Portland cement . This cement

912-544: The Dawn Spacecraft in Occator Crater on the dwarf planet Ceres are most consistent with reflected light from magnesium sulfate hexahydrate. Almost all known mineralogical forms of MgSO 4 are hydrates. Epsomite is the natural analogue of "Epsom salt". Meridianiite , MgSO 4 ·11H 2 O , has been observed on the surface of frozen lakes and is thought to also occur on Mars. Hexahydrite

950-453: The UK , a medication containing magnesium sulfate and phenol , called "drawing paste", is useful for small boils or localized infections and removing splinters. Internally, magnesium sulfate may be administered by oral, respiratory, or intravenous routes. Internal uses include replacement therapy for magnesium deficiency , treatment of acute and severe arrhythmias , as a bronchodilator in

988-538: The digestive system . This application saw particularly widespread use among veterinarians during the early-to-mid 20th century; Epsom salt was already available on many farms for agricultural use, and it was often prescribed in the treatment of farm animals that had inadvertently ingested lead. Magnesium sulfate is used as: Anhydrous magnesium sulfate is commonly used as a desiccant in organic synthesis owing to its affinity for water and compatibility with most organic compounds. During work-up , an organic phase

1026-406: The pH of a solution containing a mixture of the two components to the acid dissociation constant , K a of the acid, and the concentrations of the species in solution. To derive the equation a number of simplifying assumptions have to be made. Assumption 1 : The acid, HA, is monobasic and dissociates according to the equations C A is the analytical concentration of the acid and C H

1064-404: The Henderson–Hasselbalch equation pH = p K a + log 10 ⁡ ( [ A − ] [ HA ] ) {\displaystyle {\ce {pH}}={\ce {p}}K_{{\ce {a}}}+\log _{10}\left({\frac {[{\ce {A^-}}]}{[{\ce {HA}}]}}\right)} The equilibrium constant for the protonation of a base, B,

1102-630: The anhydrous form is stable. It decomposes without melting at 1124 °C into magnesium oxide (MgO) and sulfur trioxide ( SO 3 ). The heptahydrate takes its common name "Epsom salt" from a bitter saline spring in Epsom in Surrey , England, where the salt was produced from the springs that arise where the porous chalk of the North Downs meets the impervious London clay . The heptahydrate readily loses one equivalent of water to form

1140-490: The concentration of the undissociated acid, HA, of the hydrogen ion H, and of the anion A; the quantities γ {\displaystyle \gamma } are the corresponding activity coefficients . If the quotient of activity coefficients can be assumed to be a constant which is independent of concentrations and pH, the dissociation constant, K a can be expressed as a quotient of concentrations. Rearrangement of this expression and taking logarithms provides

1178-683: The hexahydrate. It is a natural source of both magnesium and sulphur . Epsom salts are commonly used in bath salts , exfoliants , muscle relaxers and pain relievers. However, these are different from Epsom salts that are used for gardening, as they contain aromas and perfumes not suitable for plants. Magnesium sulfate monohydrate, or kieserite, can be prepared by heating the heptahydrate to 120 °C. Further heating to 250 °C gives anhydrous magnesium sulfate. Kieserite exhibits monoclinic symmetry at pressures lower than 2.7 GPa after which it transforms to phase of triclinic symmetry. The undecahydrate MgSO 4 ·11H 2 O , meridianiite ,

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1216-431: The mid 1970s, its production was 2.3 million tons per year. The anhydrous form and several hydrates occur in nature as minerals , and the salt is a significant component of the water from some springs . Magnesium sulfate can crystallize as several hydrates , including: As of 2017, the existence of the decahydrate apparently has not been confirmed. All the hydrates lose water upon heating. Above 320 °C, only

1254-490: The pH of a biological solution is maintained at a constant value by adjusting the position of the equilibria where H C O 3 − {\displaystyle \mathrm {HCO_{3}^{-}} } is the bicarbonate ion and H 2 C O 3 {\displaystyle \mathrm {H_{2}CO_{3}} } is carbonic acid . However, the solubility of carbonic acid in water may be exceeded. When this happens carbon dioxide gas

1292-406: The pH terminology, which allowed Karl Albert Hasselbalch to re-express Henderson's equation in logarithmic terms , resulting in the Henderson–Hasselbalch equation. A simple buffer solution consists of a solution of an acid and a salt of the conjugate base of the acid. For example, the acid may be acetic acid and the salt may be sodium acetate . The Henderson–Hasselbalch equation relates

1330-450: The salt precipitated in permeable pore spaces . The internal expansive force, derived from the rehydration of the salt upon re-immersion, simulates the expansion of water on freezing . Magnesium sulfate is also used to test the resistance of concrete to external sulfate attack (ESA). Magnesium sulfate heptahydrate is also used to maintain the magnesium concentration in marine aquaria which contain large amounts of stony corals , as it

1368-414: The treatment of asthma , preeclampsia and eclampsia . Magnesium sulfate is usually the main component of the concentrated salt solution used in isolation tanks to increase its specific gravity to approximately 1.25–1.26. This high density allows an individual to float effortlessly on the surface of water in the closed tank, eliminating stimulation of as many of the external senses as possible. In

1406-514: The treatment of asthma , preventing eclampsia and cerebral palsy , a tocolytic agent, and as an anticonvulsant . It also may be used as laxative . In agriculture , magnesium sulfate is used to increase magnesium or sulfur content in soil . It is most commonly applied to potted plants, or to magnesium-hungry crops such as potatoes , tomatoes , carrots , peppers , lemons , and roses . The advantage of magnesium sulfate over other magnesium soil amendments (such as dolomitic lime )

1444-428: Was developed by two scientists, Lawrence Joseph Henderson and Karl Albert Henderson . Lawrence Joseph Henderson was a biological chemist and Karl Albert Hasselbach was a physiologist who studied pH. In 1908, Lawrence Joseph Henderson derived an equation to calculate the hydrogen ion concentration of a bicarbonate buffer solution, which rearranged looks like this: In 1909 Søren Peter Lauritz Sørensen introduced

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