Как изменить ph буферного раствора - Исправление ошибок и поиск оптимальных решений проблем

Механизм действия буферных систем:

1.
Разбавление.
При разбавлении водой происходит
уменьшение концентрации обоих компонентов
в буферной системе в одинаковой степени,
поэтому величина их соотношения не
изменится. рК_{(кислоты)}
и рК_{(основания)}
являются постоянными при данной
температуре и не зависят от разбавления.
Действительно, одновременное понижение
концентраций кислоты и соли в ацетатной
буферной системе от 0,1М до 0,001М при
разбавлении водой изменяет рН буферного
раствора с 4,63 до 4,73 (это ничтожное
изменение рН при разбавлении буферного
раствора в 100 раз обусловлено некоторым
изменением коэффициента активности
соли). Следовательно, разбавление
в конечном итоге мало
изменяет рН буферных систем.

2.
Добавление
кислот и оснований. При
добавлении небольших количеств сильных
кислот или оснований рН буферных систем
изменяется незначительно. Например,
рассмотрим ацетатный буфер:

СН₃СООН /
СН₃СОО^–

кислотный компонент
– основной компонент–

слабая кислота
сопряженное основание

а)
При добавлении к ацетатному буферу
небольшого количества HCl, происходит
взаимодействие ионов Н⁺
с основным компонентом буферного
раствора:

Н⁺
+ СН₃СОО^–
⇄
СН₃СООН.

Степень
диссоциации СН₃СООН
мала и концентрация [H⁺]
практически не меняется. рН буферного
раствора уменьшится, но незначительно.

Таким
образом, если к ацетатному буферу
добавить Х моль/л HCl,
то уравнение для расчета рН буферной
системы принимает вид:

рН
= рК_{(кислоты)}
+ lg

б)
При добавлении
небольшого количества NaOH, –
ионы нейтрализуются кислотным компонентом
буферного раствора:

+
СН₃СООН
⇄
СН₃СОО
^–
+ Н₂О.

В
результате этого, добавленное сильное
основание заменяется эквивалентным
количеством слабого сопряженного
основания (СН₃СОО^–),
которое в меньшей степени влияет на
реакцию cреды. рН буферного раствора
увеличивается, но незначительно.

Таким
образом, если к ацетатному буферу
добавить У моль/л NaOH,
то уравнение для расчета рН буферной
системы принимает вид:

рН
= рК_{(кислоты)}
+ lg

Буферная емкость

Способность
буферного раствора сохранять значение
рН при добавлении сильной кислоты или
щелочи приблизительно на постоянном
уровне характеризует буферная емкость.

Буферная емкость
(В) — это число молей эквивалента сильной
кислоты или щелочи, которое необходимо
добавить к 1 л буферного раствора, чтобы
сместить его рН на единицу.

Буферная
емкость системы определяется по отношению
к добавляемым кислоте (В_кисл.)
или основанию (щелочи) (В_осн.)
и рассчитывается по формулам:

В_кисл.=

В_осн.=

где
V(HA), V(B) — объемы добавленных кислоты или
щелочи, л.; С_н(НА),
С_н(В)
— молярные концентрации эквивалента
соответственно кислоты и щелочи; V(б.р.)
— объем исходного буферного раствора,
л.; рН_о,
рН — значения рН буферного раствора до
и после добавления кислоты или щелочи;
|рН-рН_о|
— разность рН по модулю.

Буферная
емкость по отношению к кислоте (В_кисл.)
определяется концентрацией (количеством
эквивалентов) компонента с основными
свойствами; буферная емкость по отношению
к основанию (В_осн.)
определяется концентрацией (количеством
эквивалентов) компонента с кислотными
свойствами в буферном растворе.

Максимальная
буферная емкость при добавлении сильных
кислот и оснований достигается при
соотношении компонентов буферного
раствора равном единице, когда рН = рК,
при этом В_осн.
= В _кисл.
(рис.1).

Рис.1. Изменение
буферной емкости в зависимости от
величины

отношения
[соль]/[кислота].

Поэтому, применение
любой буферной смеси ограничено
определенной областью рН (областью
буферирования), а именно:

рН
= рК_{(кислоты)}

1 для кислотных систем, или

рН=
14 – (рК_{(основания)}

1) для основных систем.

Буферная емкость
зависит не только от отношения концентраций
компонентов буферного раствора, но и
от общей концентрации буферной смеси.

Пусть, например,
даны два буферных раствора, один из
которых содержит по 100, а другой – по 10
миллимолей уксусной кислоты и ацетата
натрия. Сравним, как изменяются их рН
при добавлении к 1 л каждого раствора 5
миллимолей соляной кислоты.

Добавляемая кислота
вступит в реакцию с ацетатом натрия, и
это отношение в первом растворе станет
равным 0,9, а во втором 0,33. В итоге у первого
раствора отношение соль/кислота и,
следовательно, величина рН изменились
меньше. Отсюда видно, что первый буферный
раствор обладает большей буферной
емкостью.

Таким
образом, буферная
емкость в основном зависит от соотношения
концентраций компонентов и их абсолютных
концентраций, а следовательно, от
разбавления.

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From Wikipedia, the free encyclopedia

A buffer solution (more precisely, pH buffer or hydrogen ion buffer) is an acid or a base aqueous solution consisting of a mixture of a weak acid and its conjugate base, or vice versa. Its pH changes very little when a small amount of strong acid or base is added to it. Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide variety of chemical applications. In nature, there are many living systems that use buffering for pH regulation. For example, the bicarbonate buffering system is used to regulate the pH of blood, and bicarbonate also acts as a buffer in the ocean.

Principles of buffering[edit]

Figure 1. Simulated titration of an acidified solution of a weak acid (pK_a = 4.7) with alkali

Buffer solutions resist pH change because of a chemical equilibrium between the weak acid HA and its conjugate base A⁻:

HA ⇌ H⁺ + A⁻

When some strong acid is added to an equilibrium mixture of the weak acid and its conjugate base, hydrogen ions (H⁺) are added, and the equilibrium is shifted to the left, in accordance with Le Chatelier’s principle. Because of this, the hydrogen ion concentration increases by less than the amount expected for the quantity of strong acid added.
Similarly, if strong alkali is added to the mixture, the hydrogen ion concentration decreases by less than the amount expected for the quantity of alkali added. In figure 1, the effect is illustrated by the simulated titration of a weak acid with pK_a = 4.7. The relative concentration of undissociated acid is shown in blue, and of its conjugate base in red. The pH changes relatively slowly in the buffer region, pH = pK_a ± 1, centered at pH = 4.7, where [HA] = [A⁻]. The hydrogen ion concentration decreases by less than the amount expected because most of the added hydroxide ion is consumed in the reaction

OH⁻ + HA → H₂O + A⁻

and only a little is consumed in the neutralization reaction (which is the reaction that results in an increase in pH)

OH⁻ + H⁺ → H₂O.

Once the acid is more than 95% deprotonated, the pH rises rapidly because most of the added alkali is consumed in the neutralization reaction.

Buffer capacity[edit]

Buffer capacity is a quantitative measure of the resistance to change of pH of a solution containing a buffering agent with respect to a change of acid or alkali concentration. It can be defined as follows:^[1]^[2]

${displaystyle beta ={frac {dC_{b}}{d(mathrm {pH} )}},}$

where ${displaystyle dC_{b}}$ is an infinitesimal amount of added base, or

${displaystyle beta =-{frac {dC_{a}}{d(mathrm {pH} )}},}$

where ${displaystyle dC_{a}}$ is an infinitesimal amount of added acid. pH is defined as −log₁₀[H⁺], and d(pH) is an infinitesimal change in pH.

With either definition the buffer capacity for a weak acid HA with dissociation constant K_a can be expressed as^[3]^[4]^[2]

${displaystyle beta =2.303left([{ce {H+}}]+{frac {T_{{ce {HA}}}K_{a}[{ce {H+}}]}{(K_{a}+[{ce {H+}}])^{2}}}+{frac {K_{text{w}}}{[{ce {H+}}]}}right),}$

where [H⁺] is the concentration of hydrogen ions, and ${displaystyle T_{text{HA}}}$ is the total concentration of added acid. K_w is the equilibrium constant for self-ionization of water, equal to 1.0×10⁻¹⁴. Note that in solution H⁺ exists as the hydronium ion H₃O⁺, and further aquation of the hydronium ion has negligible effect on the dissociation equilibrium, except at very high acid concentration.

Figure 2. Buffer capacity β for a 0.1 M solution of a weak acid with a pK_a = 7

This equation shows that there are three regions of raised buffer capacity (see figure 2).

In the central region of the curve (coloured green on the plot), the second term is dominant, and

${displaystyle beta approx 2.303{frac {T_{{ce {HA}}}K_{a}[{ce {H+}}]}{(K_{a}+[{ce {H+}}])^{2}}}.}$

Buffer capacity rises to a local maximum at pH = pK_a. The height of this peak depends on the value of pK_a. Buffer capacity is negligible when the concentration [HA] of buffering agent is very small and increases with increasing concentration of the buffering agent.^[2] Some authors show only this region in graphs of buffer capacity.^[1] Buffer capacity falls to 33% of the maximum value at pH = pK_a ± 1, to 10% at pH = pK_a ± 1.5 and to 1% at pH = pK_a ± 2. For this reason the most useful range is approximately pK_a ± 1. When choosing a buffer for use at a specific pH, it should have a pK_a value as close as possible to that pH.^[1]
With strongly acidic solutions, pH less than about 2 (coloured red on the plot), the first term in the equation dominates, and buffer capacity rises exponentially with decreasing pH:

${displaystyle beta approx 10^{-mathrm {pH} }.}$

This results from the fact that the second and third terms become negligible at very low pH. This term is independent of the presence or absence of a buffering agent.
With strongly alkaline solutions, pH more than about 12 (coloured blue on the plot), the third term in the equation dominates, and buffer capacity rises exponentially with increasing pH:

${displaystyle beta approx 10^{mathrm {pH} -mathrm {p} K_{text{w}}}.}$

This results from the fact that the first and second terms become negligible at very high pH. This term is also independent of the presence or absence of a buffering agent.

Applications of buffers[edit]

The pH of a solution containing a buffering agent can only vary within a narrow range, regardless of what else may be present in the solution. In biological systems this is an essential condition for enzymes to function correctly. For example, in human blood a mixture of carbonic acid (H
₂CO
₃) and bicarbonate (HCO⁻
₃) is present in the plasma fraction; this constitutes the major mechanism for maintaining the pH of blood between 7.35 and 7.45. Outside this narrow range (7.40 ± 0.05 pH unit), acidosis and alkalosis metabolic conditions rapidly develop, ultimately leading to death if the correct buffering capacity is not rapidly restored.

If the pH value of a solution rises or falls too much, the effectiveness of an enzyme decreases in a process, known as denaturation, which is usually irreversible.^[5] The majority of biological samples that are used in research are kept in a buffer solution, often phosphate buffered saline (PBS) at pH 7.4.

In industry, buffering agents are used in fermentation processes and in setting the correct conditions for dyes used in colouring fabrics. They are also used in chemical analysis^[4] and calibration of pH meters.

Simple buffering agents[edit]

Buffering agent	pK_a	Useful pH range
Citric acid	3.13, 4.76, 6.40	2.1–7.4
Acetic acid	4.8	3.8–5.8
KH₂PO₄	7.2	6.2–8.2
CHES	9.3	8.3–10.3
Borate	9.24	8.25–10.25

For buffers in acid regions, the pH may be adjusted to a desired value by adding a strong acid such as hydrochloric acid to the particular buffering agent. For alkaline buffers, a strong base such as sodium hydroxide may be added. Alternatively, a buffer mixture can be made from a mixture of an acid and its conjugate base. For example, an acetate buffer can be made from a mixture of acetic acid and sodium acetate. Similarly, an alkaline buffer can be made from a mixture of the base and its conjugate acid.

«Universal» buffer mixtures[edit]

By combining substances with pK_a values differing by only two or less and adjusting the pH, a wide range of buffers can be obtained. Citric acid is a useful component of a buffer mixture because it has three pK_a values, separated by less than two. The buffer range can be extended by adding other buffering agents. The following mixtures (McIlvaine’s buffer solutions) have a buffer range of pH 3 to 8.^[6]

0.2 M Na₂HPO₄ (mL)	0.1 M citric acid (mL)	pH
20.55	79.45	3.0
38.55	61.45	4.0
51.50	48.50	5.0
63.15	36.85	6.0
82.35	17.65	7.0
97.25	2.75	8.0

A mixture containing citric acid, monopotassium phosphate, boric acid, and diethyl barbituric acid can be made to cover the pH range 2.6 to 12.^[7]

Other universal buffers are the Carmody buffer^[8] and the Britton–Robinson buffer, developed in 1931.

Common buffer compounds used in biology[edit]

For effective range see Buffer capacity, above. Also see Good’s buffers for the historic design principles and favourable properties of these buffer substances in biochemical applications.

Common name (chemical name)	pK_a, 25 °C	Temp. effect, dpH/dT (K⁻¹)^[9]	Mol. weight
TAPS, ([tris(hydroxymethyl)methylamino]propanesulfonic acid)	8.43	−0.018	243.3
Bicine, (2-(bis(2-hydroxyethyl)amino)acetic acid)	8.35	−0.018	163.2
Tris, (tris(hydroxymethyl)aminomethane, or 2-amino-2-(hydroxymethyl)propane-1,3-diol)	8.07^[a]	−0.028	121.14
Tricine, (N-[tris(hydroxymethyl)methyl]glycine)	8.05	−0.021	179.2
TAPSO, (3-[N-tris(hydroxymethyl)methylamino]-2-hydroxypropanesulfonic acid)	7.635		259.3
HEPES, (4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid)	7.48	−0.014	238.3
TES, (2-[[1,3-dihydroxy-2-(hydroxymethyl)propan-2-yl]amino]ethanesulfonic acid)	7.40	−0.020	229.20
MOPS, (3-(N-morpholino)propanesulfonic acid)	7.20	−0.015	209.3
PIPES, (piperazine-N,N′-bis(2-ethanesulfonic acid))	6.76	−0.008	302.4
Cacodylate, (dimethylarsenic acid)	6.27		138.0
MES, (2-(N-morpholino)ethanesulfonic acid)	6.15	−0.011	195.2

^ Tris is a base, the pK_a = 8.07 refers to its conjugate acid.

Calculating buffer pH[edit]

Monoprotic acids[edit]

First write down the equilibrium expression

HA ⇌ A⁻ + H⁺

This shows that when the acid dissociates, equal amounts of hydrogen ion and anion are produced. The equilibrium concentrations of these three components can be calculated in an ICE table (ICE standing for «initial, change, equilibrium»).

ICE table for a monoprotic acid

	[HA]	[A⁻]	[H⁺]
I	C₀	0	y
C	−x	x	x
E	C₀ − x	x	x + y

The first row, labelled I, lists the initial conditions: the concentration of acid is C₀, initially undissociated, so the concentrations of A⁻ and H⁺ would be zero; y is the initial concentration of added strong acid, such as hydrochloric acid. If strong alkali, such as sodium hydroxide, is added, then y will have a negative sign because alkali removes hydrogen ions from the solution. The second row, labelled C for «change», specifies the changes that occur when the acid dissociates. The acid concentration decreases by an amount −x, and the concentrations of A⁻ and H⁺ both increase by an amount +x. This follows from the equilibrium expression. The third row, labelled E for «equilibrium», adds together the first two rows and shows the concentrations at equilibrium.

To find x, use the formula for the equilibrium constant in terms of concentrations:

${displaystyle K_{text{a}}={frac {[{ce {H+}}][{ce {A-}}]}{[{ce {HA}}]}}.}$

Substitute the concentrations with the values found in the last row of the ICE table:

${displaystyle K_{text{a}}={frac {x(x+y)}{C_{0}-x}}.}$

Simplify to

${displaystyle x^{2}+(K_{text{a}}+y)x-K_{text{a}}C_{0}=0.}$

With specific values for C₀, K_a and y, this equation can be solved for x. Assuming that pH = −log₁₀[H⁺], the pH can be calculated as pH = −log₁₀(x + y).

Polyprotic acids[edit]

Polyprotic acids are acids that can lose more than one proton. The constant for dissociation of the first proton may be denoted as K_a1, and the constants for dissociation of successive protons as K_a2, etc. Citric acid is an example of a polyprotic acid H₃A, as it can lose three protons.

Stepwise dissociation constants

Equilibrium	Citric acid
H₃A ⇌ H₂A⁻ + H⁺	pK_a1 = 3.13
H₂A⁻ ⇌ HA²⁻ + H⁺	pK_a2 = 4.76
HA²⁻ ⇌ A³⁻ + H⁺	pK_a3 = 6.40

When the difference between successive pK_a values is less than about 3, there is overlap between the pH range of existence of the species in equilibrium. The smaller the difference, the more the overlap. In the case of citric acid, the overlap is extensive and solutions of citric acid are buffered over the whole range of pH 2.5 to 7.5.

Calculation of the pH with a polyprotic acid requires a speciation calculation to be performed. In the case of citric acid, this entails the solution of the two equations of mass balance:

${displaystyle {begin{aligned}C_{{ce {A}}}&=[{ce {A^3-}}]+beta _{1}[{ce {A^3-}}][{ce {H+}}]+beta _{2}[{ce {A^3-}}][{ce {H+}}]^{2}+beta _{3}[{ce {A^3-}}][{ce {H+}}]^{3},\C_{{ce {H}}}&=[{ce {H+}}]+beta _{1}[{ce {A^3-}}][{ce {H+}}]+2beta _{2}[{ce {A^3-}}][{ce {H+}}]^{2}+3beta _{3}[{ce {A^3-}}][{ce {H+}}]^{3}-K_{text{w}}[{ce {H+}}]^{-1}.end{aligned}}}$

C_A is the analytical concentration of the acid, C_H is the analytical concentration of added hydrogen ions, β_q are the cumulative association constants. K_w is the constant for self-ionization of water. There are two non-linear simultaneous equations in two unknown quantities [A³⁻] and [H⁺]. Many computer programs are available to do this calculation. The speciation diagram for citric acid was produced with the program HySS.^[10]

N.B. The numbering of cumulative, overall constants is the reverse of the numbering of the stepwise, dissociation constants.

Relationship between cumulative association constant (β) values and stepwise dissociation constant (K) values for a tribasic acid.

Equilibrium	Relationship
A³⁻ + H⁺ ⇌ AH²⁺	Log β₁= pk_a3
A³⁻ + 2H⁺ ⇌ AH₂⁺	Log β₂ =pk_a2 + pk_a3
A³⁻ + 3H⁺⇌ AH₃	Log β₃ = pk_a1 + pk_a2 + pk_a3

Cumulative association constants are used in general-purpose computer programs such as the one used to obtain the speciation diagram above.

References[edit]

^ ^a ^b ^c Skoog, Douglas A.; West, Donald M.; Holler, F. James; Crouch, Stanley R. (2014). Fundamentals of Analytical Chemistry (9th ed.). Brooks/Cole. p. 226. ISBN 978-0-495-55828-6.
^ ^a ^b ^c Urbansky, Edward T.; Schock, Michael R. (2000). «Understanding, Deriving and Computing Buffer Capacity». Journal of Chemical Education. 77 (12): 1640–1644. Bibcode:2000JChEd..77.1640U. doi:10.1021/ed077p1640.
^ Butler, J. N. (1998). Ionic Equilibrium: Solubility and pH calculations. Wiley. pp. 133–136. ISBN 978-0-471-58526-8.
^ ^a ^b Hulanicki, A. (1987). Reactions of acids and bases in analytical chemistry. Translated by Masson, Mary R. Horwood. ISBN 978-0-85312-330-9.
^ Scorpio, R. (2000). Fundamentals of Acids, Bases, Buffers & Their Application to Biochemical Systems. ISBN 978-0-7872-7374-3.
^ McIlvaine, T. C. (1921). «A buffer solution for colorimetric comparaison» (PDF). J. Biol. Chem. 49 (1): 183–186. doi:10.1016/S0021-9258(18)86000-8. Archived (PDF) from the original on 2015-02-26.
^ Mendham, J.; Denny, R. C.; Barnes, J. D.; Thomas, M. (2000). «Appendix 5». Vogel’s textbook of quantitative chemical analysis (5th ed.). Harlow: Pearson Education. ISBN 978-0-582-22628-9.
^ Carmody, Walter R. (1961). «Easily prepared wide range buffer series». J. Chem. Educ. 38 (11): 559–560. Bibcode:1961JChEd..38..559C. doi:10.1021/ed038p559.
^ «Buffer Reference Center». Sigma-Aldrich. Archived from the original on 2009-04-17. Retrieved 2009-04-17.
^ Alderighi, L.; Gans, P.; Ienco, A.; Peters, D.; Sabatini, A.; Vacca, A. (1999). «Hyperquad simulation and speciation (HySS): a utility program for the investigation of equilibria involving soluble and partially soluble species». Coordination Chemistry Reviews. 184 (1): 311–318. doi:10.1016/S0010-8545(98)00260-4. Archived from the original on 2007-07-04.

External links[edit]

«Biological buffers». REACH Devices.

Источник

From Wikipedia, the free encyclopedia