# Study of Estimation of Hardness of Water Using pH-Meter

Abhijit Mallick

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Abhijit Mallick. Study of Estimation of Hardness of Water Using pH-Meter. International Research Journal of Pure and Applied Chemistry, 2024, 25 (6), pp.78-86. 10.9734/irjpac/2024/v25i6886. hal-04993359

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# Study of Estimation of Hardness of Water Using pH-Meter

Abhijit Mallick a*

<sup>a</sup>Department of Engineering Science (Chemistry), Academy of Technology, P.O. Aedconagar, Adisaptagram, District- Hooghly, 712121, West Bengal, India.

**Author's contribution**

The sole author designed, analyzed, interpreted and prepared the manuscript.

**Article Information**

DOI: https://doi.org/10.9734/irjpac/2024/v25i6886

**Open Peer Review History:**

This journal follows the Advanced Open Peer Review policy. Identity of the Reviewers, Editor(s) and additional Reviewers, peer review comments, different versions of the manuscript, comments of the editors, etc are available here: https://www.sdiarticle5.com/review-history/127054

Received: 22/09/2024

Accepted: 25/11/2024

Published: 03/12/2024

**Original Research Article**

## ABSTRACT

The hardness of water is one of the important parameters of water quality. The complexometric titration method is a prevalent technique to estimate concentrations of Ca²⁺ and Mg²⁺ ions individually, which are primarily responsible for the hardness of water. However, the method needs two external indicators to mark the end points of titrations. Furthermore, accuracy of the method is sacrificed due to inevitable parallax errors during marking of the endpoint of titration.

This present work reports that during titration of a hard water sample with a complexing agent (here, Na₂EDTA solution), pH changes continuously. This change in pH is closely monitored and recorded graphically. Hence the endpoint of titration is determined. The neutralization volume, thus obtained, is used to estimate Ca⁻ and Mg⁻ hardness of the water sample separately. This novel technique obviates the use of any external indicators and eliminates any possible parallax error.

<footnote>*Corresponding author: E-mail: dramallick12@gmail.com;</footnote>
Keywords: Hardness of water; complexometric titration; pH-metric titration; buffer solution; NaOH solution; disodium EDTA.

# 1. INTRODUCTION

The hardness of water arises primarily due to the presence of profuse amount of $Ca^{2+}$ and $Mg^{2+}$ ions in the natural water resources. However, extent of hardness depends on the type of land, e.g., water is soft in hilly areas, but the same is sufficiently hard in industrialized areas, commercial areas and coastal area. Melian et al. (1999) attempted to estimate the hardness of groundwater and rural drinking water using the volumetric titration method. The latter is a very popular method to determine water hardness and well documented in the literature (Amelin, 2000, Gudzenko, 2023, Sawyer and McCarty (1978). Diogo Ferreira et al. (2019) reported the uncertainty of visual detection of the endpoint of titration during determination of total hardness of water. Another researcher, Sengupta (2013) documented the adverse impact of water hardness on health. Ramya et al. (2015) studied the estimation of hardness in ground water samples using the volumetric titration method. Divya et al. (2012) reported the total hardness of freshwater resources. The volumetric method of determination of calcium and magnesium hardness of coastal water and sub-surface water is well documented in the literature (Padmavati et al., 2011, Venkatasubramani et al., 2007, Kumar, 2016, Joshi et al., 2023).

This present work proposes a novel technique, the pH-metric method, to estimate the concentrations of $Ca^{2+}$ and $Mg^{2+}$ ions or in other words, calcium and magnesium hardness of a given water sample.

# 2. MATERIALS

## 2.1 Chemicals and Hard Water Samples

Details of chemicals used in the present work are documented in the Table 1. Two different hard water samples are prepared as shown in the Table 2.

# 3. METHODS

## 3.1 Volumetric Titration

a) 1 litre standard $Na_2EDTA$ solution of strength 0.601 (M/10) is prepared. 40 ml of it is poured into a burette.

b) 10 ml of the hard water sample, SC-20, is taken into a conical flask. 1 ml buffer solution with a pinch of EBT indicator is added into the conical flask. The solution turns to a wine-red colour. It is then titrated against $Na_2EDTA$ solution, running from the burette. At the end point wine red colour changes to sky blue. The initial and final burette readings are noted. Triplicate readings are recorded. The total hardness can be calculated using the mean burette reading.

c) For the hard water sample, SCM-20, the process (b) is followed. Here also triplicate readings are recorded. The total hardness, caused by $Ca^{2+}$ and $Mg^{2+}$ ions can be calculated using the mean burette reading.

d) 10 ml of the hard water sample, SCM-20, is taken in a conical flask. Add 1 ml 1(N) NaOH solution. The function of NaOH is to block $Mg^{2+}$ to avoid the formation of any Mg-complex during the titration process. A pinch of Murexide indicator is added. The solution turns to pink colour due to the formation of [Ca-Murexide]. It is then titrated against $Na_2EDTA$ solution, running from the burette, till the pink colour changes to purple. The initial and final burette readings are noted. Triplicate readings are recorded. Ca-hardness can be calculated using the mean burette reading.

e) Using the results of the processes (c) and (d) Mg-hardness can be calculated by subtracting Ca-hardness from the total hardness.

## 3.2 pH-Metric Titration

(a) 20 ml of prepared $Na_2EDTA$ solution is poured into another burette.

(b) 10 ml of the hard water sample, SC-20, is taken into a 250 ml beaker. 90 ml distilled water is added into it in order to immerse the electrodes safely into the solution. 1 ml buffer solution is added into the beaker. The mixture is shaken and the pH electrode-set is immersed into it. The 1st reading is taken. The beaker is taken out and 0.5 ml $Na_2EDTA$ solution is added to it from the burette. The mixture is shaken
and pH electrode-set is again immersed into it. The 2nd reading is taken. The process is continued till the pH reads around 10.

(c) The pH readings are plotted against the volume of Na₂EDTA solution added.

(d) The step (b) is repeated for the other hard water sample, SCM-20. In this case, also, pH readings are plotted against volume of Na₂EDTA solution.

(e) In case of SCM-20 hard water sample, the step (b) is repeated once more using 1 ml 1(N) NaOH solution instead of 1 ml buffer solution. The pH readings are plotted against volume of Na₂EDTA solution added.

# 4. RESULTS AND DISCUSSION

## 4.1 Sample SC-20

This sample contains only Ca²⁺ ions. The results of volumetric titration of the sample are shown in the Table 3.

The results of pH-metric titration of the sample SC-20 are shown in the Table 4.

pH readings are plotted against volume of Na₂EDTA solution added. It is shown in the Fig.1.

Two straight lines with different slopes are quite distinguished from the Fig.1. These two straight lines are drawn separately in the Fig.2.

EDTA has four acidic H-atoms. So, it is best represented by H₄EDTA. In aqueous solution

disodium salt of EDTA or Na₂H₂EDTA dissociates to form [H₂EDTA]²⁻. The latter reversibly dissociates to produce [EDTA]⁴⁻, which forms complexes with metal cations. In case of SC-20 hard water sample, only one type of complex, i.e., [Ca – EDTA] is formed. The reactions are given below

$$[H_2EDTA]^{2-} \rightleftharpoons 2H^+ + [EDTA]^{4-} \cdots\cdots (1)$$

$$[EDTA]^{4-} + Ca^{2+} \rightarrow [Ca – EDTA] \cdots\cdots (2)$$

The buffer consumes the H⁺ ions, accelerating the formation of [EDTA]⁴⁻ so that the latter can form stable complex, [Ca – EDTA]. As the reaction continues, the concentration of [OH]⁻ in the buffer decreases, due to which, sharp drop of pH is observed (blue curve in the Fig.2) till the end point is reached. After the end point the 2nd step of the above reaction [Equation(2)] ceases to occur and hence only a slow change in pH is observed due to buffer action (red curve in the Fig. 2.

The Intersection of the two straight lines occurs at 1.9 ml, which is assumed to be the endpoint of titration. So, the endpoint, obtained by pH-metric method, is almost same as that obtained by the volumetric method (Table 3).

## 4.2. Sample SCM-20

This sample contains both Ca²⁺ and Mg²⁺ ions. Two sets of volumetric titrations are performed to estimate the individual concentrations of Ca²⁺ and Mg²⁺ ions. Two sets of pH-metric titrations are also performed.

<table><caption>Table 1. Details of chemicals used in this research work</caption><thead><tr><th>Chemicals</th><th>Molecular Weight (gm/mole)</th><th>Composition</th></tr></thead><tbody><tr><td>Fused CaCl<sub>2</sub></td><td>111</td><td>NA</td></tr><tr><td>MgSO<sub>4</sub>, 7H<sub>2</sub>O</td><td>246</td><td>NA</td></tr><tr><td>Disodium salt of ethylene diamine tetraacetic acid (Na<sub>2</sub>EDTA)</td><td>372</td><td>NA</td></tr><tr><td>Buffer solution (NH<sub>4</sub>OH/NH<sub>4</sub>Cl)</td><td>NA</td><td>1:1</td></tr><tr><td>Eriochrome Black T (EBT) indicator</td><td>461</td><td>NA</td></tr><tr><td>Murexide indicator</td><td>284</td><td>NA</td></tr></tbody></table>

NA = Not Applicable

<table><caption>Table 2. Composition of hard water samples</caption><thead><tr><th>Serial No.</th><th>Sample Code</th><th>CaCl<sub>2</sub> (Fused)</th><th>MgSO<sub>4</sub>, 7H<sub>2</sub>O</th><th>Weight ratio</th><th>Distilled water</th></tr></thead><tbody><tr><td>1</td><td>SC-20</td><td>225 mg</td><td>0</td><td>NA</td><td>100 ml</td></tr><tr><td>2</td><td>SCM-20</td><td>150 mg</td><td>150 mg</td><td>1:1</td><td>100 ml</td></tr></tbody></table>

The sample SC-20 is responsible for Ca-hardness only, while the sample SCM-20 is responsible for both Ca- and Mg-hardness.
<table><caption>Table 3. Volumetric titration for the hard water sample SC-20</caption><thead><tr><th rowspan="2">No. of observations</th><th rowspan="2">Volume of SC-20 sample hard water taken (ml)</th><th colspan="4">Volume of Na<sub>2</sub>EDTA consumed (ml)</th></tr><tr><th>Initial</th><th>Final</th><th>Difference</th><th>Mean volume</th></tr></thead><tbody><tr><td>1</td><td>10</td><td>0</td><td>1.8</td><td>1.8</td><td>1.8</td></tr><tr><td>2</td><td>10</td><td>1.8</td><td>3.7</td><td>1.9</td><td></td></tr><tr><td>3</td><td>10</td><td>3.7</td><td>5.5</td><td>1.8</td><td></td></tr></tbody></table>

The mean volume (1.8 ml) represents the volume of Na₂EDTA required to absorb all Ca²⁺ ions from the aliquotted sample solution (10 ml) to form stable [Ca - EDTA] complex

<table><caption>Table 4. pH-Metric titration for the hard water sample SC-20</caption><thead><tr><th>No. of observations</th><th>Volume of Na<sub>2</sub>EDTA solution added (ml)</th><th>Total volume of Na<sub>2</sub>EDTA solution added (ml)</th><th>pH reading</th></tr></thead><tbody><tr><td>1</td><td>0</td><td>0</td><td>10.54</td></tr><tr><td>2</td><td>0.5</td><td>0.5</td><td>10.39</td></tr><tr><td>3</td><td>0.5</td><td>1</td><td>10.21</td></tr><tr><td>4</td><td>0.5</td><td>1.5</td><td>10.04</td></tr><tr><td>5</td><td>0.5</td><td>2</td><td>9.88</td></tr><tr><td>6</td><td>0.5</td><td>2.5</td><td>9.77</td></tr><tr><td>7</td><td>0.5</td><td>3</td><td>9.69</td></tr><tr><td>8</td><td>0.5</td><td>3.5</td><td>9.59</td></tr><tr><td>9</td><td>0.5</td><td>4</td><td>9.5</td></tr><tr><td>10</td><td>0.5</td><td>4.5</td><td>9.37</td></tr><tr><td>11</td><td>0.5</td><td>5</td><td>9.3</td></tr><tr><td>12</td><td>0.5</td><td>5.5</td><td>9.2</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>Fig. 1. SC-20 sample: plot of pH-readings versus volume of titrant added</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Fig. 2. SC-20 sample: Linear plot of pH –readings versus volume of titrant added</figcaption></figure>

### 4.2.1 Set-1

#### 4.2.1.1 Volumetric titration using 1 ml buffer solution

Volumetric titration of the sample SCM-20 has been performed using buffer solution and EBT indicator. The results are shown in the Table 5. Mean burette reading is 2.4 ml.

#### 4.2.1.2 pH – metric titration using 1 ml buffer solution

pH –metric titration results are given in the Table 6. The plot of pH –readings versus volume of disodium EDTA gives rise to two straight lines of different slopes as shown in the Fig. 3.

The Intersection of the two straight lines occurs at 2.52 ml, which is believed to be the endpoint of titration. So total hardness due to Ca²⁺ and Mg²⁺ ions can be calculated pH –metrically.

### 4.2.2 Set-2

#### 4.2.2.1 Volumetric titration is performed using 1 ml 1(N)NaOH solution

Volumetric titration of the sample SCM-20 has been performed using NaOH solution and Murexide indicator. The results are shown in the Table 7. Mean burette reading is 1.6 ml.

#### 4.2.2.2 pH – metric titration using 1 ml 1(N)NaOH solution

pH –metric titration results are given in the Table 8. A similar plot of pH –readings versus volume of disodium EDTA is shown in the Fig. 4.

The Intersection of the two straight lines occurs at 1.74 ml, which is believed to be the end point of titration. So hardness, due to Ca²⁺ ions only, can also be calculated pH –metrically. Using the results of Fig.3 and Fig.4, hardness due to Mg²⁺ ions can be calculated.

According to Table 2, in the hard water sample SCM-20 ratio of weights of CaCl₂ and MgSO₄·7H₂O is 1:1. So the following relation holds good.

$$ \frac{Ca - hardness}{Mg - hardness} = \frac{MW \ of \ MgSO_4 \cdot 7H_2O}{MW \ of \ CaCl_2} \\ = \frac{246}{111} = 2.216 $$

If V<sub>Ca</sub> and V<sub>Mg</sub> are the volumes (in ml) of Na₂EDTA consumed due to Ca²⁺ ions and Mg²⁺ ions respectively, the following relation also holds good.

$$ \frac{Ca - hardness}{Mg - hardness} = \frac{V_{Ca}}{V_{Mg}} $$
<table><caption>Table 5. Volumetric titration for the hard water sample SCM-20 using 1 ml buffer solution</caption><thead><tr><th rowspan="2">No. of observations</th><th rowspan="2">Volume of SCM-20 sample hard water taken (ml)</th><th colspan="4">Volume of Na<sub>2</sub>EDTA consumed (ml)</th></tr><tr><th>Initial</th><th>Final</th><th>Difference</th><th>Mean volume</th></tr></thead><tbody><tr><td>1</td><td>10</td><td>0</td><td>2.5</td><td>2.5</td><td>2.4</td></tr><tr><td>2</td><td>10</td><td>2.5</td><td>4.8</td><td>2.3</td><td></td></tr><tr><td>3</td><td>10</td><td>4.8</td><td>7.2</td><td>2.4</td><td></td></tr></tbody></table>

The mean volume (2.4 ml) represents the volume of Na₂EDTA required to absorb all Ca²⁺ and Mg²⁺ ions from the aliquoted sample solution (10 ml) to form stable [Ca – EDTA] and [Mg – EDTA] complexes

<table><caption>Table 6. pH-metric titration for the hard water sample SCM-20 using 1 ml buffer solution</caption><thead><tr><th>No. of observations</th><th>Volume of Na<sub>2</sub>EDTA solution added (ml)</th><th>Total volume of Na<sub>2</sub>EDTA solution added (ml)</th><th>pH reading</th></tr></thead><tbody><tr><td>1</td><td>0</td><td>0</td><td>11.43</td></tr><tr><td>2</td><td>0.5</td><td>0.5</td><td>11.28</td></tr><tr><td>3</td><td>0.5</td><td>1</td><td>11.17</td></tr><tr><td>4</td><td>0.5</td><td>1.5</td><td>11.05</td></tr><tr><td>5</td><td>0.5</td><td>2</td><td>10.95</td></tr><tr><td>6</td><td>0.5</td><td>2.5</td><td>10.85</td></tr><tr><td>7</td><td>0.5</td><td>3</td><td>10.81</td></tr><tr><td>8</td><td>0.5</td><td>3.5</td><td>10.76</td></tr><tr><td>9</td><td>0.5</td><td>4</td><td>10.7</td></tr><tr><td>10</td><td>0.5</td><td>4.5</td><td>10.64</td></tr><tr><td>11</td><td>0.5</td><td>5</td><td>10.6</td></tr><tr><td>12</td><td>0.5</td><td>5.5</td><td>10.58</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>Fig. 3. SCM-20 sample in the presence of buffer: Linear plot of pH readings versus volume of titrant added</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 4. SCM-20 sample in presence of NaOH: Linear plot of pH –readings versus volume of titrant added</figcaption></figure>

<table><caption>Table 7. Volumetric titration for the hard water sample SCM-20 using 1 ml NaOH solution</caption><thead><tr><th rowspan="2">No. of observations</th><th rowspan="2">Volume of SCM-20 sample hard water taken (ml)</th><th colspan="4">Volume of Na<sub>2</sub>EDTA consumed (ml)</th></tr><tr><th>Initial</th><th>Final</th><th>Difference</th><th>Mean volume</th></tr></thead><tbody><tr><td>1</td><td>10</td><td>0</td><td>1.6</td><td>1.6</td><td>1.6</td></tr><tr><td>2</td><td>10</td><td>1.6</td><td>3.2</td><td>1.6</td><td></td></tr><tr><td>3</td><td>10</td><td>3.2</td><td>4.9</td><td>1.7</td><td></td></tr></tbody></table>

The mean volume (1.6 ml) represents the volume of Na₂EDTA required to absorb all Ca²⁺ from the aliquotted sample solution (10 ml) to form stable [Ca – EDTA] complexes

<table><caption>Table 8. pH-metric titration for the hard water sample SCM-20 using 1 ml NaOH solution</caption><thead><tr><th>No. of observations</th><th>Volume of Na<sub>2</sub>EDTA solution added (ml)</th><th>Total volume of Na<sub>2</sub>EDTA solution added (ml)</th><th>pH reading</th></tr></thead><tbody><tr><td>1</td><td>0</td><td>0</td><td>12.46</td></tr><tr><td>2</td><td>0.5</td><td>0.5</td><td>12.34</td></tr><tr><td>3</td><td>0.5</td><td>1</td><td>12.18</td></tr><tr><td>4</td><td>0.5</td><td>1.5</td><td>11.99</td></tr><tr><td>5</td><td>0.5</td><td>2</td><td>11.78</td></tr><tr><td>6</td><td>0.5</td><td>2.5</td><td>11.53</td></tr><tr><td>7</td><td>0.5</td><td>3</td><td>11.28</td></tr><tr><td>8</td><td>0.5</td><td>3.5</td><td>11.05</td></tr><tr><td>9</td><td>0.5</td><td>4</td><td>10.83</td></tr><tr><td>10</td><td>0.5</td><td>4.5</td><td>10.55</td></tr><tr><td>11</td><td>0.5</td><td>5</td><td>10.22</td></tr><tr><td>12</td><td>0.5</td><td>5.5</td><td>9.88</td></tr></tbody></table>
$$So, \frac{V_{Ca}}{V_{Mg}} = 2.216 \text{ (Using theoretical approach)}$$

(a) Considering volumetric titration results of sets 1 and 2 (Table 5 and Table 7), the following equations are true

$$ \begin{array}{l} V_{Ca} + V_{Mg} = 2.4 \text{ ml} \text{ and } V_{Ca} = 1.6 \text{ ml. So,} \\ V_{Mg} = 0.8 \text{ ml} \end{array} $$

$$ So, \quad \frac{V_{Ca}}{V_{Mg}} = 2 $$

(Using volumetric titration approach)

(b) Considering pH-metric titration results of sets 1 and 2 (Fig.3 and Fig.4), the above equations become

$$ \begin{array}{l} V_{Ca} + V_{Mg} = 2.52 \text{ ml} \text{ and } V_{Ca} = 1.74 \text{ ml.} \\ \text{So, } V_{Mg} = 0.78 \text{ ml} \end{array} $$

$$ So, \quad \frac{V_{Ca}}{V_{Mg}} = 2.23 $$

(Using pH-metric titration approach)

So, the pH-metric titration result is very close to the theoretical value (2.216) compared to the volumetric titration result. Thus, it is believed that the pH-metric titration method is more accurate than the volumetric titration method.

## 5. CONCLUSIONS

1. The hardness of a given water sample can be estimated accurately using pH-meter.

2. The pH-metric determination of the hardness of water is more accurate than the volumetric determination of the same as the endpoint of titration in pH-metric method is obtained from the graph without any parallax error.

3. No indicator is required in the pH-metric method of determination of hardness of water, which is considered a distinct advantage over the volumetric method.

4. This novel technique of determining the hardness of water is expected to explore

future research works, based on pH-meter.

## DISCLAIMER (ARTIFICIAL INTELLIGENCE)

Author(s) hereby declare that NO generative AI technologies such as Large Language Models (ChatGPT, COPILOT, etc) and text-to-image generators have been used during writing or editing of this manuscript.

## COMPETING INTERESTS

Author has declared that no competing interests exist.

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