Solutions buffers

Buffers are defined as substances that resist changes in the pH of a system. All weak acids or bases, in the presence of their salts, form buffer systems. The action of buffers and their role in maintaining the pH of a solution can best be explained with the aid of the Henderson-Hasselbalch equation, which may be derived as follows. 

The ionization of a weak acid, HA, and of a salt of that acid, BA, can be represented as  

The dissociation constant for a weak acid (K ) may be calculated from the following equation  

Because A is derived principally from the salt, the equation may, for practical purposes, be written  

Consequently, the pH of the system is determined by the piQ of the acid and the ratio of [A l to [HA]. The buffer has its greatest buffer capacity at its piC, that is, that pH at which the [A ] = [HA]. This entered into the preceding equation gives  

Buffers appear in chemical and biological systems as a means of controlling the pH. They have two important properties  

Buffer solutions consist of a weak acid and its salt with a strong base, or a weak base and its salt with a strong acid. Although most of the standard buffers are made up from weak acids plus their salts with strong bases (Table 5.1), there are also buffer solutions which can be prepared from the weak base plus its salt. The buffers quoted in Table 5.1 illustrate, however, that it is not necessary to rely on the weak base plus salt buffer to help to cover the whole range of pH. Some of these buffers are made from dibasic acids and make use of  

These equations represent the two stages of ionisation of the dibasic phthalic acid. 

Buffer pH 2.2 to 3.8 this corresponds to the phthalic acid/potassium hydrogen phthalate buffer 

Three simultaneous equilibria are set up in a buffer solution, and all must be considered when formulating the expressions for [H30 ]actuai or [OH ]actuai- Carrying out actual calculations of the pH of a buffer solution is straightforward provided that approximate expressions for deriving the expressions for [H30 ]actuai or [OH ]actuai are used. However, the reasoning used in the derivations and approximations is more tricky, and demonstrates the absolute necessity to be aware of what approximations are being made, and their implications and limitations. 

A buffer solution keeps its pH almost constant by resisting changes in pH when small amounts of acid or alkali are added to it. 

Buffer solutions play an important role in many processes where the pH of a system needs to be maintained at an optimum value. For instance, several synthetic and processed foods contain buffers so that they may be digested without causing undue changes in the chemistry of the body. Buffer solutions are also important in agriculture and medicine for example, intravenous injections are carefully buffered so as not to alter the blood pH from its normal value of 7.4. 

The main use of buffers in the laboratory is in the preparation of solutions of known and constant pH. It is difficult to ensure that the pH of a solution is accurate simply by preparing an acid or alkali of a given concentration because, for instance, atmospheric gases such as carbon dioxide dissolve in them, and so the pH will vary slightly over a period of time. 

Water is a major constituent of all living organisms, and the seas support millions of different species of plant and animal life. Yet the pH values of both water and saline (salt) solutions are particularly sensitive to the addition of acids or alkalis. Look  

A change in the pH of water by 0.5 up or down will have a most adverse affect on this plant 

A list of buffer solutions that show round values of pH at 25°C is given in Table 16.5. The final volume of all the mixtures is adjusted to 100 ml. 

Source Reproduced with permission from CRC Handbook of Chemistry and Physics 2008-2009, 89th ed., D. R. Lide  

Organic Chemist s Desk Reference, Second Edition 

NOTE TO THE STUDENT Buffer solutions are discussed in detail in Special Topic I in the Study Guide and Solutions Manual. By working the problems you will find there, you will see just how useful the Henderson-Hasselbalch equation can be for dealing with buffer solutions. 

A solution of a weak acid (HA) and its conjugate base (A ) is called a buffer solution. A buffer solution will maintain nearly constant pH when small amounts of acid or base are added to it, because the weak acid can give a proton to any HO added to the solution, and its conjugate base can accept any H that is added to the solution. 

Write the equation that shows how a buffer made by dissolving CH3COOH and CH3COO Na in watCT prevents the pH of a solution from changing appreciably when 

You are planning to carry out a reaction that produces hydroxide ion. In ordo for the reaction to take place at a constant pH, it will be buffered at pH=4.2. Would it be betto to use a formic acid/ formate buffer or an acetic acid/acetate buffer (Note the pk of formic acid = 3.75 and the pk of acetic acid = 4.76.) 

Solution Constant pH wOl be maintained because the hydroxide ion produced in the reaction wDl remove a proton from the acidic form of the buffer. Thus the betto choice of buffer is the one that has the highest concentration of buffer in the acidic form at pH = 4.2. Because formic 

We will begin our study of buffer solutions by first identifying the active components of a buffer solution. Then, we will discuss how these components give a buffer the ability to resist attempts to change its pH. Next, we will develop an equation that highlights the relationship between the pH of a buffer solution and the concentrations of the two active components. Finally, we will consider the very practical matter of preparing a buffer solution with a specified pH. 

The term appreciable warrants some additional explanation. With both components present in appreciable amounts, the solution will be able to neutralize either an appreciable amoimt of an added acid or an appreciable amount of an added base. A less obvious but equally important point is that to obtain appreciable amounts of the two active components, we must add two components to the solution. The ionization of a weak acid HA never produces an appreciable amount of A . Similarly, the hydrolysis of A (a weak base) never produces an appreciable amount of HA. Therefore, neither 0.100 M CHgCCXDH nor 0.100 M NaCHgCOO is a buffer solution, but a solution that is simultaneously 0.100 M CHgCOOH and 0.100 M NaCHjCOO is a buffer solution. 

Let s focus first on reaction (17.5) to explain qualitatively what happens when a small amount of a strong acid is added to a solution that is simultaneously 0.100 M in both CH3COOH and NaCH3CCX). We begin by writing the expression for CHgCCXDH and solving it for [H3O+]. 

Buffer with conjugate base and acid in equal concentrations 

EXAMPLE 17-3 Predicting Whether a Solution Is a Buffer Solution 

Cells cease to function and may be damaged Irreparably If the pH changes significantly, so we need to understand how the pH Is stabilized by a buffer. 

Suppose that we make an aqueous solution by dissolving known amounts of a weak acid (which provides the species HA) and its conjugate base (which provides the species A ). To calculate the pH of this solution, we make use of the expression for of the weak acid, eqn 4.22, with [HA] = [acid] and [A ] = [base], 

When the concentrations of the conjugate acid and base are equal, the second term on the right of eqn 4.35 is log 1 = 0, so under these conditions pH = pK. Although the equation has been derived without making any assumptions about [acid] and [base], it is common to suppose that, because the acid is weak, [add] and [base] are unchanged from the values used to make up the solution that is, we disregard the small amount of deprotonation of the added acid and the small amount of protonation of the added base. 

An acid buffer stabilizes the pH of a solution because the abundant supply of A ions (from the salt) can remove any H3O+ ions brought by additional strong acid furthermore, the abundant supply of HA molecules (from the acid component of the buffer) can provide H3O ions to react with any strong base that is added. Similarly, in a base buffer the weak base B can accept protons when a strong acid is added and its conjugate acid BH+ can supply protons if a strong base is added. The following example explores the quantitative basis of buffer action. 

Sometimes it may be necessary to prepare a solution with an approximately constant pH, prepared in such a way that this pH changes only slightly with the addition of an acidic or basic substance. This kind of solution is called a buffer solution. 

Daily body activities are quite sensitive to large pH changes, and must be kept within a small range of H30 and OH concentrations. Human blood, for example, has a pH of approximately 7.4 maintained by a buffer system. If our blood pH drops below 7.35, it can cause symptoms such as drowsiness, disorientation and numbness. If the pH level drops below 6.8, a person can die. To maintain pH stability, there is a carbonic acid - bicarbonate buffer system in the blood. 

An acidic buffer solution consists of a weak acid with a salt of the acid - its conjugate base. 

Let us consider a weak acid acetic acid (CH3COOH), and its salt, sodium acetate (CHgCOONa). 

If we add extra H to the solution, the equilibrium shifts to the left in accordance with Le ChMelier s principle. The added acid changes some of the conjugate base (CH3C00 ) to its weak acid, CH3COOH. 

It is an experimental fact that solutions obtained by dissolving a weak acid and its conjugate base exhibit only a very weak pH change and even no change at all when a strong acid or base is added to them, at least in certain concentration conditions. These solutions are called buffers. We also say that they have acidity and basicity in reserve. They are of considerable interest. It is sufficient to be convinced that the maintenance of a certain life form requires very narrow pH ranges. This must be related to the enzymatic systems, which actually can work only in very narrow pH regions. 

1 pH of a Buffer Solution Before Addition of a Strong Add or Base 

Let s consider a solution of a weak acid HA at the analytical concentration C moI/L and of its conjugate base at the concentration C moI/L dissolved as the sodium salt, for example. The pH value is calculated by solving the following system of simultaneous equations that must be satisfied  

The system can be reduced to a third-order equation in [H3O+], which would be difficult to solve. It is sometimes written in the literature in the form 

The system becomes considerably simplified by assuming that the concentrations [H30 ] and [OH ] can be neglected with respect to those of [Na+] and [A ] in the charge balance relation. With this hypothesis, the system can be reduced to the following relations  

A buffer solution is a solution of a weak acid and its conjugate base or a weak base and its conjugate acid. The main property of a buffer solution is its resistance to changes in its pH despite the addition of small quantities of strong acid or strong base. The student must know the following three things about buffer solutions  

A buffer solution may be prepared by the addition of a weak acid to a salt of that acid or addition of a weak base to a salt of that base. For example, a solution of acetic acid and sodium acetate is a buffer solution. The weak acid (HC2H3O2) and its conjugate base (C2H302, from the sodium acetate) constitute a buffer solution. There are other ways to make such a combination of weak acid plus conjugate base (Problem 17.26). 

A buffer solution resists change in its acidity. For example, a certain solution of acetic acid and sodium acetate has a pH of 4.0. When a small quantity of NaOH is added, the pH goes up to 4.2. If that quantity of NaOH had been added to the same volume of an unbuffered solution of HCl at pH 4, the pH would have gone up to a value as high as 12 or 13. 

The buffer solution works on the basis of Le Chatelier s principle. Consider the equation for the reaction of acetic acid with water  

The solution of HC2H3O2 and C2H302 in H2O results in the relative quantities of each of the species in the equation as shown under the equation. If H3O+ is added to the equilibrium system, the equilibrium shifts left to use up some of the added H3O+. If the acetate ion were not present to take up the added H3O+, the pH would drop. Since the acetate ion reacts with much of the added H3O+, there is little increase in H3O+ and little drop 

Formic acid, HCOOH, is the simpiest carboxyiic acid, with oniy a hydrogen atom attached to the —COOH. 

Consider a typical weak acid, formic acid (HCOOH), and its conjugate base, formate ion (HCOO ). The latter can be obtained by dissolving a salt such as sodium formate (NaHCOO) in water. The acid-base equilibrium established between 

UCOOH(aq) + HiOj ) HsO iaq) + HCOO (aq) with an acid ionization constant 

Section 15.2 describes the pH of a solution containing only a weak acid (such as HCOOH) or only a weak base (such as HCOO ). Suppose now that the weak acid and its conjugate base are both present initially. The resulting calculations resemble closely the calculation of Example 14.15, in which equilibrium was established from an initial mixture containing both reactants and products. 

Because y is likely to be small relative to 1.00 and to 0.500, we write the approximate 

This equilibrium applies to a mixture of an acid HA and its salt, say MA. If the concentration of the acid be ca and that of the salt be c5, then the concentration of the undissociated portion of the acid is (cfl — [H + ]). The solution is electrically neutral, hence [A ] = cs + [H + ] (the salt is completely dissociated). Substituting these values in the equilibrium equation (18), we have  

This is a quadratic equation in [H + ] and may be solved in the usual manner. It can, however, be simplified by introducing the following further approximations. In a mixture of a weak acid and its salt, the dissociation of the acid is repressed by the common ion effect, and [H + ] may be taken as negligibly small by 

The equations can be readily expressed in a somewhat more general form when applied to a Bronsted-Lowry acid A and its conjugate base B  

Similarly for a mixture of a weak base of dissociation constant Kb and its salt with a strong acid  

Confining attention to the case in which the concentrations of the acid and its salt are equal, i.e. of a half-neutralised acid then pH = pKa. Thus the pH of a half-neutralised solution of a weak acid is equal to the negative logarithm of the dissociation constant of the acid. For acetic (ethanoic) acid, Ka = 1.75 x 10 5 mol L 1, pKfl = 4.76 a half-neutralised solution of, say 0.1M acetic acid will have a pH of 4.76. If we add a small concentration of H + ions to such a solution, the former will combine with acetate ions to form undissociated acetic acid  

In most equations it is assumed that the reaction is in aqueous solution and the (aq) etc. are omitted. 

Salts can also be formed by the neutralization of the acid with other basic materials, including metal carbonates, bicarbonates and metal oxides. 

Acid + metal carbonate (or bicarbonates) — salt + water + carbon dioxide gas 

All sodium, potassium and ammonium salts dissolve in water. Look at the instructions and contents of a medicine or food and you will see what salts are present to make the material water soluble and so make it more easily absorbed in the stomach. 

This is the process whereby the quantity of an acid is just balanced by the addition of a base or alkali. The hydrogen ions are just balanced by the OH- ions in an aqueous solution to form neutral water 

Let us consider now a mixture of a weak acid and its salt, such as a mixture of acetic acid and sodium acetate. In such a solution the sodium acetate, like any other salt, is almost completely dissociated. The dissociation of acetic acid 

In general, buffer solutions contain a mixture of a weak acid and its salt or a weak base and its salt. The hydrogen-ion concentration can be calculated from considerations of the chemical equilibrium which exists in such solutions. Considering a buffer made up of a weak acid and its salt, the dissociation equilibrium 

The free acid present is almost completely undissociated, because the presence of large amounts of the anion A-, which originates from the salt. The total concentration of the acid, c, will therefore be (approximately) equal to the concentration of the undissociated acid, 

For the same reason the total concentration of the salt, c, will be (approximately) equal to the concentration of the anion  

Similarly, if the buffer is made up from a weak base MOH and its salt, containing the cation M+, the dissociation equilibrium which prevails in such a solution is 

Check Comparing the results in (a) and (b), we see that when the common ion (CH3COO ) is present, according to Le Chatelier s principle, the equilibrium shifts from right to left. This action decreases the extent of ionization of the weak acid. Consequently, fewer H ions are produced in (b) and the pH of the solution is higher than that in (a). As always, you should check the validity of the assumptions. 

Practice Exercise What is the pH of a solution containing 0.30 M HCOOH and 0.52 M HCOOK Compare your result with the pH of a 0.30 M HCOOH solution. 

The common ion eiTect also operates in a solution containing a weak base, such as NH3, and a salt of the base, say NH4CI. At equiUbrium, 

We can derive the Henderson-Hasselbalch equation for this system as follows. Rearranging the above equation we obtain 

Taking the negative logarithm of both sides gives 

Think About It The equilibrium concentrations of CH3COOH, CH3COO , and H are the same regardless of whether we add sodium acetate to a solution of acetic acid, add acetic acid to a solution of sodium acetate, or dissolve both species at the same time. We could have constructed an equilibrium table starting with the equilibrium concentrations in the 0.10 Af acetic acid solution  

In this case, the reaction proceeds to the left. (The acetic acid concentration increases, and the concentrations of hydrogen and acetate ions decrease.) Solving fory gives 1.304 X 10 M [H ] = 1.34 X 10 — y = 3.6 X 10 M and pH = 4.44. We get the same pH either way. 

Practice Problem A Determine the pH at 25°C of a solution prepared by dissolving 0.075 mole of sodium acetate in 1.0 L of 0.25 M acetic acid. (Assume that the addition of sodium acetate does not change the volume of the solution.) 

In this case, the percent ionization of acetic acid is 

The ion pair Na+Cl is not a molecule. A chemical bond is not formed between the ions, which are held together by electrostatic attraction. Each ion retains at least part of its attached water molecules hydration sphere) and one or more water molecules can lie between the ions. Equilibrium constants have been determined for the formation of some ion pairs. Multiply charged ions have a greater tendency to form ion pairs than do singly charged ions. For example. 

Write expressions for y and m for Mg3(P04)2 in terms of the stoichiometric molality and the activity coefficients of the ions. Neglect hydrolysis (a poor approximation). 

85 molkg aqueous HCl solution at 298.15 K. Use the Davies equation to estimate y . 

39 Write the expressions for y and m for each of the following solutes (assume strong electrolytes)  

If )/(A ) is also assumed to equal unity, this equation can be written in the form known as the Henderson-Hasselbalch equation  

This is considerably smaller than the percent ionization prior to the addition of sodium acetate. 

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Henderson-Hasselbach equation A simplified version of the relationships used in calculations on buffer solutions. 

The paper-electrophoretic behavior of 2-amino-4-methylthiazoie in a buffer solution containing AgNOj shows that migration increases at low and high pH an increase of pAg produces the opposite result (147). 

Suppose you take two flasks one containing pure water and the other a buffer solution mam tamed at a pH of 7 0 If you add 0 1 mole of acetic acid to each one and the final volume m each flask IS 1 L how much acetic acid is present at equi librium How much acetate ion In other words what IS the extent of ionization of acetic acid m an unbuffered medium and m a buffered one ... 

Table 8.14 National Bureau of Standards (U.S.) Reference pH Buffer Solutions 8.105...

Table 8.15 Compositions of Standard pH Buffer Solutions [National Bureau of...

Table 8.18 pH Values for Buffer Solutions in Alcohol-Water Solvents at 25°C 8.109... 

The buffer values for the NBS reference pH buffer solutions are given below ... 

To prepare the standard pH buffer solutions recommended by the National Bureau of Standards (U.S.), the indicated weights of the pure materials in Table 8.15 should be dissolved in water of specific conductivity not greater than 5 micromhos. The tartrate, phthalate, and phosphates can be dried for 2 h at 100°C before use. Potassium tetroxalate and calcium hydroxide need not be dried. Fresh-looking crystals of borax should be used. Before use, excess solid potassium hydrogen tartrate and calcium hydroxide must be removed. Buffer solutions pH 6 or above should be stored in plastic containers and should be protected from carbon doxide with soda-lime traps. The solutions should be replaced within 2 to 3 weeks, or sooner if formation of mold is noticed. A crystal of thymol may be added as a preservative. 

TABLE 8.16 Composition and pH Values of Buffer Solutions (Continued)... 

In Section 8, the material on solubility constants has been doubled to 550 entries. Sections on proton transfer reactions, including some at various temperatures, formation constants of metal complexes with organic and inorganic ligands, buffer solutions of all types, reference electrodes, indicators, and electrode potentials are retained with some revisions. The material on conductances has been revised and expanded, particularly in the table on limiting equivalent ionic conductances. 

H.2 Representing Buffer Solutions with Ladder Diagrams... 

In one version of the urea electrode, shown in Figure 11.16, an NH3 electrode is modified by adding a dialysis membrane that physically traps a pH 7.0 buffered solution of urease between the dialysis membrane and the gas-permeable... 

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