29
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
H3O+, although the actual form in solution is more correctly (H2O)nH+. 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.
2CO3
+
H+ <==========> HCO3
(1)
Bicarbonate is able to combine with another proton to form carbonic acid:
HCO3 + H+
<==========> H2CO3
(2)
Equilibrium expressions for the dissociation of bicarbonate and carbonic acid may
be written
2[H+] [CO3 ]
K2 =
(3)
[HCO3]
and
K1 =
[H+] [HCO3]
[H2CO3]
(4)
30
where K1 and K2 are the first and second acid dissociation constants for H2CO3;
the experimentally determined values are K1 = 3.5 x 10-7 and K2 = 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
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 HCO3 and OH-1:
2CO3
+ H2O <==========> HCO3
+ 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
Kb =
[HCO3] [OH-]
2[CO3 ]
(6)
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.
1
31
Figure 1.
Curve for
the titration
of carbonate
with hydrochloric acid.
Multiplying the right side of Equation (6) by [H+]/[H+], we see that Kb is equal to
Kw/K2, where Kw is the dissociation constant for water.
Kw = [H+] [OH-] = 10-14 at 25°C
(7)
and K2 is the second dissociation constant for carbonic acid [Equation 3]. If the
initial concentration of carbonate and the values of Kw and K2 are known, [OH-]
can be calculated from
Kw
K2
=
[HCO3] [OH-]
2[CO3 ]
(8)
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,
[HCO3 ] = [OH-]
Substitution of numerical values and Equation (9) in Equation (8) gives
(9)
32
10-14
[OH-]2
=
0.1
5 x 10-11
(10)
[OH-] = 4.5 x 10-3 M
(11)
and
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
HCO3 + H2O <=========> H2CO3 + 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
calculating [H2CO3]. If [H2CO3] 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 [H2CO3] at Point A is negligibly small, so our assumption
2is valid. The additional assumption that [CO3 ] is essentially 0.1 M also is
confirmed because Equations (9) and (11) show that [HCO3 ] is less than 5% of
2[CO3 ] .
Kw
Note from this discussion that K
= Kb, or Kw = K2Kb. Thus, if Ka for an
2
acid HA is known, Kb for the corresponding base A- can be calculated in aqueous
33
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, 0.5 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+] =
[HCO3] K2
(14)
2[CO3 ]
Since the bicarbonate and carbonate concentrations are equal, the hydrogen ion
concentration is equal to K2, 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 + v), where V is the volume of the original
solution and v 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.
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+] =
(15)
K1K2
=
(3.5 x 10-7) (5 x 10-11)
= 4.2 x 10-9 M
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
34
handled in the same way as for Point B, with K1 used in place of K2, 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):
K1 = 3.5 x 10-7 =
[H+] [HCO3]
(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.
H2CO3 <=========> H2O + CO2 (g)
(18)
Shaking or boiling a solution of carbonic acid causes the equilibrium to be 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
In mammals the CO2 produced through biological oxidation is carried by the blood to the lungs,
where it is exchanged for oxygen. Part of the CO2 is present in the blood as H2CO3. Since the time
available in the lungs for exchange is short, the dissociation of H2CO3 to CO2 and H2O 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.
2
35
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 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.
36
PROCEDURE
Reagent List:
Unknown Sample - must be mixed thoroughly and dried
HCl concentrated - approx. 12M
sodium carbonate (Na2CO3) - 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 ( conc. ) 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 Na2CO3
Dry 1.5 to 2.0 g of pure Na2CO3 in a glass weighing bottle or vial at 150 to 160°C
for at least 2 hours.3,4 Check to see if the standard reagent was previously dried
for the class. 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 250-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 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.
Na2CO3 tends to absorb H2O from the air to form Na2CO3.H2O, and CO2 to form NaHCO3. At
least several hours of drying at 140°C is necessary to remove all H2O and CO2.
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.
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
37
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 Na2CO3 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 Na2CO3 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 Na2CO3 from titrations of the sample.
1.
Molarity of HCl. In titrations of Na2CO3 with HCl to the pH 4 end point, 2
moles of HCl are added for each mole of Na2CO3:
2HCl + Na2CO3 <=========> H2CO3 + 2NaCl
(19)
The HCl molarity is obtained from the following relations:
MHCl =
moles HCl
liter
=
moles Na2CO3 x 2
(ml HCl/1000)
(20)
(wt of Na2CO3) x 2
= (mol wt Na CO ) (ml HCl/1000)
2 3
The factor 2 required because each mole of Na2CO3 reacts quantitatively with
2 moles of HCl.
38
2.
Percentage of Na2CO3 in Sample. The percentage of Na2CO3 in the sample
is calculated as follows:
%Na2CO3 =
Remember:
wt of Na2CO3 in sample
g sample
x 100
=
(moles Na2CO3)(mol. wt. Na2CO3)
wt of sample
=
(ml HCl) (molarity HCl) (mol wt Na2CO3)
1000 x 2 x wt. of sample
x 100
(21)
x 100
Poor results are often caused by errors in calculation rather than by
faulty laboratory technique. Check all calculations and significant
figures before reporting results. Ensure you have reported the
correct unknown number.