Buffers, Titration Curves and Indicators-2 PDF

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EXP. 5 BUFFERS, TITRATION CURVES, AND INDICATORS Learning Objectives Now that you have completed the Standardization of an NaOH Solution and Titration of Strong and Weak Acids lab simulations, you should be familiar with some of the principles and techniques of volumetric analysis. In this experiment, you will study the properties of a pH titration curve and of a buffer solution. You will determine the: 1. concentration of a weak acid from its titration curve, and 2. pKa of the same weak acid from both its titration curve, and from the pH of the appropriate buffer solution. When you are ready, carefully read the Background Information and Experimental Procedure below. This document describes an experiment that would be performed in a traditional classroom laboratory. Ensure that you understand the concepts and procedure, as you will be provided with data corresponding to this activity and will need to analyze it. The lab report worksheets directly within this document are only for reference and will not be submitted. After you have read the Background Information and Experimental Procedure below, go to the course main page and click on the Buffers, Titration Curves, and Indicators Smart Worksheet. When you are done with the smart worksheet activity for this lab, submit it for grading. Make sure you submit before the scheduled due date. Note that you will be required to complete the Introduction to Smart Worksheets activity (also available via the course main page) before you will be able to access the Buffers, Titration Curves, and Indicators Smart Worksheet.

Background Information A convenient way to express the actual acidity of an aqueous solution is in terms of the pH scale. For our purposes, the pH may be defined as the negative of the logarithm of the hydrogen ion concentration, i.e., pH = – log10[H+] = – log[H3O+] where [H3O+] the concentration of (solvated) hydrogen ion in the solution in moles per liter. During an acid-base titration the pH is constantly changing. Figure 1 (shown at the end of “What is a Buffer Solution?”) illustrates how the pH changes when a weak acid, acetic acid, CH3COOH (frequently written HAc for short), is titrated with a strong base, sodium hydroxide, NaOH.

EXP. 5 BUFFERS, TITRATION CURVES, AND INDICATORS The equivalence point in a titration occurs when the amount of moles of base which has been added is stoichiometrically (chemically) equal to the initial number of moles of acid. The equivalence point is identified as the region of the curve where the pH rises abruptly; theoretically, it is the point of steepest slope, but in practice it is often chosen as the center of the very nearly straight-upand-down section of the curve. As OH– is added, the acid present (in this case acetic acid) reacts with it, and the effect on the pH is quite small because no excess OH– remains. Therefore, the pH increases only gradually until the equivalence point is reached. However, at the equivalence point, all of the HAc has reacted (by definition!). Therefore, the effect on the pH of the solution is very much the same as if OH– were added to water alone.

What is a Buffer Solution? A buffer is a solution containing appreciable amounts of both a weak acid and its conjugate weak base. During the titration of a weak acid with a strong base, the types of compounds present and their concentrations are constantly changing. Refer to the titration curve for acetic acid in Figure 1. The net ionic equation for this reaction is: CH3COOH(aq) + OH–(aq) → CH3COO–(aq) + H2O(l) or HAc(aq) + OH–( aq) → Ac–( aq) + H2O(l)

(1)

The net ionic equation indicates that as acetic acid, a weak acid, reacts with OH-, it is converted to an equal amount of acetate ion, Ac-, the conjugate weak base. During much of the titration, insufficient OH– has been added to consume all of the HAc; therefore, appreciable amounts of unreacted HAc are present plus Ac– formed from the reaction. Because the solution contains both HAc and Ac–, the solution is, by definition, a buffer. The most important characteristic of a buffer is its resistance to change in its pH; that is, if a small proportion of strong acid or strong base is added to it, the pH of the solution changes very little. The portion of the titration where the solution is normally considered to be a buffer is easily found. See the titration curve below. The effective buffer range can be determined through analyzing the titration curve. At the equivalence point, 20.13 mL of NaOH has been added. The mid-point or half-way point of this titration is found by dividing this “equivalence” volume by two: 20.13 ÷ 2 = 10.07 mL of titrant added. Find the pH at this point. The effective buffer range is usually accepted to be the part of the curve that falls between ±1 pH units of this pH. You will find these points and regions on the curve you make in this experiment. Buffered solutions are necessary both in the laboratory, where many reactions "won't work" if the pH changes, and in many biological systems. For example, the pH of

EXP. 5 BUFFERS, TITRATION CURVES, AND INDICATORS human blood plasma is about 7.4. A change of more than 0.10 pH units causes serious disruption of the body biochemistry, and a larger change is fatal.

Figure 1. Titration curve of a weak acid titrated with a strong base. Note, the equivalence and half equivalence points, as represented by stars, are not data points.

How to Prepare a Buffer Solution There are several common methods of preparing a buffer, and we will illustrate with two examples: 1. Dissolve appropriate quantities of a pure weak acid and its weak base in water. For example, in an ammonia–ammonium ion buffer (NH3/NH4+), the weak acid is in the form of a salt, often NH4Cl. This salt completely dissociates in water to produce NH4+ and Cl–. The latter ion will normally not appear in chemical equations describing buffer action; this is because it is a spectator ion. In the acetic acid-acetate ion buffer (HAc/Ac–), the weak base is in the form of a soluble salt, often NaC2H3O2 or KC2H3O2, and likewise the Na+ or K+ is a spectator ion. 2. Partially neutralize an excess of a weak acid by addition of strong base, such as NaOH, as limiting reagent. Note: some conjugate weak base is produced, while some weak acid remains. HA(aq) + OH –(aq) → A–(aq) + H2O(l) (where HA represents a weak acid, HC2H3O2, HCN, etc.)

(2)

EXP. 5 BUFFERS, TITRATION CURVES, AND INDICATORS Of course, partial neutralization of a weak base by a strong acid also produces a buffer. In both cases, the end result is to prepare a solution which contains both partners of a weak acid-weak base conjugate pair. Method 2 is used in today's experiment.

How a Buffer Works A strong acid (H3O+) or a strong base (OH–), when added to an unbuffered solution, causes a substantial change in the pH. When H3O+ ions are added to a buffer, however, the weak base component of the acid-base conjugate pair reacts with the H3O+ ions, effectively removing them. Therefore, the pH of the solution changes very little, i.e., A–(aq) + H3O+(aq) → HA(aq) + H2O(l) (where A– represents a weak base, C2H3O2–, CN–, etc.) Conversely, OH– ions are removed by the weak acid component of the acid-base conjugate system. HA(aq) + OH –(aq) → A–(aq) + H2O(l) The products of these reactions are a weak acid (when H3O+ is added) or a weak base (when OH – is added); these products produce few H3O+ and OH – ions in solution, and therefore the pH changes by very little. In other words, strong acid reacts with the weak base in a buffer, producing more weak acid. Strong base reacts with the weak acid in a buffer, producing more weak base. These reactions occur quantitatively; this means that equilibrium calculations on the reaction cannot be carried out until the quantitative reaction with strong acid or base has been taken into account. The pH of any buffer solution may be calculated from the basic principles of aqueous equilibria. Because a weak acid is present, the equilibrium expression for the acid dissociation constant, Ka, must hold: Ka =

[H 3O + ][ A− ] [ HA]

or

[ H 3O + ] = K a

[HA ] [ A− ]

(3)

Because a buffer contains both weak acid and weak base, the equilibrium can be expressed in terms of the Ka expression or the Kb (i.e. the base dissociation constant). However, since the Kb expression relates to [OH–] rather than to [H3O+], it is frequently convenient to use Ka when doing calculations to determine pH.

EXP. 5 BUFFERS, TITRATION CURVES, AND INDICATORS Taking the negative logarithm of both sides of Equation (3) results in a useful equation known as the Henderson-Hasselbalch equation, i.e., pH = pKa + log

[ A− ] [ HA]

(4)

In this equation, often (and certainly in this experiment): [ A −] ≅ cA−

and

[HA] ≅ cHA

(where c is the stoichiometric concentration of the species) Thus, if the concentrations, or the ratio of the concentrations, of the weak acid and conjugate weak base are known along with the Ka, the pH can be calculated. Also note that since the buffer solution is contained in a set volume, then the volume for both the weak acid and conjugate weak base is the same. This allows for the following simplification: n − pH = pK a + log A (5) n HA

(where n is the number of moles of the species) An important special case is the buffer in which the concentration of weak acid equals the concentration of weak base. This is commonly called a 1:1 buffer. The ratio of [HA]/[A– ] then equals unity, and we find: from Equation (3), from Equation (4),

[H3O+] = Ka pH = pKa

(because log 1 = 0)

The pKa of any weak acid may now be found from its titration curve. Refer to Figure 1, which represents a titration between acetic acid and sodium hydroxide. The pH will equal pKa at some point on the curve where equal parts of weak acid and weak base exist. A little thought will show that this occurs when the original weak acid has been half-neutralized, i.e. when half of the original weak acid HA has been converted to weak base A–, and half remains unreacted as HA. This takes exactly half as much OH – as is needed to reach the equivalence point. Note that dilution does not affect the pH of a buffer solution: see Equations (3) and (4). If the solution is diluted by a factor, for example, of 5, then both [HA]and [A–] are reduced by a factor of 5, but the ratio [HA]/[A– ] stays the same.

Indicators When using a visual indicator during an acid-base titration, the colour of the solution depends on the pH. Indicators are weak acids or weak bases in which the conjugate acid-conjugate base pair have different colours. Consider, an indicator in which the

EXP. 5 BUFFERS, TITRATION CURVES, AND INDICATORS conjugate acid form is an uncharged protonated acid, HIn. In aqueous solution, HIn is in equilibrium with H3O+ and In– according to the equation: HIn(aq) + H2O(l) ↔ H3O+(aq) + In–(aq) The equilibrium constant expression is: [H3 O+ ][In − ] (6a) [HIn] Since HIn and In– have different colours, the colour of the solution depends on the relative concentrations of HIn and In–. An expression for this ratio may be obtained by rearrangement of Equation (6a): [HIn] (6b) [H3O + ] = KHIn [In− ] This is very similar to Equation 3. However, in Equation 3 the concentrations of weak acid-weak base are much greater than [H3O+], and so their equilibrium controls [H3O+]. In Equation (6b) the concentration of [HIn] and [In–] is very low, and therefore the ratio [HIn]/[In– ] is controlled by [H3O+]. K HIn =

Taking the negative logarithm of each side:

− log[H3O + ] = − logKHIn − log

[HIn] [In− ]

and

(7)

[In− ] pH = pK HIn + log [HIn ]

If [In–] > [HIn], the solution takes the colour of In–. Conversely, if [HIn] > [In–], the solution is the colour of HIn. If [HIn] = [In–], the solution is at the point of changing colour. By definition, the endpoint of a titration occurs when the indicator changes colour. The important point is that the endpoint must closely match the equivalence point. This is seen in today's experiment when you will generate a titration curve for the acetic acid/sodium hydroxide titration, and locate on it the theoretical endpoints of several indicators. From Equation (7) it is seen that the ratio of [In–]/[HIn], and hence the colour of the solution, depends on both pKHIn and pH. We will assume that if the indicator is 90% in the HIn form and 10% in the In– form, the solution has the colour of HIn. Likewise, 10% HIn and 90% In– will confer the colour of In– on the solution. Therefore, the solution changes colour as the constitution of the indicator changes from: {90% HIn and 10% In–}

to

{ 10% HIn and 90% In–}

EXP. 5 BUFFERS, TITRATION CURVES, AND INDICATORS Mathematically, [In − ] 10 = ≈ 0. 1 [ HIn] 90

and

[In − ] 90 = ≈ 10 [ HIn] 10

and, accepting the above approximation, log

[In− ] = log 0. 1 = − 1 [HIn ]

and

log

[In− ] = log 10 = 1 [HIn ]

Then, from Equation (7), we know colour changes over a range of roughly 2 pH units: pH = pKHIn – 1

to

pH = pKHIn + 1

A common mistake is to think that KHIn should be equal to Ka for the acid being titrated. The pKa of a given acid is found half-way to the equivalence point; the indicator must change colour at the equivalence point of the titration. If the indicator and the acid being titrated have the same pKa, the endpoint (colour change) will occur at the half-equivalence point instead of at the equivalence point. We have already seen that an indicator changes colour when its pKa equals the pH of whatever solution it is in. Therefore, the indicator must have a pKHIn equal to the pH expected at the equivalence point in the titration. As different indicators turn colour at different pHs, and as titration equivalence points occur at different pHs, it is evident that considerable knowledge of both the titration reaction and of indicators is required before a wise choice of indicator can be made. A titration curve gives a picture of what is happening throughout the titration. An indicator tells nothing about the titration: it will change colour at its own pre-ordained pH, regardless of whether this is anywhere near the equivalence point. The pH ranges for the colour changes of several common indicators are given in Table 1 below. Table 1: pH Range of Several Indicators Indicator

pKIN

Thymol blue – 1st change Methyl orange Bromocresol green Methyl red Bromothymol blue Thymol blue – 2nd change Phenolphthalein Thymolphthalein Alizarin yellow R

1.7 3.7 4.7 5.1 7.0 8.9 9.3 9.9 11.0

pH Range of Colour Change 1.2 - 2.8 3.1 – 4.4 3.8 – 5.4 4.4 – 6.3 6.0 – 7.7 8.0 – 9.6 8.2 – 10.0 9.4 – 10.6 10.1 – 12.0

HIn Colour red red yellow red yellow yellow colourless colourless yellow

In– Colour yellow yellow blue yellow blue blue pink blue red

EXP. 5 BUFFERS, TITRATION CURVES, AND INDICATORS You may wonder why it is that if the indicator is a weak acid, its presence does not affect the results of an acid–base titration. The answer is that the amount of the weakly acidic indicator is very much smaller than the amount of the acid being titrated. For very precise work, however, it is necessary to do a blank titration; this involves adding the same few drops of indicator to water, and doing a titration to determine how much of the titrant needs to be added just to change the colour of the indicator. The volume of the blank is then subtracted from each of the actual determinations of the volume.

Summary of Experiment In Part 1: You will plot a titration curve for an acetic acid-sodium hydroxide titration, using your previously standardized NaOH solution as titrant. The equivalence point will be found on the graph and the concentration of the unknown acetic acid determined. Although indicators will not be used in the actual experiment, you will mark on the graph the endpoint, the point at which several indicators would have changed colour, had indicators been used. To do this, mark on the graph the two extremes of the pH range over which the colour changes. In Part 2: You will prepare a 1:1 buffer (acetic acid-sodium acetate). The volumes of acetic acid and sodium hydroxide solution that are needed to prepare the 1:1 buffer solution will be deduced from the titration curve which you made in Part 1. In Part 3: You will examine the properties of a buffer solution.

EXP. 5 BUFFERS, TITRATION CURVES, AND INDICATORS Experimental Procedure Part 1 – Titration Curves All readings from the burette and the pH meter should be recorded and plotted directly onto your graph paper. By graphing the data as it is acquired, you will be able to easily identify the end of the titration and better anticipate the equivalence point. 1. Prepare the burette for titration: a) Rinse and fill a clean 50 mL burette with your standard ~0.1 M NaOH solution (concentrations will vary, but will be close to 0.1 M and be accurate to 4 decimal places). b) To make it easier to plot your data, set the NaOH level to exactly 0.00 mL. Low concentration NaOH solutions are mildly caustic. If spilled on skin or clothing, wash immediately with water. NaOH solutions are also slippery, so hold containers securely. 2. Prepare your “unknown” for analysis: a) In a 150 mL beaker, obtain approximately 100 mL of the ~0.2 M acetic acid provided. Label the beaker as 0.2 M acetic acid. b) Using a pipette, transfer exactly 10.00 mL of the acid to a clean, wet 250 mL beaker. Add approximately 100 mL of deionized water from a graduated cylinder. Mix thoroughly. This is the unknown acid solution you will titrate; label the beaker as “unknown” acid solution. Note: This is called our “unknown” acid solution, as we do not know the exact concentration of the acetic acid. The concentration will be determined by titrating it with your standardized NaOH solution. 3. Calibrate (standardize) the pH meter: a) The standard buffer used in this experiment has a pH of 7.0. b) Rinse the electrode thoroughly. 4. Set-up for the titration (refer to Figure 2): a) Place the pH electrode into the “unknown” acid solution prepared in Step 2b above. Swirl the beaker around the pH electrode for a few seconds. b) When the pH reading is stable, record the pH of the “unknown” acid solution onto your graph for the NaOH volume of zero (as no titrant has been added). c) The electrode should remain immersed in the solution throughout the entire titration process.

EXP. 5 BUFFERS, TITRATION CURVES, AND INDICATORS

Figure 2. Titration set-up with pH meter. 5. Titrate the “unknown” acid: a) Add NaOH in ~2 mL increments. Swirl the beaker after every addition of NaOH to ensure proper mixing, and hence a smooth curve. Do not use a stirring rod. For each addition of NaOH, read the NaOH volume on the burette, read the pH, and record the point on the graph and in your table. b) Reduce to ~1 mL increments after about 10 mL NaOH has been added. c) As you approach the equivalence point the curve will bend slightly upward. Watch the graph. If it appears to bend upward, or if the pH rises by 0.3 units or more after adding a 1 mL aliquot, then you should add NaOH in smaller increments than 1 mL. The smallest quantities should be about 0.1 mL (~ 2 drops) or even less (see Figure 1) in the region of the equivalence point. The pH rises so steeply that these quantities are easily recorded, even though the increment in NaOH volume is very small. Extra and very thorough mixing is required in the region of the equivalence point, because the electrode is sensitive to infinitesimal changes in hydrogen ion concentration. The titration ends when the curve is "around the bend" at the top; however, you should continue until you are certain that the curve has "levelled off". 6. Wash pH electrode: a) Wash the electrode thoroughly in water. b) Obtain about 25 mL...