Make your own free website on Tripod.com
 Acid-Base Titrations
 
Table of Contents
Purpose   page 1
Introduction   page 1
Procedure   page 2
Data and Results  page 3
Graphical Analysis  pages 9-11
Conclusion   page 12
References   page 12
 
Purpose
The purpose of this experiment was the determination of the percent by weight of carbonate in a solid unknown sample using proper titration techniques.  A standardized solution of hydrochloric acid was prepared, and the precise molarity of the solution determined.  The prepared solution of unknown sample was titrated with the standardized solution to establish the equivalence points of the carbonate sample.

Introduction
The percent by weight of a carbonate sample may be determined through proper titration techniques.  By titrating an unknown sample with a standardized hydrochloric acid solution one can determine the equivalence points of the reaction that occurs.  In the case of this experiment two reactions take place at different intervals during the titration process, and correspond to two different equivalence points.  The two reactions that occur are:
  HCl + Na2CO3 ßà NaHCO3 + NaCl
  NaHCO3 + HCl ßà H2CO3 + NaCl
The use of two indicators, Thymol Blue/Cresol Red and Screened Methyl Orange, allows a visual cue that reveals when the equivalence points are reached—as indicated by a change in color of the titrate.
The equivalence point of the carbonate sample can also be determined by titration using a pH meter.  Upon the addition of the titrant to the titrate the change in pH that is the greatest indicates the equivalence point of the titration process at that volume.  The data obtained from the titrations can be represented graphically to help determine the equivalence points.
Procedure
1. Preparation of an approximate 0.1 M HCl solution:
A 1 Liter glass bottle was obtained—it was cleaned and rinsed with deionized water.  The glass bottle was then filled with almost 1 Liter of deionized water.  The volume of 12 M HCl solution needed to prepare 1 Liter of a 0.1 M solution was calculated, and this volume was added to the water in the glass bottle.  The mixture was shaken and labeled appropriately.
2. Standardization of the 0.1 M HCl solution:
About 1 gram of dried primary standard Na2CO3 was obtained in a weighing bottle.
Samples of the Sodium Carbonate weighing between 0.18 to 0.22 grams were weighed out by difference into each of 3 pre-numbered 250 mL Erlenmeyer flasks (with a precision of +/- 0.1 mg).
The samples were dissolved in about 75 mLs of deionized water, and were mixed well.
For the titration process the smallest sample was titrated first.  To the smallest sample, 4 drops of Bromocresol Green indicator was added, and the solution was titrated with the 0.1 M HCl until it began to change from blue to green.  The solution was then boiled for 2 to 3 minutes, and then cooled to room temperature.  The titration was finished until the new blue color changed to green.  Titration dropwise in the vicinity of the endpoint was performed, and split drops were added at the endpoint.
The Molarity of HCl for each sample was then calculated.
3. Determination of the Unknown Carbonate:
Three samples of the unknown were weighed out by difference, each with a weight between 0.4 and 0.5 grams (with a precision of +/- 0.1 mg).  Two of the samples were then weighed into 250 mL Erlenmeyer flasks, and the third into a 250 mL beaker (the sample in this beaker was made to be heavier than the other two samples).
To the smallest sample in the Erlenmeyer flask about 100 mLs of water was added, as was 3 to 4 drops of the mixed Thymol Blue/Cresol Red indicator.  This solution was then titrated with the standardized 0.1063 M HCl until the color changed from violet to a definite yellow.
The second Erlenmeyer flask about 100 mLs of water was added along with 3 to 4 drops of the Screened Methyl Orange indicator.  The solution was then titrated with the standardized 0.1063 M HCl until the color changed from green to grey—which is the endpoint—to magenta.
About 100 mLs of deionized water was added to the sample contained in the 250 mL beaker.  No indicator was added to this sample.  Titration of this sample was performed with the pH meter, and readings of both pH and mLs added were recorded at respective intervals.
Data and Results

A. Standardization of the HCl solution:

Data Used For the Standardization
of the 0.1 M HCl Solution
Sample Wt. mLs 0.1 M HCl used M HCl
0.1993 g 35.45 0.1061
0.1969 g 34.90 0.1065
0.2003 g 35.60 0.1062
 Avg. M 0.1063

M HCl = (0.1993g Na2CO3 * 1 mol Na2CO3/105.99g Na2CO3) * 2 = 0.1061 M HCl
   0.03545L
M HCl = (0.1969g Na2CO3 * 1 mol Na2CO3/105.99g Na2CO3) * 2 = 0.1065 M HCl
   0.03490L
M HCl = (0.2003g Na2CO3 * 1 mol Na2CO3/105.99g Na2CO3) * 2 = 0.1062 M HCl
   0.03560L

Avg. Molarity = (0.1993g Na2CO3 + 0.1969g Na2CO3 + 0.2003g Na2CO3) = 0.1063
      3
Avg. Deviation = |0.1061 – 0.1063|+ |0.1065 – 0.1063| + |0.1062 – 0.1063| = 0.0001667
      3

Relative Average Deviation (RAD) = (0.0001667) * 1/0.1063 = 1.568

B. Determination of the Unknown CO32- Sample:

Unknown CO32- sample used was number 43.

The equation that took place for Reaction 1 using the Thymol Blue/Cresol Red indicator was as follows—
 H+ + CO32- ßà HCO3-
The equation that took place for Reaction 2 using the Screened Methyl Orange indicator was as follows—
 2H+ + CO32- ßà H2CO3
The percent CO32- (%CO32-) for each of the above reactions was determined as follows—
Reaction 1:
 %CO32- = (0.0154 L HCl * 0.1063 M HCl * 60 g/mol) * 100% = 23.88%
      0.4113 g sample
Reaction 2:

 %CO32- = (0.03055 L HCl * 0.1063 M HCl * 0.5 * 60 g/mol) * 100% = 23.80%
      0.4093 g sample

Data Used to Determine %CO32-
Using the Two Indicators
 Sample Wt. mLs HCl used M HCl % CO32-
Reaction 1 0.4113 g 15.40 mL 0.1063 23.88%
Reaction 2 0.4093 g 30.55 mL 0.1063 23.80%

The percent CO32- for the titration using a pH meter was determined as follows—
First Equivalence Point:
 %CO32- = (0.01505 L HCl * 0.1063 M HCl * 60 g/mol) * 100% = 23.48%
      0.4088 g sample
Second Equivalence Point:
 (0.02998 L HCl * 0.1063 M HCl * 0.5 * 60 g/mol) * 100% = 23.39%
      0.4088 g sample

Data Used to Determine %CO32-
Using the pH Meter
 Sample Wt. mLs HCl Used M HCl CO32-
1st Endpoint 0.4088 g 15.05 0.1063 23.48%
2nd Endpoint 0.4088 g 29.98 0.1063 23.39%

The average %CO32- was determined to be 23.64% according to the following calculation—
 Avg. %CO32- = (23.88% + 23.80% + 23.48% + 23.80%) = 23.64%
      4

The standard deviation was calculated to be 0.239 as depicted below—
 SD = Ö(23.88-23.64)2 + (23.80-23.64)2 + (23.48-23.64)2 + (23.39-23.64)2 = 0.239
      3
Using the student’s t-test the 95% confidence interval of the average was determined to be 23.64 ± 0.3802 as follows—
 U = 23.64 ± (3.182)(0.239) = 23.64 ± 0.3802
   Ö 4

Data Gathered and Determined from the Titration
of 0.1063 M HCl with the Unknown Carbonate Sample
mL HCl pH dpH dmL dpH/dmL V1 d2pH/dmL dV1 d2pH/dmL2 V2
0.00 11.21 -0.21 1.00 -0.21 0.50 0.04 1 0.04 1.00
1.00 11.00 -0.17 1.00 -0.17 1.50 0.00 1 0.00 2.00
2.00 10.83 -0.17 1.00 -0.17 2.50 0.03 1 0.03 3.00
3.00 10.66 -0.14 1.00 -0.14 3.50 0.02 1 0.02 4.00
4.00 10.52 -0.12 1.00 -0.12 4.50 -0.01 1 -0.01 5.00
5.00 10.40 -0.13 1.00 -0.13 5.50 0.01 0.75 0.01 5.88
6.00 10.27 -0.06 0.50 -0.12 6.25 0.00 0.5 0.00 6.50
6.50 10.21 -0.06 0.50 -0.12 6.75 0.00 0.5 0.00 7.00
7.00 10.15 -0.06 0.50 -0.12 7.25 0.02 0.5 0.04 7.50
7.50 10.09 -0.05 0.50 -0.10 7.75 -0.02 0.5 -0.04 8.00
8.00 10.04 -0.06 0.50 -0.12 8.25 0.00 0.5 0.00 8.50
8.50 9.98 -0.06 0.50 -0.12 8.75 -0.01 0.75 -0.01 9.13
9.00 9.92 -0.13 1.00 -0.13 9.50 -0.02 1 -0.02 10.00
10.00 9.79 -0.15 1.00 -0.15 10.50 -0.01 0.75 -0.01 10.88
11.00 9.64 -0.08 0.50 -0.16 11.25 -0.02 0.5 -0.04 11.50
11.50 9.56 -0.09 0.50 -0.18 11.75 -0.02 0.5 -0.04 12.00
12.00 9.47 -0.10 0.50 -0.20 12.25 0.04 0.5 0.08 12.50
12.50 9.37 -0.08 0.50 -0.16 12.75 -0.24 0.5 -0.48 13.00
13.00 9.29 -0.20 0.50 -0.40 13.25 -0.04 0.5 -0.08 13.50
13.50 9.09 -0.22 0.50 -0.44 13.75 0.04 0.3 0.13 13.90
14.00 8.87 -0.04 0.10 -0.40 14.05 -0.25 0.15 -1.67 14.13
14.10 8.83 -0.13 0.20 -0.65 14.20 -0.10 0.2 -0.50 14.30
14.30 8.70 -0.15 0.20 -0.75 14.40 -0.15 0.15 -1.00 14.48
14.50 8.55 -0.09 0.10 -0.90 14.55 -0.10 0.1 -1.00 14.60
14.60 8.46 -0.10 0.10 -1.00 14.65 -0.10 0.1 -1.00 14.70
14.70 8.36 -0.11 0.10 -1.10 14.75 0.10 0.1 1.00 14.80
14.80 8.25 -0.10 0.10 -1.00 14.85 0.10 0.1 1.00 14.90
14.90 8.15 -0.09 0.10 -0.90 14.95 -0.40 0.1 -4.00 15.00
15.00 8.06 -0.13 0.10 -1.30 15.05 0.30 0.075 4.00 15.09
15.10 7.93 -0.05 0.05 -1.00 15.13 0.60 0.05 12.00 15.15
15.15 7.88 -0.02 0.05 -0.40 15.18 -0.40 0.075 -5.33 15.21
15.20 7.86 -0.08 0.10 -0.80 15.25 0.10 0.1 1.00 15.30
15.30 7.78 -0.07 0.10 -0.70 15.35 0.00 0.1 0.00 15.40
15.40 7.71 -0.07 0.10 -0.70 15.45 0.20 0.1 2.00 15.50
15.50 7.64 -0.05 0.10 -0.50 15.55 0.10 0.1 1.00 15.60
15.60 7.59 -0.04 0.10 -0.40 15.65 -0.10 0.1 -1.00 15.70
15.70 7.55 -0.05 0.10 -0.50 15.75 0.10 0.1 1.00 15.80
15.80 7.50 -0.04 0.10 -0.40 15.85 0.10 0.1 1.00 15.90
15.90 7.46 -0.03 0.10 -0.30 15.95 -0.10 0.1 -1.00 16.00
16.00 7.43 -0.04 0.10 -0.40 16.05 0.10 0.1 1.00 16.10
16.10 7.39 -0.03 0.10 -0.30 16.15 0.00 0.1 0.00 16.20
16.20 7.36 -0.03 0.10 -0.30 16.25 0.03 0.2 0.17 16.35
16.30 7.33 -0.08 0.30 -0.27 16.45 -0.07 0.3 -0.22 16.60
16.60 7.25 -0.10 0.30 -0.33 16.75 0.10 0.45 0.22 16.98
16.90 7.15 -0.14 0.60 -0.23 17.20 0.05 0.55 0.10 17.48
17.50 7.01 -0.09 0.50 -0.18 17.75 0.00 0.5 0.00 18.00
18.00 6.92 -0.09 0.50 -0.18 18.25 0.02 0.5 0.04 18.50
18.50 6.83 -0.08 0.50 -0.16 18.75 0.00 0.5 0.00 19.00
19.00 6.75 -0.08 0.50 -0.16 19.25 0.04 0.5 0.08 19.50
19.50 6.67 -0.06 0.50 -0.12 19.75 -0.02 0.75 -0.03 20.13
20.00 6.61 -0.14 1.00 -0.14 20.50 0.02 1 0.02 21.00
21.00 6.47 -0.12 1.00 -0.12 21.50 -0.01 1 -0.01 22.00
22.00 6.35 -0.13 1.00 -0.13 22.50 0.01 1 0.01 23.00
23.00 6.22 -0.12 1.00 -0.12 23.50 -0.01 1 -0.01 24.00
24.00 6.10 -0.13 1.00 -0.13 24.50 0.01 1 0.01 25.00
25.00 5.97 -0.12 1.00 -0.12 25.50 -0.05 1 -0.05 26.00
26.00 5.85 -0.17 1.00 -0.17 26.50 -0.01 0.75 -0.01 26.88
27.00 5.68 -0.09 0.50 -0.18 27.25 -0.06 0.5 -0.12 27.50
27.50 5.59 -0.12 0.50 -0.24 27.75 -0.04 0.5 -0.08 28.00
28.00 5.47 -0.14 0.50 -0.28 28.25 0.08 0.35 0.23 28.43
28.50 5.33 -0.04 0.20 -0.20 28.60 -0.27 0.25 -1.07 28.73
28.70 5.29 -0.14 0.30 -0.47 28.85 -0.03 0.25 -0.13 28.98
29.00 5.15 -0.10 0.20 -0.50 29.10 0.10 0.15 0.67 29.18
29.20 5.05 -0.04 0.10 -0.40 29.25 -0.50 0.1 -5.00 29.30
29.30 5.01 -0.09 0.10 -0.90 29.35 0.30 0.1 3.00 29.40
29.40 4.92 -0.06 0.10 -0.60 29.45 -0.20 0.1 -2.00 29.50
29.50 4.86 -0.08 0.10 -0.80 29.55 -0.90 0.1 -9.00 29.60
29.60 4.78 -0.17 0.10 -1.70 29.65 0.30 0.075 4.00 29.69
29.70 4.61 -0.07 0.05 -1.40 29.73 0.00 0.05 0.00 29.75
29.75 4.54 -0.07 0.05 -1.40 29.78 -2.20 0.05 -44.00 29.80
29.80 4.47 -0.18 0.05 -3.60 29.83 1.60 0.05 32.00 29.85
29.85 4.29 -0.10 0.05 -2.00 29.88 0.00 0.05 0.00 29.90
29.90 4.19 -0.10 0.05 -2.00 29.93 -2.40 0.05 -48.00 29.95
29.95 4.09 -0.22 0.05 -4.40 29.98 2.60 0.05 52.00 30.00
30.00 3.87 -0.09 0.05 -1.80 30.03 0.20 0.05 4.00 30.05
30.05 3.78 -0.08 0.05 -1.60 30.08 -1.00 0.05 -20.00 30.10
30.10 3.70 -0.13 0.05 -2.60 30.13 1.80 0.05 36.00 30.15
30.15 3.57 -0.04 0.05 -0.80 30.18 -0.40 0.075 -5.33 30.21
30.20 3.53 -0.12 0.10 -1.20 30.25 0.60 0.075 8.00 30.29
30.30 3.41 -0.03 0.05 -0.60 30.33 -1.00 0.05 -20.00 30.35
30.35 3.38 -0.08 0.05 -1.60 30.38 1.00 0.075 13.33 30.41
30.40 3.30 -0.06 0.10 -0.60 30.45 0.00 0.1 0.00 30.50
30.50 3.24 -0.06 0.10 -0.60 30.55 -0.10 0.1 -1.00 30.60
30.60 3.18 -0.07 0.10 -0.70 30.65 0.20 0.1 2.00 30.70
30.70 3.11 -0.05 0.10 -0.50 30.75 0.10 0.1 1.00 30.80
30.80 3.06 -0.04 0.10 -0.40 30.85 -0.10 0.1 -1.00 30.90
30.90 3.02 -0.05 0.10 -0.50 30.95 0.15 0.15 1.00 31.03
31.00 2.97 -0.07 0.20 -0.35 31.10 0.05 0.2 0.25 31.20
31.20 2.90 -0.06 0.20 -0.30 31.30 0.10 0.3 0.33 31.45
31.40 2.84 -0.08 0.40 -0.20 31.60 -0.05 0.3 -0.17 31.75
31.80 2.76 -0.05 0.20 -0.25 31.90 0.07 0.35 0.20 32.08
32.00 2.71 -0.09 0.50 -0.18 32.25 0.04 0.5 0.08 32.50
32.50 2.62 -0.07 0.50 -0.14 32.75 0.02 0.5 0.04 33.00
33.00 2.55 -0.06 0.50 -0.12 33.25 0.02 0.5 0.04 33.50
33.50 2.49 -0.05 0.50 -0.10 33.75 0.00 0.5 0.00 34.00
34.00 2.44 -0.05 0.50 -0.10 34.25 0.02 0.5 0.04 34.50
34.50 2.39 -0.04 0.50 -0.08 34.75 0.01 0.75 0.01 35.13
35.00 2.35 -0.07 1.00 -0.07 35.50 0.02 1 0.02 36.00
36.00 2.28 -0.05 1.00 -0.05 36.50 0.00 1.5 0.00 37.25
37.00 2.23 -0.10 2.00 -0.05 38.00 0.01 2 0.01 39.00
39.00 2.13 -0.08 2.00 -0.04 40.00 0.01 2 0.01 41.00
41.00 2.05 -0.06 2.00 -0.03 42.00 0.00 2 0.00 43.00
43.00 1.99 -0.06 2.00 -0.03 44.00 0.01 2 0.00 45.00
45.00 1.93 -0.05 2.00 -0.03 46.00 0.01 2.5 0.00 47.25
47.00 1.88 -0.06 3.00 -0.02 48.50 0.02 -48.5 0.00 24.25
50.00 1.82

 

Titration of 0.1063 M HCl vs. the
Unknown Carbonate Sample
 

First Derivative Plot for the Titration of 0.1063
M HCl vs. the Unknown Carbonate Sample
 

Second Derivative Plot for the Titration of 0.1063 M
HCl vs. the Unknown Carbonate Sample
 
Conclusion
The titration method is often a tricky technique when using indicators to determine the equivalence point of a reaction.  This is because the color change of the titrate is often difficult to recognize.  In such instances some level of error is therefore likely.
The Molarity of the solution of standardized hydrochloric acid was standardized at 0.1063 M.  The titration of a carbonate (CO32-) sample with the HCl determined the percent by weight carbonate to be 23.88% for the first reaction, and 23.80% for the second reaction.  Using data obtained from graphical analysis two other values of percent by weight of carbonate were determined.  A value of 23.48% was found for the first equivalence point, and 23.39% was found for the second equivalence point.  The average of these four values was calculated to be 23.64%.
The standard deviation was found to be 0.239, and a confidence interval of 23.64 ± 0.3802 was also determined.  The value obtained for the standard deviation shows a relatively high accuracy and precision for the experiment.

References
Morales-Martinez, Zaida C.  1999.  Quantitative Analysis Laboratory Manual.  Florida International University.
Harris, Daniel C.  1997.  Exploring Chemical Analysis.  W.H. Freeman and Company, New York, NY.