Abstract
Determination of alkalinity of water sample is generally carried out experimentally by titration method using a proper indicator. In the literature, five different cases of possible alkalinities are reported based on the experimental data of acid titration of water sample using phenolphthalein and methyl orange. The reported data is the volume of acid consumption and the relationship between the alkalinity causing ions present in the water sample. However, no systematic approach is available in the literature to understand these experimentally reported volume of acid utilized for neutralization reaction. To make students understand the key features of the reported experimental data, a systematic approach is presented in this study. By using a simple mathematics and a theoretical explanation to the reported reactions taking place during acid titration of water sample, a supplementary document is developed. The theoretical concept in the form of supplementary information is introduced without altering any data reported in the literature or experimental procedure.
1 Introduction
Water Technology is included in first year engineering chemistry syllabus. The course content includes topics on determination of alkalinity of water, five different cases of probable type of alkalinities presented as an experimental data, numerical and laboratory session. The experimental data presented in the course is based on the titration of water sample given as the relationship between the type of ions and alkalinity as a function of volume of acid utilized for neutralization.
However, many students were finding it difficult to interpret and understand the concept behind the data presented. This impeded their understanding and conceptual approach towards the concept which was reflected from their performance in class room interaction. To make teaching and learning effective, the concept was approached in a different way and presented before the students as supplementary information. This inquiry-based approach strategy was used to facilitate student’s scientific learning and the performance was evaluated based on the traditional teaching and assessment approach.
1.1 Water alkalinity and its determination
Alkalinity is one of the important characteristics of water, which is a measure of the ability of water to neutralize the acid. It is observed that the alkalinity of the water is primarily due to the presences of bicarbonates, carbonates and hydroxides of sodium, potassium, calcium and magnesium. Depending upon the ions present, the alkalinity can be classified as caustic alkalinity (due to OH− and CO3 2− ions) and bicarbonate alkalinity (due to HCO3 − ions) (Gray, 2017 pp. 44–46; Hammer & Hammer, 2013 pp. 17–18; Maiti, 2004 pp. 33–37; Manahan, 2010 p. 56; Patton, 1991, pp. 23–29).
Estimation of alkalinity due to different ions is based on the titration of the water samples against a standard acid (e.g. sulphuric acid) making selective use of an indicator (Hammer & Hammer, 2013, pp. 17–18). Typical indicators used are phenolphthalein and methyl orange. The volume of acid consumed during the titration can be used to determine the strength of various alkalinity causing ions.
The typical analytical procedure to estimate the alkalinity of water makes use of well-established and documented acid-base titration method that involves following steps.
Step 1
A known volume of water sample is pipette out into a conical flask to which 2 to 3 drops of phenolphthalein indicator is added. Depending upon the type of alkalinity present the water sample will either remain colorless or will turn pink. If no cooler is produced, phenolphthalein alkalinity is not present.
If the solution turns pink, titrate water sample with standard H2SO4 solution taken in a burette until the pink colour disappears or the pH of the solution is 8.3.
Record the volume of acid consumed (Burette reading) as ‘P’ mL.
Step 2
To the same sample add 2 to 3 drops of methyl orange indicator. The colour of the solution will turn orange.
Continue titration until the colour changes from orange to pink or the pH of the solution is 4.5.
Record the total volume of acid consumed as “M” mL or “T” mL.
Repeat the above procedure (Step 1 and Step 2) to get concordant values.
Using the mean values of volume of acid consumed obtained in step 1 and step 2 respectively, the type and amount of alkalinity expressed in mg/L of CaCO3 is calculated using following equation:
The typical alkalinity titration curve (pH versus volume) for a hydroxide-carbonate system showing two points of inflections that corresponds to phenolphthalein alkalinity (Step 1) and total alkalinity (Step 2) is shown in Figure 1 [Maiti, 2004 p. 34]. At first point of inflection (pH 8.3), de-colourization of phenolphthalein indicator indicates complete neutralization of OH− and ½ CO3 2−. At second inflection point (pH 4.5), de-colourization of methyl orange indicator indicates complete neutralization of ½ CO3 2− and HCO3 −.
Typical acid titration curve for hydroxide carbonate system.
The reactions taking place during titration (Manahan, 2010, p. 56) and their corresponding equilibrium expression at 25 °C are represented by following equations (Frank, 2004, pp. 246–247; Hammer & Hammer, 2013, pp. 12):
Note that dissolved CO2 in water is represented as H2CO3 by equation (d) and the equilibrium constant is expressed as follows:
The volume of acid used up to phenolphthalein end point corresponds to the complete neutralization of hydroxide ion (reaction a) and half-neutralization of carbonate ions (reaction b) and is known as phenolphthalein (P) alkalinity (Manahan, 2010, p. 56; Patton, 1991, pp. 23–29). The volume of acid used up to methyl orange end point corresponds to the reaction (a), (b) and (c) i.e. complete neutralization of hydroxide, carbonate and bicarbonate ions and is known as total (T) alkalinity (Manahan, 2010, p. 56; Patton, 1991, pp. 23–29). Once the phenolphthalein and total alkalinities are determined, the types of alkalinity can be due to different ions and their relationship is estimated using the experimental data reported in Table 1 (Maiti, 2004, pp. 33–37).
Alkalinity due to different ions and their relationship.
| Case no | Results of titration | Amount of OH− alkalinity | Amount of CO3 2− alkalinity | Amount of HCO3 − alkalinity |
|---|---|---|---|---|
| Case 1 | P = 0 | Absent | Absent | T |
| Case 2 | P = T | T | Absent | Absent |
| Case 3 | P = 1/2 T | Absent | 2P | Absent |
| Case 4 | P > 1/2 T | 2P−T | 2 [T−P] | Absent |
| Case 5 | P < 1/2 T | Absent | 2P | T−2P |
1.2 Students learning difficulties
When this topic was introduced in the class room teaching, it was observed that students were not able to understand, visualize and apply the concept to the data reported in Table 1. The major problems identified during class room interaction that were associated with learning this topic and understanding Table 1 were: (i) they were not able to identify the type of alkalinity present in water sample and correlate with their relationship, (ii) Unable to explain the meaning all five cases, (iii) Unable to understand why phenolphthalein (P) alkalinity is related to 1/2 times methyl orange or total (T) alkalinity, (iv) Unable to visualise half reaction between carbonate ion and H+ ion during phenolphthalein (P) alkalinity and (iv) unable to evaluate the distribution of total volume of acid utilize among the different ions at the end of titration. They were also found to memorise Table 1 instead of applying it conceptually.
1.3 Strategy adopted for effective learning
To overcome learning difficulties, no systematic approach was available in the literature to understand these experimentally reported volumes of acid utilized for neutralization reaction as per author’s knowledge. Therefore, for easy understanding and application of concept to water technology supplementary information was developed by applying a simple mathematical approach to Table 1. The supplementary information developed was presented in class room teaching and the performance outcome of students was evaluated by performing assessments in terms of class test (theory, numerical and quiz) and practical’s. A systematic theoretical approach for each case reported in Table 1 along with students learning assessments and outcomes is discussed.
2 Theoretical discussion
Case 1, P = 0
When phenolphthalein alkalinity (P) is zero, it is an indication that the water sample will not turn to pink colour on the addition of phenolphthalein indicator. Thus, we can say that the ionic species which are responsible for phenolphthalein alkalinity is absent.
Now, to determine the methyl orange or total alkalinity, methyl orange indicator is added to the water sample. The water sample turns to orange colour. On titration with acid, the total alkalinity of water sample is represented as
Putting, P = 0 in equation (ii) we get,
Therefore, the volume of acid utilized is only for the neutralization of bicarbonate ions that are originally present in the water sample.
Thus, alkalinity of water in terms of CaCO3 equivalent is given by
Case 2, P = T
The situation, where phenolphthalein alkalinity (P) is equal to total alkalinity is only possible when the water sample contains no ionic species that can be detected by methyl orange indicator during titration with an acid.
Thus, the ionic species which are responsible for phenolphthalein alkalinity are represented as.
and the absence of methyl orange alkalinity is represented as
Since, no methyl orange alkalinity is present, it indicates that the HCO3 − (generated) by half-neutralization reaction of CO3 2− is also absent.
This implies absences of carbonates (CO3 2−) in the water sample.
Therefore, equation (4) becomes P = OH−, which is the theoretical volume of acid consumed for neutralization of OH− only.
Thus, alkalinity of water in terms of CaCO3 equivalent is given by.
Case 3, P = ½ T or 2P = T
The situation, where phenolphthalein alkalinity (P) is equal to half of total alkalinity indicates that the volume of acid consumed for the first end point and the corresponding second end point of the titration is exactly same. This is only possible if OH− and HCO3 − (originally present) are absent in the water sample.
and
Thus, for the first end point of the titration with phenolphthalein indicator we have,
and for the second end point of the titration with methyl orange indicator we have,
Therefore, above reactions indicates that exactly same moles of H+ are consumed satisfying the condition 2P = T = CO3 2− , which is the theoretical volume of acid consumed for neutralization of CO3 2− only.
Thus, alkalinity of water due to CO3 2− in terms of CaCO3 equivalent is given by,
Case 4, P > 1/2 T
For the situation, where phenolphthalein alkalinity (P) is greater than half the total alkalinity indicates that the volume of acid required for the first end point is greater than second end point of the titration.
Thus, one can assume that HCO3 − (originally present) is absent in water sample and the alkalinity of water is due to OH− and CO3 2− only.
For the first end point of the titration with phenolphthalein indicator we have,
Rearranging equation (12) we have
And for the second end point of the titration with methyl orange indicator we have,
Since, HCO3 − (Originally present) = 0.
We have,
Subtracting equation (13) and (14), we get 2P–T = OH−
Which is the theoretical volume of acid consumed for neutralization of OH−only = 2P–T
Thus, alkalinity of water due to OH− in terms of CaCO3 equivalent is given by,
Now,
Putting value of OH− = 2P–T in equation (14) we get.
which is the theoretical volume of acid consumed for neutralization of CO3 2− only = 2 (T–P)
And
Thus, alkalinity of water due to CO3 2− in terms of CaCO3 equivalent is given by,
Case 5, P < 1/2 T
For the situation, where phenolphthalein alkalinity (P) is less than half the total alkalinity indicates that the volume of acid required for the first end point is lesser than second end point of the titration.
Thus, one can assume that OH− is absent in water sample and the alkalinity of water is due to CO3 2− and HCO3 2− only.
For the first end point of the titration with phenolphthalein indicator we have,
Since, OH− = 0
We have,
Which is the theoretical volume of acid consumed for neutralization of CO3 2− only = 2P.
Thus, alkalinity of water due to CO3 2− in terms of CaCO3 equivalent is given by,
And for the second end point of the titration with methyl orange indicator we have,
Or
Putting value of 2P = CO3 2− in equation (22) we get.
Which is the theoretical volume of acid consumed for neutralization of HCO3 − only = T–2P.
Thus, alkalinity of water due to CO3 2− in terms of CaCO3 equivalent is given by,
3 Learning assessments
In order to measure the understanding of the students towards the introduction of supplementary information developed, learning assessments in terms of class test and practical test were carried out.
3.1 Class room session
A class test that includes theory, numerical and quiz comprising of 20 marks each (total 60 marks) was conducted to assess the level of understanding of theoretical concept. The questions were designed taking into consideration the Bloom’s taxonomy levels (knowledge, comprehension, application, analysis, evaluate and create) for students learning assessment.
3.2 Laboratory session
For laboratory session two practical tests were conducted each of 20 marks (total 40 marks). For the test two water samples were prepared in laboratory that meet case 4 and case 5 of Table 1, respectively. For case 4 the water sample comprise of calculated amount of NaOH and Na2CO3 in one litre water, while for case 5 the water sample comprise of calculated amount of Na2CO3 and NaHCO3 in one litre water. The titrant used was 0.01 M HCl. Students were instructed to follow the titration procedure to identify the type and calculate the amount of alkalinity.
For both class test and practical test a threshold of 95 percentage mark was set. Therefore, number of students out of total 120 students scoring 57 marks in class test and 38 marks in practical test was set as criteria for evaluation. Finally, the percentage of attainment level in terms of learning outcome was determined using following relation.
where, a = percentage of students scoring ≥ threshold of 95 % marks in class test out of 60. b = percentage of students scoring ≥ threshold of 95 % marks in practical test out of 40.
A schematic of learning assessment strategy adapted to evaluated learning outcome is shown in Figure 2.
Schematic showing assessment strategy and learning outcome evaluation.
3.3 Learning outcomes
Total 120 students were introduced with the supplementary material in both class room and laboratory session. The impact of this supplementary information on conceptual understanding and learning ability of the students was monitored by traditional teaching and assessment tools like class room interaction, subject concentric class test, quiz, assignments, numerical solving and laboratory sessions. The percentage learning outcome obtained was 95 % indicating that the use of this supplementary material had a profound impact on understanding the key features of experimental data reported in Table 1. Students were able to explore and demonstrate better understanding for analysis of water by the combination of experimental and theoretical approach. In both, class room teaching and laboratory session, students were able to easily identify alkalinity due to different ions and their relationship. Using the theoretical description as a supplementary material presented in this study, students were able to deduce the theoretical volume of acid required for neutralization. This was reflected by the ease with which students were able to solve numerical on determination of water alkalinity.
4 Conclusions
A systematic theoretical description using simple mathematics applied to the chemical reaction for water alkalinity determination was presented to first year engineering students as a part of chemistry curriculum on water technology. Based on the overall assessment of the student’s response in both class test and practical test, it might be suggested that the supplementary information has an innovative reform on understanding the concept and learning ability of the students.
Acknowledgments
The author acknowledges Army Institute of Technology Pune for providing library facility and encouragement to write this manuscript.
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Author contributions: Acquisition, analysis of published data and drafting of manuscript.
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Research funding: This research received no specific grant from any funding agency.
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Conflict of interest statement: The author declares no conflicts of interest regarding this article.
References
Frank, M. D. (2004). Determination of alkalinity of natural waters environmental laboratory exercises for instrumental analysis and environmental chemistry (pp. 246–247). John Wiley & Sons, Inc.Search in Google Scholar
Gray, N. F. (2017). Factor determining the distribution of animals and plants in freshwaters, water science and technology an Introduction (pp. 44–46). CRC Press.Search in Google Scholar
Hammer, M.Sr., & Hammer, M.Jr. (2013). Chemistry, water and wastewater technology (pp. 17–18). Pearson New International Edition.Search in Google Scholar
Maiti, S. K. (2004). Handbook of methods in environmental studies. In Water and wastewater analysis (1, pp. 33–37). ABD Publisher.Search in Google Scholar
Manahan, S. E. (2010). Fundamentals of aquatic chemistry, water chemistry: Green science and technology of nature’s most renewable resource (p. 56). CRC Press.10.1201/b11794Search in Google Scholar
Patton, C. C. (1991). Water sampling and analysis, applied water technology (pp. 23–29). Campell Petroleum Series.Search in Google Scholar
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