Chapter 15 Acid Base Equilibria

Transcription

1 Buffer Solutions The ph changes by a large amount even when a small amount of acid or base is added to pure water: Chapter 15 Acid Base Equilibria A buffer solution is a solution which resists a change in ph when small amounts of acid or base are added: Making Buffer Solutions A buffer solution can be made in two ways: 1. Acidic Buffer: a mixture of a solution of a weak acid and a salt of its conjugate base 2. Basic Buffer: a mixture of a solution of a weak base and a salt of its conjugate acid By choosing the appropriate components it is possible to create a buffer solution at any chosen ph Which of the following combinations could make a buffer solution? a. HClO 4, KClO 4 b. HMnO 4, LiMnO 4 c. C 6 H 5 N, C 6 H 5 NH + Br - d. HI, NaI Blood is a good example of a buffer solution The Common Ion Effect This occurs when a salt, NaA is added to the solution of a weak acid, HA, sharing the common ion A - Addition of the common ion causes the dissociation equilibrium of the acid to shift to the left (according to Le Châtelier s Principle), making the solution less acidic than if the ion were not present Example: If the salt NaF is added to the solution of the weak acid, the presence of the common ion F - causes the equilibrium to shift to the left and the [H + ] concentration to decrease and hence the ph to increase: 1

2 Procedure for Calculating the ph Change when an Acid or Base is added to a Buffer Solution Acidic Buffers Solutions Acidic buffer solutions are made by mixing a weak acid, HA and a salt of its conjugate base, A - The weak acid is present in large amounts since it only dissociates slightly while the salt provides large quantities of its conjugate base When a small amount of OH - ions are added to the solution they are neutralized by the acid producing water: HA(aq) + OH - (aq) A - (aq) + H 2 O(l) There will be a small decrease in HA (present in large amounts) and a small increase in A - (also present in large amounts) but the concentration of H + won t change much. In other words the OH - ions are replaced by A - and are not allowed to accumulate The ph stability can be understood from the equilibrium expression for the acid: K a = [H + ][A - ]/[HA] or [H + ] = K a x [HA]/[A - ] so the equilibrium concentration of [H + ] (and hence the ph) depends on the ratio [HA]/[A - ] When a small amount of OH - is added to the solution, HA is converted into A - so the ratio [HA]/[A - ] decreases. However, if the amounts of HA and A - are large compared to the amount of OH - added, the change in the [HA]/[A - ] ratio and hence the change in [H + ] will be small When a small amount of H + ions are added to the solution they react with A - forming the weak base: H + (aq) + A - (aq) HA(aq) There will be a small decrease in A - (present in large amounts) and a small increase in HA (also present in large amounts) but the concentration of H + won t change much. In other words the H + ions are replaced by HA and are not allowed to accumulate Buffering action of mixture of acetic acid (HC 2 H 3 O 2 ) and sodium acetate (NaC 2 H 3 O 2 ) Again, the ph stability can be understood from the equilibrium expression for the acid: [H + ] = K a x [HA]/[A - ] When a small amount of H + is added to the solution, A - is converted into HA so the ratio [HA]/[A - ] increases. However, if the amounts of HA and A - are large compared to the amount of H + added, the change in the [HA]/[A - ] ratio and hence the change in [H + ] will be small In order for buffering to be effective, [HA] and [A - ] have to large compared to the amount of H + or OH - added! 2

3 The Henderson-Hasselbalch Equation Starting with the equilibrium expression for a weak acid: [H + ] = K a x [HA]/[A - ] then taking the negative log of both sides we obtain: -log[h + ] = -logk a log([ha]/[a - ]) Since ph = -log[h + ] and pk a = -logk a we get: ph = pk a log([ha]/[a - ]) Finally, inverting the log term we obtain: ph = pk a + log([a - ]/[HA]) = pk a + log([base]/[acid]) This equation is useful for calculating the ph of solutions when the ratio [A - ]/[HA] is known For any buffering system (conjugate acid-base pair), all solutions with the same [A - ]/[HA] ratio will have the same ph: Use of this equation assumes that the equilibrium concentrations of A - and HA are equal to their initial concentrations: [A - ] = [A - ] 0 + x [A - ] 0 [HA] = [HA] 0 - x [HA] 0 where x is the amount of acid that dissociates (small) This assumption is valid because in a buffer solution, the concentrations of A - and HA are relatively large 3

4 Basic Buffer Solutions Basic buffer solutions are made by mixing a weak base, B and a salt of its conjugate acid, BH + The weak base is present in large amounts since it only dissociates slightly while the salt provides large quantities of its conjugate acid When a small amount of OH - ions are added to the solution they are neutralized by the conjugate acid producing water: BH + (aq) + OH - (aq) B(aq) + H 2 O(l) There will be a small decrease in BH + (present in large amounts) and a small increase in B (also present in large amounts) but the concentration of H + won t change much. In other words the OH - ions are replaced by B and are not allowed to accumulate The ph stability can be understood from the equilibrium expression for the base: K b = [BH + ][OH - ]/[B] or [OH - ] = K b x [B]/[BH + ] so the equilibrium concentration of [OH - ] (and hence the ph) depends on the ratio [B]/[BH + ] When a small amount of OH - is added to the solution, BH + is converted into B so the ratio [B]/[BH + ] increases. However, if the amounts of BH + and B are large compared to the amount of OH - added, the change in the [B]/[BH + ] ratio and hence the change in [OH - ] will be small When a small amount of H + ions are added to the solution they react with the weak base B forming the weak acid BH + : H + (aq) + B(aq) BH + (aq) There will be a small decrease in B (present in large amounts) and a small increase in BH + (also present in large amounts) but the concentration of H + won t change much. In other words the H + ions are replaced by BH + and are not allowed to accumulate Again, the ph stability can be understood from the equilibrium expression for the base: [OH - ] = K b x [B]/[BH + ] When a small amount of H + is added to the solution, B is converted into BH + so the ratio [B]/[BH + ] decreases. However, if the amounts of BH + and B are large compared to the amount of H + added, the change in the [B]/[BH + ] ratio and hence the change in [OH - ] will be small The Henderson-Hasselbalch Equation for Weak Base Buffers Starting with the equilibrium expression for a weak acid: [OH - ] = K b x [B]/[BH + ] then taking the negative log of both sides we obtain: -log[oh - ] = -logk b log([b]/[bh + ]) Since poh = -log[oh - ] and pk b = -logk b we get: poh = pk b log([b]/[bh + ]) Finally, inverting the log term we obtain: poh = pk b + log([bh + ]/[B]) = pk b + log([acid]/[base]) Since ph + poh = 14.00: ph = pk b - log([bh + ]/[B]) 4

5 Summary Buffering Capacity The buffering capacity of a buffer solution is a measure of the amount of acid or base it can absorb without a significant change in its ph The larger the concentrations of buffering components the more acid or base it can absorb The ph of a buffer solution is determined by its [A - ]/[HA] ratio while the capacity of a buffer solution is determined by the sizes of [A - ] and [HA] Preparing Buffer Solutions Since large changes in the [A - ]/[HA] ratio will result in large changes in ph, optimal buffering occurs when the [A - ] and [HA] concentrations are equal Therefore when selecting a buffer for a particular ph we want [A - ]/[HA] to be a close to 1 as possible Substituting this condition into the Henderson-Hasselbalch equation we obtain: ph = pk a + log([a - ]/[HA]) = pk a + log(1) = pk a The other words the pk a of the weak acid used in the buffer should be a close to the desired ph as possible! 5

6 Titrations and ph Curves A titration is a technique used to determine the amount of acid or base present in a solution This process involves delivering a solution of known concentration from a burette (the titrant) into a solution of unknown concentration (the analyte) until the substance being analyzed is consumed at the equivalence (stoichiometric) point This can be signaled by a color change in an indicator or by using an electronic ph meter: The Equivalence Point The shape of a titration curve and the ph at the equivalence point depends on the nature of the titrant and the analyte i.e. whether they are strong or weak acids or bases The ph at the equivalence point of a titration is usually not 7! The equivalence point in an acid-base titration is defined by stoichiometry not ph since the equivalence point is reached when just enough titrant has been added to react exactly with all the analyte being titrated When a ph meter is used, a titration (ph) curve is generated which is a plot of ph against titrant volume 6

7 Strong Base Titrant with Strong Acid Analyte Strong Acid Titrant with Strong Base Analyte The ph increases slowly at first until close to the equivalence when it increases rapidly. This is because early on in the titration there is a large amount of H + so the addition of OH - only produces a small ph change. However, near the equivalence point where the amount of H + is small, the addition of OH - produces a large ph change. At the equivalence point the ph is 7 The ph decreases slowly at first until close to the equivalence when it decreases rapidly. This is because early on in the titration there is a large amount of OH - so the addition of H + only produces a small ph change. However, near the equivalence point where the amount of OH - is small, the addition of H + produces a large ph change. At the equivalence point the ph is 7 Strong Base Titrant with Weak Acid Analyte The equivalence point of a strong acid/strong base titration always occurs at 7 since only water is present at equivalence The ph increases rapidly at first and then levels off in the buffering region as a buffer solution containing the acid and its conjugate base is produced which resists a large increase in ph. Beyond the equivalence point (once OH - is in excess) the curve is identical to the end of a strong base-strong acid titration. At the equivalence point the ph is greater than 7 since the conjugate base of the weak acid is present which reacts with water to form OH - What is the ph at the equivalence point when 50.0 ml of M acetic acid is titrated with M sodium hydroxide? The weaker the acid, the higher the ph value and the smaller the ph change at the equivalence point 7

8 Weak Acid Titrant with Strong Base Analyte What is the ph at the equivalence point when 50.0 ml of M magnesium hydroxide is titrated with M chlorous acid? Initially OH - is in excess so the curve is identical to the beginning a strong acid-strong base titration. However, after the equivalence point is reached a buffer solution containing the acid and its conjugate base is formed which resists any large fall in ph. Again, at the equivalence point the ph is greater than 7 since the conjugate base of the weak acid is present which reacts with water to form OH - Weak Base Titrant with Strong Acid Analyte What is the ph at the equivalence point when 60.0 ml of M hydrochloric acid is titrated with M methylamine? Initially H + is in excess so the curve is identical to the beginning of a strong base-strong acid titration. However, after the equivalence point is reached a buffer solution containing excess base and its conjugate acid is formed which resists any large increase in ph. At the equivalence point the ph is less than 7 since the conjugate acid of the weak base is present which produces H + is solution Strong Acid Titrant with Weak Base Analyte What is the ph at the equivalence point when 45.0 ml of M ethylamine is titrated with M hydrobromic acid? The ph decreases rapidly at first but then levels off as a buffer solution containing excess base and its conjugate acid is formed which resists any large decrease in ph. After the equivalence point is reached, the H + is in excess so the curve is identical to the end of a strong acid-strong base titration. Again, at the equivalence point the ph is less than 7 since the conjugate acid of the weak base is present which produces H + is solution 8

9 Weak Base Titrant with Weak Acid Analyte Weak Acid Titrant with Weak Base Analyte The ph increases rapidly at first and then levels off as a buffer solution containing the acid and its conjugate base is produced which resists a large increase in ph. However, after the equivalence point is reached another buffer solution containing excess base and its conjugate acid is formed which also resists any large increase in ph. Since the acid and the base in this example are both equally weak, the equivalence point is close to 7 The ph decreases rapidly at first but then levels off as a buffer solution containing excess base and its conjugate acid is formed which resists any large decrease in ph. However, after the equivalence point is reached a buffer solution containing the acid and its conjugate base is formed which also resists any large fall in ph. Since the acid and the base in this example are both equally weak, the equivalence point is close to 7 The exact ph at the endpoint of a weak acid-weak base titration depends on the relative size of K a for the acid ion compared to K b for the base as in the case of solutions of salts containing the cations of weak bases and the anions of weak acids : K a > K b K b > K a Strong Base Titrant with Weak Diprotic Acid Analyte Acid-Base Indicators An acid-base indicator is compound (typically organic) which changes color over a narrow ph range. The ph at which the indicator changes color is called the end point and is not necessarily the same as the equivalence point defined by stoichiometry. However, with careful choice of indicator it is possible to arrange for the end point to be close to the equivalence point Diprotic acids like sulfurous acid can donate two protons so the reaction occurs in two stages (with two distinct equivalence points): H 2 SO 3 (aq) + OH - (aq) HSO 3- (aq) + H 2 O(l) K a1 = 1.3 x 10-2 The most common indicators are weak acids, represented by the generic formula HIn They exhibit one color when the proton is attached (HIn) and another when the proton is absent (In - ) HSO 3- (aq) + OH - (aq) SO 3 2- (aq) + H 2 O(l) K a2 = 5.6 x

10 Phenolphtalein Methyl Orange HIn In - How Indicators Work Consider a hypothetical indicator which is red in its acidic form and blue in its basic form with K a = 1.0 x 10-8 : HIn(aq) H + (aq) + In - (aq) red blue K a = [H + ][In - ] / [HIn] or [In - ] / [HIn] = K a / [H + ] If we add a few drops of indicator to an acid solution with a ph = 1 ([H + ] = 1.0 x 10-1 M) the solution will be red: [In - ] / [HIn] = 1.0 x 10-8 / 1.0 x 10-1 = 1 / 10,000,000 As OH - is added to the acid in a titration the H + is consumed and the equilibrium shifts to the right changing HIn into In -. At some point enough In - will be present to turn the solution from red to purple and eventually blue Detecting the Color Change in Acidic Titrations For most indicators about a tenth (10 %) of the initial form must be converted into the other form before the human eye can detect a color change. Therefore, in the titration of an acid with a base, the color change will occur at a ph where: [In - ] / [HIn] = 1 / 10 Writing the Henderson-Hasselbalch equation for the equilibrium: ph = pk a + log([in - ] / [HIn]) = pk a + log(1 / 10) = pk a 1 Thus a color change will be detectable at a ph given by: ph = pk a 1 Bromothymol Blue [In-] / [HIn] << 1 [In-] / [HIn] = 1 / 10 [In-] / [HIn] >> 1 10

11 Detecting the Color Change in Basic Titrations When a basic solution is titrated, the indicator HIn will initially exist as In - but as the acid is added more and more HIn will form and a color change will eventually be noticeable Therefore, in the titration of an base with an acid, the color change will occur at a ph where: [In - ] / [HIn] = 10 / 1 Substituting this into the Henderson-Hasselbalch equation gives: ph = pk a + log([in - ] / [HIn]) = pk a + log(10 / 1) = pk a + 1 Thus a color change will be detectable at a ph given by: ph = pk a + 1 The Useful ph Range of an Indicator When an indicator is used to titrate an acid, the starting form will be HIn and the color change occurs at a ph of about: pk a 1 Methyl orange, an indicator with a K a value of 1.8 x 10-4 is pink in its HIn form and yellow in its In - form. Suppose we put a few drops of this indicator in a strongly basic solution. If the solution is then titrated with HCl, at what ph will the color change first become visible? When an indicator is used to titrate a base, the starting form will be In - and the color change occurs at a ph of about: pk a + 1 Thus, the useful ph range (the range of ph values where a color change will be detected) for an indicator will be given by: useful ph range = pk a ±1 When we choose an indicator for a titration, we want the indicator end point (where the color changes) to be as close to the equivalence point as possible 11

12 Choosing an indicator is much easier if there is a large ph change at the equivalence point as is the case for a strong acid-base titration In this case even a single drop of titrant added at the end point will cause a color change. We refer this a sharp end point In these cases there are a wide range of indicators which can be used since the ph change is so dramatic However, in the case of a weak acid titration there is a much smaller vertical area around the equivalence point so there is much less flexibility in choice of indicator When a M hydrocyanic acid solution is titrated with a M NaOH solution. What would be a good indicator to use for this titration? Here, phenophthalein would be a good choice since it changes color close to the equivalence point. Methyl red, however, would not be a good since it has a lower useful ph range and hence the end point would occur before the equivalence point has been reached If ml of 0.10 M ammonia, NH 3, K b = 1.8 x 10-5 is to be titrated with a 0.10 M HCl solution. What would be a good indicator to use for this titration? 12