Dr. Omar AJOUYED Chem 2210 Chapter 3: Acid-Base (Neutralization) Titrations

Transcription

1 Chapter 3: Acid-Base (Neutralization) Titrations 3. Weak Base vs Strong Acid Titration This titration is completely analogous with previous titration, but the titration curves are the reverse of those for a weak acid versus a strong base. The titration curve for weak base with strong acid is shown in Figure 7. ph BUFFER ZONE A calculation conjugate ratios are known, use Henderson-Hasselbach to calculate ph. ph s are generally above 7 here. The START of the titration is the same as a regular weak base problem. You know K b and [base] so you can calculate ph. B + H 2O BH + + OH - Half-Equivalence: [base] = [salt] ph = pk a 7 The EQUIVALENCE POINT is the same as a regular salt of a weak base problem. You know [BH + ] and you can calculate ph. Also note that the ph must be less than 7 due to the ionization of BH + BH + + H2O B + H3O + OVERSHOOT This region is calculated simply by determining the amount of H + in EXCESS that has been added. No equilibrium calculations necessary. Volume of acid added (ml) Figure 7: Titration curve of weak base with strong acid. From Figure 7, there are five regions on titration curve of weak base with strong acid that require specific approaches to calculate the ph: Initial region: ph = 14 poh = 14 + log K b [weak base] The ph will reflect the weak base only no strong acid has been added. Recall that for weak bases (see chapter 2), [OH ] = K b [weak base] Recall that poh = -log [OH - ] and that ph = 14 poh ; therefore, ph = 14 + log K b [weak base] Pre-Equivalence region: This region uses a modified version of the Henderson-Hasselbalch equation to calculate ph: ph = pk a + log ( n b n a n a ) Because nb > na in this region, the ph will be affected by two factors: i) the remaining weak base in the solution, and ii) the conjugate acid present upon addition of strong acid. For a weak base B reacting with strong acid HCl (H + ), B + H + BH + The species BH + is the conjugate acid of the weak base B, and it will react with water to re-form the weak acid:

2 BH + + H2O B + H3O + The generation of H3O + from the conjugate acid will affect ph. As in the weak acid/strong base scenario, the weak base/conjugate acid system can be treated like a buffer; hence, the usefulness of the Henderson-Hasselbalch equation. Recall that the Henderson- Hasselbalch equation is (see chapter 2): poh = pk b + log ( [salt] [base] ) We will modify the Henderson-Hasselbalch equation to our weakly basic system. [base] and [salt] can be re-written as (nb - na)/vt and na/vt, respectively, and since pka + pkb = 14 and ph + poh = 14, we can re-write our equation as: ph = pk a + log ( n b n a n a ) Half-Equivalence Region: ph = pk a At half-equivalence, 1 2 n b = n a [salt] = [base]or n b n a = n a, and the log term in the pre-equivalence equation goes to zero (log 1 = 0). Equivalence: ph = log K a [salt] = log K w K b M bv b V t At the equivalence point, n b = n a, and the only factor affecting ph is the conjugate acid (salt). To find [H3O + ] for a weak acid (see chapter 2): [H 3 O + ] = K a [salt] Converting [H3O + ] to ph provides the necessary equation: ph = log K a [salt] Post-Equivalence Region: ph = log ( n an b V t ) The ph will reflect the excess strong acid remaining after neutralizing the weak base. n a > n b, in this region. Note that the contribution of the conjugate acid will have no appreciable effect on the ph assuming even a small portion of strong acid is present in solution; therefore, it is omitted from the calculation. 4. Indicators Indicators are weak organic acids or weak organic bases that change color as the ph changes over a specific portion of the ph scale. We can use this change in color to determine when a solution has been exactly neutralized. This color change is termed the endpoint of the titration. The color change and the ph range of some common indicators are tabulated below: Indicator ph range Color change Methyl Orange Methyl Red Litmus Phenolphthalein Red to Yellow Red to Yellow Red to Blue Colorless to Red violet

3 There are two theories which explain the change of colour indicators with change in ph Ostwald s theory or Ionic theory Most of the discussion given earlier for characterizing an indicator belongs to this theory. The main features of this theory are as follows: 1) All the acid-base indicators are either weak acids or weak bases. They ionize partially to give H + or OH - as in the case of simple weak acids and bases. HIn(weak acid) H + + In (conjugate base) InOH(weak base) OH + In + (conjugate acid) We can write a Henderson-Hasselbalch equation for this, just as for other weak acids (see chapter 2): ph = pk In + log ( [In ] [HIn] ) The value of the ratio( [In ] ) can be determined by a visual color comparison or, more [HIn] accurately, by a spectrophotometric method. Both forms of the indicator are present at any hydrogen-ion concentration. Experience shows that the solution will appear to have the acid color, i.e. of HIn, when the ratio of [HIn] to [In ] is above approximately 10, and the alkaline color, i.e. of In -, when the ration of [In ] to [HIn] is above approximately 10. Thus only the acid color will be visible when( [In ] ) > 10; the corresponding limit of ph given by [HIn] equation: ph = pkin 1. Only the alkaline color will be visible when( [HIn] ) > 10, and the corresponding limit of ph [In ] is: ph = pkin + 1. The color-change interval is according ph = pk In ± 1, i.e. over approximately two ph units. Within this range the indicator will appear to change form one color to the other. The change will be gradual, since it depends upon the ratio of the concentration of the two colored forms (acidic form and basic form). When the ph of the solution is equal to apparent dissociation constant of the indicator pkin, the ratio [HIn] to [In ] becomes equal to1, and the indicator will have a color due to an equal mixture of the acid and alkaline forms. This is sometimes known as the middle tint of the indicator. This applies strictly only if the two colors are of equal intensity. If one form is more intensely colored than the other or if the eye is more sensitive to one color than the other, then the middle tint will be slightly displaced along the ph range of the indicator. 2) All the indicators with pkin < 7 are called acid indicators and with pkin > 7 are called base indicators. In other words, the acid indicators undergo ionization in acidic medium and base indicators in basic medium. According to this definition methyl orange, methyl red, etc., are acid indicators and phenolphthalein, nitrobenzene, etc., are base indicators. 3) A conjugate acid-base couple must possess different colors to act as an indicator. In other words the ionization and unionization forms of indicator should possess different colors. HIn(color A) H + + In (color B) OR InOH(color C) OH + In + (color D) 4) While titrating a weak acid (or base), the indicator should be such that its ph range falls in the ph equivalence range. Following this rule we cannot use methyl orange and methyl red as indicators for the titration of acetic acid by strong base

4 4.2. Quinonoid theory Though ionic theory was successful in correlating the indicator constant (pkin) and indicator ph range to the ph of the titration mixture and existence of various ionic forms, it has no answer as to what makes any indicator acquire its color. An answer to this part of the question was provided by quinonoid theory. The following features explain the quinonoid theory: 1) Organic compounds which have benzene ring (benzenoid structures) are colorless or very lightly colored, while those having quinonoid structure with extended conjugation are highly colored. Benzenoid structure Quinonoid structure 2) The benzenoid and quinonoid structures are two tautomeric forms and are at dynamic equilibrium. 3) The concentration of a particular form depends on the ph condition of the solution. Therefore the color of the indicator solution varies with ph. For example, in case of phenolphthalein; the structures are: Similarly for methyl orange: 4.3. Choice of indicator in neutralization reactions As a general rule, for a titration to be feasible there should be a change of approximately two units of ph at near the equivalence point produced by the addition of a small volume of the reagent. The ph at equivalence point may be calculated by using the equations given in this chapter, the ph at either

5 side of the equivalence point may be calculated as described in the preceding sections, and the difference will indicate whether the change is large enough to permit a sharp end point to be observed. Alternatively, the ph change on both sides of the equivalence point may be obtained from the neutralization curve determined by potentiometric titration. If the ph change is satisfactory, an indicator should be selected that changes at or near the equivalence point. For convenience of reference, the conclusions already deduced from theoretical principles are summarized below. 1) Strong acid vs. strong base For 0.1 M or more concentrated solutions, any indicator may be used which has a range between the limits ph 4.5 and ph 9.5. With 0.01 M solutions, the ph range is somewhat smaller ( ). In general, ph curve of strong acid and strong base is vertical over almost the ph range So the indicators phenolphthalein (ph range 8.3 to 10.5), methyl red (ph range ) and methyl orange (ph range ) are suitable for such a titration. But, an indicator such as bromothymol blue is more suitable. Because, its ph range (6-7.6) contains the ph of equivalence point. 2) Weak acid vs. strong base The ph range for acids with Ka > 10-5 is ; for weaker acids (Ka < 10-6 ) the range is reduced (8-10). Generally, ph curve of weak acid and strong base is vertical over the approximate ph range 7 to 11. So phenolphthalein is the suitable indicator for such a titration. 3) Weak base vs. strong acid The ph range for bases with Kb > 10-5 is 3-7; for weaker bases (Kb < 10-6 ) the range is reduced (3-5). In general, ph curve of weak base and strong acid is vertical over the approximate ph range 4 to 7. So the indicators methyl red and methyl orange are suitable for such a titration. 4) Weak acid vs. weak base There is no sharp rise in the neutralization curve and, generally, no simple indicator can be used. The titration should therefore be avoided, if possible. The approximate ph at the equivalence point can be computed from the equation: ph = ½pKw + ½pKa - ½pKb. It is sometimes possible to employ a mixed indicator which exhibits a color change over a very limited ph range, for example, neutral red-methylene blue for dilute ammonia solution and acetic acid. 5. Titration of Sodium Carbonate In this experiment, a solution of Na2CO3 (weak base) will be titrated with a solution of HCl (strong acid). Carbonate ion, CO3-2, is a diprotic base, and shows the following ionization reactions in aqueous solution: 2 CO 3 (aq) HCO 3 (aq) + H 2 O (l) HCO 3 (aq) + OH (aq) + H 2 O (l) H 2 CO 3 (aq) + OH (aq) K b1 = [HCO 3 ][OH ] [CO 2 3 ] K b2 = [H 2CO 3 ][OH ] [HCO 3 ] The designation Kb1 refers to this being the first base ionization constant for CO3-2. CO3-2 should be recognized as the conjugate base of HCO3 - and Kb1 equals Kw/Ka2 where Ka2 is the Ka for HCO3 -, which is also the second ionization constant for H2CO3. Likewise, Kb2 refers to the second base ionization constant for CO3-2. HCO3 - should be recognized as the conjugate base of H2CO3 and Kb2 equals Kw/Ka1 where Ka1 is the first ionization constant for H2CO

6 ph Dr. Omar AJOUYED Chem 2210 CO3-2 requires two hydrogen ions for complete neutralization to carbonic acid. The neutralization occurs in two consecutive steps represented by the equations: 2 CO 3 (aq) HCO 3 (aq) + H + (aq) HCO 3 (aq) + H + (aq) H 2 CO 3 (aq) Two equivalence points can be detected, one when all of the CO3-2 has been converted to the amphiprotic HCO3 -, and second when all of the HCO3 - has subsequently been converted to H2CO3 (see Figure 8) CO3-2 /HCO3 - buffer A B HCO3 - /H2CO3 buffer Excess H C 6.35 D 4.1 E Volume of acid added (ml) ½Veq1 Veq1 ½Veq2 Veq2 Phenolphthalein is used to detect the first end point, and methyl orange is used to detect the second one. Neither end point, however, is very sharp. In actual practice, the phenolphthalein end point is used only to get an approximation of where the second end point will occur; phenolphthalein is colorless beyond the first end point and does not interfere. The second end point, which is used for accurate titrations, is normally not very accurate with methyl orange indicator, because of the gradual change in the color of the methyl orange. This is caused by the gradual decrease in the ph to the HCO3 - /CO2 buffer system beyond the first end point. Calculate the ph ph at point A in Figure 8: Initial ph (CO3 2- treat as monoprotic weak base). No acid has been added, and only sodium carbonate is present in solution. The ph is determined by the extent of carbonate reaction with water: Where, Figure 8: Titration curve for 50 ml of 0.02 M Na2CO3 vs. 0.1 M HCl. 2 CO 3 (aq) + H 2 O (l) HCO 3 (aq) + OH (aq) K b1 = [HCO 3 ][OH ] [CO 2 3 ] Therefore, K b1 = K w = = [HCO 3 ][OH ] x 2 K a1 [CO 2 = 3 ] x x = [OH ] = and poh = ph =

7 ph at point B in Figure 8: 5 ml of HCl added. Here we are ½ way to 1 st equivalence point, and we have a 1:1 mixture of CO3 2- and HCO3 - = a buffer. 2 CO 3 (aq) + H + (aq) HCO 3 (aq) Therefore, ph = pk a2 + log ( [CO 3 2 ] [HCO 3 ] ) = pk a2 + log ( 1 1 ) ph = ph at point C in Figure 8: 10 ml of HCl added. The first equivalence point. Therefore, ph = pk a1 + pk a2 2 ph = ph at point D in Figure 8: 15 ml of HCl added. Here we are ½ way to 2 nd equivalence point, and we have a 1:1 mixture of HCO3 - and H2CO3 = a buffer. + H + (aq) H 2 CO 3 (aq) Therefore, HCO 3 (aq) ph = pk a1 + log ( [HCO 3 ] [H 2 CO 3 ] ) = pk a1 + log ( 1 1 ) ph = ph at point E in Figure 8: 20 ml of HCl added. Here we are at the 2 nd equivalence point, and the only thing we have is carbonic acid. H 2 CO 3 (aq) HCO 3 (aq) + H + (aq) Therefore, Where, K a1 = [HCO 3 ][H + ] [H 2 CO 3 ] [H 2 CO 3 ] = M b V b V t = = x 2 [H 2 CO 3 ] x = [H + ] = ph = 4. 1 = M 6. Titration of Polyprotic Acids Diprotic acids can be titrated stepwise just as sodium carbonate was. In order to obtain good end point beaks for titration of the first proton, Ka1 should be at least 10 4 x Ka2. If Ka2 is in the required range of 10-7 to 10-8 for a successful titration, an endpoint break is obtained for titrating the second proton. Triprotic acids can be titrated similarly, but Ka3 is generally too small to obtain an end point break for titration of the third proton. Polyprotic acids ionize one step at a time. For a weak diprotic acid, the equilibria reactions are: H 2 A (aq) + H 2 O (l) HA (aq) + + H 3 O (aq) K a1 = [H 3O + ][HA ] [H 2 A]

8 ph Dr. Omar AJOUYED Chem 2210 HA (aq) + H 2 O (l) A 2 (aq) + + H 3 O (aq) K a2 = [H 3O + ][A 2 ] [HA ] The neutralization of such acids also occurs in steps where the first proton is neutralized, then the second proton is neutralized. H 2 A (aq) + OH (aq) HA (aq) HA (aq) + OH (aq) A 2 (aq) + H 2 O + H 2 O Each reaction will have its own, distinct equivalence point. The ph at each equivalence point depends on the respective Ka value. The titration curve looks like two S-shaped curves connected to each other (Figure 9). HA /H 2 A buffer A 2 /HA buffer Excess OH - Equivalence point 1 Equivalence point 2 Volume of base added (ml) ½Veq1 Veq1 ½Veq2 Veq2 Figure 9: Titration curve of a diprotic acid with strong base. 7. Mixture of Acids or Bases Mixtures of acids or bases can be titrated stepwise if there is an appreciable difference in their strength. There must generally be a difference in Ka values of at least 10 4, unless perhaps a ph meter is used to construct the titration curve. If one of the acids is a strong acid, one end point will be observed for the strong acid only if Ka is about 10-5 or smaller. See, for example, Figure 10, where only a small break is seen for the HCl. The strong acid will titrate first and will give a ph break at its equivalence 1. This will be followed by titration of the weak acid and a ph break at its equivalence point 2. At the equivalence point for HCl, a solution of HOAc and NaCl remais, and so the equivalence point is acidic. Beyond the equivalence point, the OAc - /HOAc buffer region is established, and this markedly suppresses the ph break for HCl. If two strong acids are titrated together, there will be no differentiation between them, and only one equivalence point break will occur, corresponding to the titration of both acids. The same is true for two weak acids, if their Ka values are not too different. For example, a mixture of acetic acid, Ka = 1.75x10-5, and propionic acid, Ka = 1.3x10-5, would titrate together to give a single equivalence point. Phosphoric acid in mixture with a strong acid acts in a manner similar to the above example. The first proton titrates with the strong acid, followed by titration of the second proton to give a second equivalence point; the third proton is too weakly ionized to titrate. Similarly, mixtures of bases can be titrated if their strengths are sufficiently different. Again, the difference in Kb values must be at least Also, if one base is a strong base, the weak base must have Kb no greater than about For example, NaOH does not give a separate end point from that for the titration of CO3 2- to HCO3 -, when titrated in the presence of Na2CO3 (Kb = 2.1x10-4 )

9 ph Dr. Omar AJOUYED Chem 2210 Equivalence point 1: HCl Equivalence point 2: HOAc Volume of base added (ml) Veq1 Veq2 Figure 10: Titration curve of a mixture of HCl and HOAc with NaOH. 8. Preparation of Standard Base Solutions

10 9. Preparation of Standard Acid Solutions