#3. Acid - Base Titrations 27 EXPERIMENT 3. ACID-BASE TITRATIONS: DETERMINATION OF CARBONATE BY TITRATION WITH HYDROCHLORIC ACID BACKGROUND Carbonate Equilibria In this experiment a solution of hydrochloric acid is prepared, standardized against pure sodium carbonate, and used to determine the percentage of carbonate in a sample. An aqueous solution of hydrochloric acid is almost completely dissociated into hydrated protons and chloride ions. Therefore, in a titration with hydrochloric acid the active titrant species is the hydrated proton. This species is often written H 3 O +, although the actual form in solution is more correctly (H 2 O) n H +. For convenience we designate it simply H +. Carbonate in aqueous solution acts as a base; that is, it is able to accept a proton to form bicarbonate ion. CO 2-3 + H + <==========> HCO - 3 (1) Bicarbonate is able to combine with another proton to form carbonic acid: HCO - 3 + H + <==========> H 2 CO 3 (2) Equilibrium expressions for the dissociation of bicarbonate and carbonic acid may be written K 2 = [H+ ] [CO 2-3 ] [HCO - 3 ] (3) and K 1 = [H+ ] [HCO - 3 ] [H 2 CO 3 ] (4) where K 1 and K 2 are the first and second acid dissociation constants for H 2 CO 3 ; the experimentally determined values are K 1 = 3.5 x 10-7 and K 2 = 5 x 10-11. When successive protonation reactions such as (1) and (2) occur, the extent to which the first reaction proceeds before the second begins depends on the
28 #3. Acid- Base Titrations difference between the two acid dissociation constants. By combination of Equations (3) and (4) with those for charge and mass balance, [H + ] can be calculated for any ratio of hydrochloric acid to initial carbonate concentration, that is, at any point on a titration curve of carbonate with hydrochloric acid. Because complete and rigorous solution is time consuming, here only procedures for calculating the ph at several convenient points in a titration of 0.1 M sodium carbonate with 0.1 M hydrochloric acid (Figure 1) are covered briefly. An analytical textbook should be consulted for a more detailed discussion of this topic. ph at Point A in Figure 1. At point A 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 to give HCO - 3 and OH- 1 : CO 2-3 + H 2 O <==========> HCO - 3 + OH- (5) Here water acts as an acid, providing a proton to carbonate ion, the base. The equilibrium constant for this reaction may be written Figure 1. Curve for the titration of carbonate with hydrochloric acid. K b = [HCO- 3 ] [OH- ] [CO 2-3 ] (6) Multiplying the right side of Equation (6) by [H + ]/[H + ], we see that K b is equal to K w /K 2, where K w is the dissociation constant for water. K w = [H + ] [OH - ] = 10-14 at 25 C (7) 1 Reactions of ions of a solute with water often are called hydrolysis reactions. They are more properly considered, however, as simply another example of a Bronsted acid-base reaction in which water acts as an acid or a base.
#3. Acid - Base Titrations 29 and K 2 is the second dissociation constant for carbonic acid [Equation 3]. If the initial concentration of carbonate and the values of K w and K 2 are known, [OH - ] can be calculated from K w K 2 = [HCO - 3 ] [OH- ] [CO 2- (8) 3 ] Assume that the equilibrium for Equation (5) lies far to the left, so that the carbonate ion concentration is still essentially 0.1 M. Since bicarbonate and hydroxide are formed in equimolar amounts, [HCO - 3 ] = [OH - ] (9) Substitution of numerical values and Equation (9) in Equation (8) gives 10-14 5 x 10-11 = [OH- ] 2 0.1 (10) and [OH - ] = 4.5 x 10-3 M (11) From Equation (7) [H + ] = 10-14 4.5 x 10-3 = 2.2 x 10-12 M (12) so the ph is 11.7. In our use of Equation (6) we assume that the reaction HCO - 3 + H 2O <=========> H 2 CO 3 + OH- (13) does not occur to an appreciable extent; that it does not can be verified by substituting the value for [H + ] found in Equation (12) in Equation (4) and
30 #3. Acid- Base Titrations calculating [H 2 CO 3 ]. If [H 2 CO 3 ] is found to be greater than 5% of the total carbonate concentration, the [H + ] calculated from Equations (6) and (7) will be appreciably in error. In this case the expression should be solved either exactly, by including all species (which is tedious), or by successive approximations. Calculation shows that [H 2 CO 3 ] at Point A is negligibly small, so our assumption is valid. The additional assumption that [CO 2-3 ] is essentially 0.1 M also is confirmed because Equations (9) and (11) show that [HCO - 3 ] is less than 5% of [CO 2-3 ]. Note from this discussion that K w K = K b, or K w = K 2 K b. Thus, if Ka for an acid 2 HA is known, K b for the corresponding base A - can be calculated in aqueous solutions. An acid HA and base A - are called a conjugate acid-base pair; HA is the conjugate acid of A - and A - the conjugate base of HA. ph at Point B. At Point B in Figure 1, 1 2 mole of hydrochloric acid has been added for each mole of carbonate. The solution now contains an equimolar mixture of carbonate and bicarbonate. We can calculate the ph at this point by rearranging Equation (3) to [H + ] = [HCO- 3 ] K 2 [CO 2-3 ] (14) Since the bicarbonate and carbonate concentrations are equal, the hydrogen ion concentration is equal to K 2, and the ph is 10.3. Accurate calculations of concentrations of species during titrations must include the effect of dilution by the titrant, but thus far those caused by the addition of hydrochloric acid have not been considered. To correct calculations of concentrations of the major components for dilution, multiply each calculated concentration by the factor V/(V + ν), where V is the volume of the original solution and ν is the volume of hydrochloric acid added at any point. Although in the present example the effect is slight, in many systems the correction is significant.
#3. Acid - Base Titrations 31 ph at Point C. The first equivalence point (C in Figure 1) is reached when 1 mole of hydrochloric acid per mole of carbonate has been added. This solution contains only sodium bicarbonate; [H + ] is calculated by [H+] = K 1 K 2 = (3.5 x 10-7 ) (5 x 10-11 ) = 4.2 x 10-9 M (15) and the ph is 8.4. ph at Point D. Protonation of half the bicarbonate gives an equimolar solution of bicarbonate and carbonic acid (Point D). This is again a buffer system, this time involving the first dissociation constant of carbonic acid. The calculation is handled in the same way as for Point B, with K 1 used in place of K 2, to yield a ph of 6.5. ph at Point E. At the second equivalence point (E) the ph is determined by the extent of dissociation of carbonic acid, the principal species present, and [H + ] is calculated from Equation (4): K 1 = 3.5 x 10-7 = [H + ] [HCO - 3 ] (0.1) [50/(50 + 100)] = [H+ ] 2 0.033 (16) Therefore, [H + ] = 1.07 x 10-4 M = 10-3.97 (17) the ph is 3.97, or rounding to 2 significant figures, 4.0. Detection of the Equivalence Point Either the first or second equivalence point (C or E in Figure 1) can be used for carbonate analysis. In neither case is the ph change large in the region of the equivalence point. An uncertainty of 0.1 ph unit at either end point results in an uncertainty of about 1% in the amount of hydrochloric acid required. The error can be reduced if the titration is carried to a preselected indicator color. When a solution is titrated to the second equivalence point, a better approach is to take advantage of the dissociation of carbonic acid into a solution of carbon dioxide in water. Shaking or boiling a solution of carbonic acid causes the equilibrium to be H 2 CO 3 <=========> H 2 O + CO 2 (g) (18)
32 #3. Acid- Base Titrations driven to the right through loss of carbon dioxide. If a carbonate or bicarbonate solution is titrated to just before the equivalence point at ph 4 and then shaken or boiled, 2 the ph will rise to about 8 as the concentration of carbonic acid drops (dotted line in Figure 2). The ph is no longer controlled by dissociation of a relatively large concentration of carbonic acid but by a small concentration of bicarbonate. When the titrations continued, the ph goes down sharply because the amount of carbonic acid formed is small and the buffering effect negligible (dashed line in Figure 2). Standard Solutions Some standard solutions can be prepared directly by weighing or measuring carefully a definite quantity of a pure substance, dissolving it in a suitable solvent, and diluting it to a known volume. None of the strong acids, however, is convenient to handle and measure accurately in concentrated form. Therefore a solution of approximately the desired molarity is prepared, and the exact value is determined by standardization against a primary-standard base. Figure 2. Effect of removal of carbon dioxide on ph change the second equivalence point in a titration of carbonate with hydrochloric acid. Band indicates region of change of indicator color. Primary standards are stable, nonhygroscopic substances that react quantitatively and are easy to purify and handle. A high equivalent weight is advantageous because weighing errors are minimized. Among the excellent primary standards available are potassium acid phthalate, benzoic acid, oxalic 2 In mammals the CO 2 produced through biological oxidation is carried by the blood to the lungs, where it is exchanged for oxygen. Part of the CO 2 is present in the blood as H 2 CO 3. Since the time available in the lungs for exchange is short, the dissociation of H 2 CO 3 to CO 2 and H 2 O is accelerated by the enzyme carbonic acid anhydrase, a zinc-containing protein of high molecular weight. Thus nature need not resort to either boiling or shaking.
#3. Acid - Base Titrations 33 acid dihydrate, and sulfamic acid for standardizing bases and sodium oxalate, tris(hydroxymethyl)aminomethane, 4-amino pyridine, and sodium carbonate for standardizing acids. Pure anhydrous sodium carbonate, besides having all the properties of a suitable primary-standard base, has the added advantage in this experiment of being the same compound as the substance determined. This tends to compensate for determinate errors in end-point selection. PROCEDURE Reagent List: Unknown Sample - must be mixed thoroughly and dried HCl concentrated - approx. 12M sodium carbonate (Na 2 CO 3 ) - must be dried Bromocresol Green - indicator Put a little less than 1 liter of distilled water into a clean 1-liter bottle. Calculate the volume of 12 M HCl required to prepare 1 liter of 0.2 M HCl, and measure this quantity into a small graduated cylinder. Transfer it to the bottle and mix thoroughly. Label. Standardization of HCl with Primary-Standard Na 2 CO 3 Dry 1.5 to 2.0 g of pure Na 2 CO 3 in a glass weighing bottle or vial at 150 to 160 C for at least 2 hr. 3, 4 Allow to cool, in a desiccator if necessary, and then weigh by difference (to the nearest 0.1 mg) three or four 0.35 to 0.45 g portions of the dry material into clean 200-ml conical (Erlenmeyer) flasks. Add about 50 ml of distilled water to each and swirl gently to dissolve the salt. Add 4 drops of bromocresol green indicator and titrate with the HCl solution to an intermediate green color. At this point stop the titration and boil the solution gently for a minute or two, taking care that no solution is lost during the process. Cool the solution to room temperature, wash the flask walls with distilled water from a wash bottle, and then continue the titration to the first appearance of yellow. Just 3 Na 2 CO 3 tends to absorb H 2 O from the air to form Na 2 CO 3.H 2 O, and CO 2 to form NaHCO 3. At least several hours of drying at 140 C is necessary to remove all H 2 O and CO 2. 4 Use a pencil or felt marking pen to label the container with the name or sample number of the contents and with your locker number. The container may be placed inside a small glass beaker, and a watch glass, raised with several bent portions of glass rod, placed on top for protection. Avoid leaving chemicals or equipment in the drying oven longer than necessary, this not only causes crowding, but increases the chance of equipment being broken or samples contaminated by spilled chemicals.
34 #3. Acid- Base Titrations before the end point the titrant is best added in fractions of a drop. 5 Record the buret reading and add to it the buret calibration correction. Calculate the molarity of the HCl solution. The procedure outlined in the discussion of calculations below may be used as a guide. Relative deviations of 1 individual values from the average should not exceed about 2 parts per 1000. Determination of Carbonate in a Sample Mix the sample VERY THOROUGHLY and then dry it in a weighing bottle or small beaker for at least 2 hours at 150 to 160 C. Weigh into clean 200-ml conical flasks, to the nearest 0.1 mg, 0.35 to 0.45 g samples and titrate as in the standardization procedure. Calculate and report the percentage of Na 2 CO 3 in the sample. Use the Q test as the criterion for rejection of suspect experimental data. Either the median or the average may be reported. When the median is chosen the median value for the molarity of the HCl should be used in the calculations rather than the average value. CALCULATIONS The percentage of Na 2 CO 3 in a sample can be calculated in two steps: (1) the determination of the molarity of the HCl titrant from the standardization titrations and (2) the calculation of the percentage of Na 2 CO 3 from titrations of the sample. 1. Molarity of HCl. In titrations of Na 2 CO 3 with HCl to the ph 4 end point, 2 moles of HCl are added for each mole of Na 2 CO 3 : 2HCl + NaCO 3 <=========> H 2 CO 3 + 2NaCl (19) The HCl molarity is obtained from the following relations: MHCl = moles HCl liter = moles Na 2 CO 3 x 2 (ml HCl/1000) 5 To deliver amounts less than 1 drop from a buret, first let a droplet form on the tip, and then touch the tip momentarily to the inside wall of the flask. Rinse the wall with a small amount of distilled water from a wash bottle to ensure that the titrant is washed into the solution. Do not rinse the tip of the buret.
#3. Acid - Base Titrations 35 = (wt of Na 2 CO 3 ) x 2 (mol wt Na 2 CO 3 ) (ml HCl/1000) (20) The factor 2 required because each mole of Na 2 CO 3 reacts quantitatively with 2 moles of HCl. 2. Percentage of Na 2 CO 3 in Sample. The percentage of Na 2 CO 3 in the sample is calculated as follows: %Na 2 CO 3 = wt of Na 2 CO 3 in sample g sample x 100 = (moles Na 2CO 3 )(mol. wt. Na 2 CO 3 ) wt of sample x 100 (21) = (ml HCl) (molarity HCl) (mol wt Na 2CO 3 ) 1000 x 2 x wt. of sample x 100 Remember: Poor results are often caused by errors in calculation rather than by faulty laboratory technique. Check all calculations before reporting results.