Determination of K a and Identification of an Unknown Weak Acid

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1 1 Determination of K a and Identification of an Unknown Weak Acid Introduction Purpose: To determine the molar mass and acid dissociation constant K a for an unknown weak acid and thereby identify the acid A Bronsted-Lowry acid is a substance which will donate a proton (H + ion) in aqueous solution to another substance. Similarly, a Bronsted-Lowry base is a substance which is capable of accepting a proton from another substance in aqueous solution. A Bronsted-Lowry acid base reaction then involves the transfer of a proton from a Bronsted-Lowry acid to a Bronsted-Lowry base. For example, in the reaction H 2 SO 3 + HCO 3 - HSO H 2 CO 3 (eq. 1) H 2 SO 3 behaves as the acid, donating a proton to HCO 3 - to yield carbonic acid, H 2 CO 3, and producing the bisulfite ion, HSO 3 -, as a result of loss of the proton from H 2 SO 3. H 2 SO 3 + HCO 3 - HSO H 2 CO 3 H + Monoprotic acids have only one ionizable, or transferable, hydrogen ion (proton). Examples include acids like hydrochloric acid (HCl), nitric acid (HNO 3 ), and acetic acid (HC 2 H 3 O 2 ). Diprotic acids have two ionizable hydrogen ions per molecule of acid, and include such acids as sulfuric acid (H 2 SO 4 ) and oxalic acid (H 2 C 2 O 4 ). Some salts are considered acids if they contain H atoms; compounds like sodium hydrogen sulfate, NaHSO 4, are produced from diprotic acids (like H 2 SO 4 ) and are thus considered to be half-neutralized. The compound NaHSO 4 is therefore treated as a monoprotic acid since it has a proton that it can potentially give up to another substance in an acid-base reaction. Acids are further classified as being either strong acids or weak acids. A strong acid is one which dissociates completely into its constituent ions in aqueous solution. A weak acid, on the other hand, is one which only partially ionizes into ions in aqueous solution. The distinction between strong and weak acids is a very important one to make, and it is very straightforward as there are only seven strong acids, and their names and formulas should be committed to memory. Any acids that you encounter that are not one of the strong acids must therefore be considered a weak acid. The formulas and names, respectively, of the seven strong acids are

2 2 HCl hydrochloric acid HNO 3 nitric acid HBr hydrobromic acid HClO 4 perchloric acid HI hydroiodic acid H 2 SO 4 sulfuric acid So weak acids only partially dissociate, or ionize, in water to produce H + ions and an anion that is characteristic of the acid. Representing a generic weak acid with the formula HA, we can write an equation for the dissociation of the weak acid in one of two ways; HA + H 2 O H 3 O + + A - (eq. 2) or as HA H + + A - (eq. 3) Since the second equation above is simpler, this is the way these equations will be written. Since the equation for the dissociation of a weak acid represents an equilibrium process, it can be represented with an equilibrium constant K a, sometimes called the acid dissociation constant. For acid HA, this can be written as either K = a + - [H3O ][A ] [HA] (eq. 4) or as K = a + - [H ][A ] [HA] (eq. 5) depending on whether equation 2 or 3 is used to represent the equilibrium reaction. Because values of K a are often quite small, chemists sometimes compare acids and their relative strengths by comparing their pk a values. pk a = -log K a (eq. 6) A relatively strong acid will have a larger value of K a, and will thus have a smaller value of pk a. Conversely, a very weak acid will have a very small K a and thus a very large value of pk a. For example, if two acids are compared in terms of their K a values and pk a s; K a pk a acetic acid, HC 2 H 3 O x hydrocyanic acid, HCN 6.2 x it becomes more obvious that the stronger acid of the two, acetic acid, has the larger K a but the smaller pk a. In this experiment you will perform an acid-base titration to experimentally determine the value of the molar mass and K a for an unknown monoprotic acid, and from that information you will determine the identity of the unknown acid.

3 3 Titration Curves A titration is an experimental procedure in which a standardized solution (one whose concentration is very precisely known), called the titrant, is carefully added to a solution whose concentration is imprecisely known. In an acid-base reaction like the one you will carry out in today s lab, one piece of useful information obtained from the titration is the exact volume of titrant (base) required to exactly neutralize the acid. The point at which the acid and base have exactly neutralized one another is called the equivalence point. The ph at the equivalence point is not necessarily equal to 7, but at that point the number of moles of H + will equal the number of moles of OH - added. The equation for the neutralization reaction is HA (aq) + NaOH (aq) NaA (aq) + H 2 O (l) (eq. 7) In a previous chemistry course, you probably carried out a titration in which you used an acid-base indicator, such as phenolphthalein, to give a color change (colorless to pink) signaling the point at which the acid and base had just neutralized one another. In this experiment, instead of using an indicator color change to mark what is called the endpoint of the titration, you will use a ph meter to continuously follow the progress of the neutralization reaction and determine the equivalence point. As you will see shortly, this will provide even more information than could be obtained from using only a visual indication of the endpoint. You will measure the ph of the titration mixture after successive portions of base have been added during the titration, and will then construct a titration curve by plotting ph (on the y-axis) versus volume NaOH (on the x-axis). A typical titration curve is shown in Figure 1 below. Notice that as base is added, the ph rises very slowly at first, then begins to rise more sharply approaching the equivalence point. Figure 1

4 4 The equivalence point is the point at which the ph rises very rapidly. Since this point is sometimes difficult to determine precisely from a titration curve (depending on how sharply the ph rises), we will use a mathematical trick to get a very precise value of the equivalence point. You may remember from a previous math course that the derivative of a curve is just the slope of the curve at a given point. On your titration curve, the slope reaches a maximum at the equivalence point, so if we make a first derivative plot of the derivative of ph versus volume NaOH, the result makes determination of the equivalence point very easy (see Figure 2). This graph is essentially a plot of the slope of Graph 1 at a given point versus volume of NaOH. Figure 2 In this case the equivalence point is clearly the top of the peak (maximum slope), which in this example occurs at ml base. The equivalence point can then be use to determine the molar mass of the acid. In this experiment, the volume of base needed to get halfway to the equivalence point, logically called the half-equivalence point, is just as important as the equivalence point. In the above example (Figure 2) this would be ml 2 = ml base. Remember that K = a + - [H ][A ] [HA] (eq. 8) But at the half-equivalence point, exactly half the acid has been converted into its conjugate base, A -, so at that point, [HA] = [A - ]. K = a + - [H ][A ] [HA] Thus K a = [H + ] and ph = pk a (eq. 9) So by first obtaining the equivalence point, and from that the ph halfway to the equivalence point, you can easily determine pk a for your unknown weak acid directly from the titration

5 5 curve. This, along with the molar mass of the unknown acid, which can be calculated from the mass of acid used and the moles of base needed to get to the equivalence point, allows you to identify the unknown acid from a list of possible unknowns. Procedure 1. Obtain a vial with a solid unknown weak acid. The vial will be marked with an unknown number and the approximate amount of acid you will need to use for each titration trial such that a reasonable volume of base (i.e. less than a buret full) will be needed for complete neutralization of the acid sample. 2. Record the acid unknown number on Data Sheet 1. Then weigh a sample of the acid using the analytical balance. The mass should be close to that shown on the vial, but must be known to four decimal places. 3. Transfer the acid sample to a clean 250 ml beaker. Add about 50 ml deionized water to dissolve the sample. Don t worry if the acid doesn t completely dissolve yet, because as you begin to titrate and the acid reacts with base, the reaction in equation 7 will be driven to the right and the acid will dissolve. 4. Carefully add a small Teflon-coated magnetic stir bar to the beaker, and position the beaker on the center of a magnetic stirring plate. SAFETY NOTE!! Handle solutions of sodium hydroxide (NaOH) with care. Avoid contact with your skin. If you do spill some on yourself, wash immediately with cold water. Notify your instructor. 5. After rinsing a buret thoroughly, first with deionized water, then with several small (~3-5 ml) portions of the standardized NaOH solution (don t forget to rinse some liquid through the buret tip, too), finally go ahead and fill the buret with the base solution to just above the 0.00 ml line. Drain liquid out until the volume reads exactly 0.00 ml. This is not a normal procedure in titrations, but in this experiment it makes subsequent calculations much easier if you start at exactly 0.00 ml. Make sure there are no air bubbles in the buret tip before starting the titration. Make sure all your buret readings are recorded to the nearest 0.01 ml; that is, to two digits to the right of the decimal point. 6. Position the buret such that the tip is over the beaker containing the unknown acid solution and near the side of the beaker, as shown in Figure 3.

6 6 Figure 3 7. Your instructor will show you correct procedures for operating the ph meter. In addition, there is a printed sheet of instructions next to each ph meter. Be especially careful not to bump the tip very hard as the glass bulb on the tip may break. After calibrating the ph meter to both ph 4.0 and 7.0 buffers, immerse the ph electrode into your acid solution such that the bulb is covered in liquid. If the bulb is not covered with liquid at this point, add just enough deionized water to cover the bulb of the electrode. You are now ready to begin titrating. 8. Begin by adding 1.0 ml of NaOH solution from the buret. (You don t have to use exactly 1.00 ml of base, but it should be close to 1.00 ml.) Once the ph meter reading is stable, record the ph and buret reading on Data Sheet 1. Then add another 1.0 ml of base and record the ph and buret reading. Initially, the ph will not go up by more than one or two hundredths ( ) of a ph unit after addition of each 1.0 ml of base. Continue in this fashion, using 1.0 ml aliquots of base until the ph rises by more than about ph units. At that point you MUST decrease the size of the portions of NaOH that are being added. If not, you risk having insufficient data through the equivalence point, in which case you will have to start all over again and anger your instructor immensely! If in doubt, ask your instructor for guidance in adjusting the portions of base when the ph begins to rise more significantly. 9. As you continue to titrate, the size of the portions of base added will have to decrease such that, ideally, as you approach the equivalence point you will be adding fractions of drops of NaOH through the most rapid ph rise region. To add a fraction of a drop of titrant (base), turn the buret stopcock just until about a half of a drop forms on the buret tip, then close the stopcock immediately before the drop falls off. Tip off the buret, i.e. gently touch the tip of the buret with the half drop, to the inside of the beaker and rinse down with a small stream of deionized water from a squeeze bottle. Then record the buret reading and ph as before.

7 7 10. Continue titrating in this fashion until the ph stops rising as fast, and increase the portions of base added again to about ml. Once the ph stops rising as fast as it did through the equivalence point, only a few more data points are needed to complete the titration curve. 11. Before cleaning up your apparatus, show your data to your instructor to confirm that the results are satisfactory. Rinse your buret thoroughly (including the tip) with lots of water and store it in the buret stand upside down with the stopcock open. All waste from this experiment can be poured down the drain along with lots of water. Calculations 1. Using Microsoft Excel or the Graphical Analysis software in the Science Learning Center, make a graph of ph on the y-axis versus volume of NaOH, in ml, on the x- axis. Print this graph and its data table, as separate printouts, and include both with your lab report. Label this graph as Graph Make a second graph that consists of the derivative of ph, and plot those values on the y- axis to obtain your first derivative plot. Print this graph and its data table as well, as separate printouts, and label this graph as Graph 2. The equivalence point in the titration is the maximum on this graph. 3. Clearly indicate on Graph 1 how you determined the volume of NaOH required to get to the half-equivalence point. The ph at this point should equal pk a for your unknown acid. Label pk a on the ph axis of Graph Use the volume of base at the equivalence point and the molarity of the NaOH solution to calculate the number of moles of base required to reach the equivalence point. moles NaOH = molarity NaOH x liters NaOH (eq. 10) Record the number of moles of base used on Data Sheet For titration of a monoprotic acid with a base, the 1:1 stoichiometry suggests that moles acid = moles base (eq. 11) Record the number of moles of acid used on Data Sheet Since you now know the mass of acid used and the moles of acid needed to neutralize the base, calculation of the molar mass of the unknown acid is as simple as dividing mass of acid, in grams, by the number of moles of acid. g acid = molar mass of acid (in g/mole) (eq. 12) moles acid

8 8 Record the molar mass of your unknown acid on Data Sheet Now that you know both the molar mass of your unknown acid and its pk a, compare these values to those in Table 1 to determine the identity of your unknown acid. Record the name of your unknown acid on Data Sheet 2. acid name Table 1 molar mass, g/mole K a pk a trans-crotonic x cis-crotonic x sodium hydrogen tartrate x mandelic x potassium hydrogen phthalate sodium hydrogen sulfite x x

9 9 Determination of K a and Identification of an Unknown Weak Acid Data Sheet 1 Name Lab Partner First Determination Unknown number Mass of acid used g Molarity of NaOH M buret reading, ml ph buret reading, ml ph buret reading, ml ph 0.00

10 10 Second Determination (if needed) Mass of acid used g buret reading, ml ph buret reading, ml ph buret reading, ml ph 0.00

11 11 Determination of K a and Identification of an Unknown Weak Acid Data Sheet 2 det. 1 det. 2 mass of acid used, g volume of base at equivalence point, ml (obtained from Graph 2) molarity of base, M moles of base to reach equivalence point moles of acid neutralized molar mass of unknown acid, g/mole half-equivalence point, ml base pk a of unknown acid K a of unknown acid name of unknown acid

12 12 Determination of K a and Identification of an Unknown Weak Acid Post-lab Question 1. Suppose that a student performing this experiment mistakenly calibrated the ph meter using ph 8 buffer instead of ph 7 buffer. As a result of this error, all of the student s ph readings were too low. a) Would this error have affected the calculated molar mass of the unknown acid? Briefly explain. b) Would this error have affected the experimentally determined pk a of the unknown acid? Briefly explain.

13 13 Determination of K a and Identification of an Unknown Weak Acid Pre-laboratory Assignment 1. Explain the difference between the terms endpoint and equivalence point. 2. Explain how to determine pk a for an unknown acid from a titration curve like the one you will prepare in this experiment. 3. Calculate pk a for an acid whose K a is 5.92 x Calculate K a for an acid whose pk a is A student does a monoprotic weak acid-strong base titration using g. of an unknown acid, and finds that ml of M NaOH are required to reach the equivalence point. a) How many moles of base were needed to reach the equivalence point? b) How many moles of acid were neutralized? c) Calculate the molar mass of the unknown acid.

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