The influence of ion composition of water on its electrical conductivity

Ivan Tikhonov

In this article I will try to tell you how the ionic composition of water affects the value of electrical conductivity and how justified is the use of the generally accepted conversion factors of electrical conductivity of water into the salt content of water (in the range of 0.5-0.55) for the vast majority of fresh water. The article also considers the possibility of using the value of water conductivity to control the process of water softening.

The electrical conductivity of water is the most important parameter of its quality, which can be determined in a simple and affordable way. The electrical conductivity of water depends on the amount of dissolved salts, acids and bases in it, i.e. on the number of ions. Accordingly, the electrical conductivity of water depends on the concentration of ions in the water. The higher the concentration of ions, the greater the electrical conductivity of the water is. Thus, the total salt content of water can be determined with the value of the electrical conductivity of water.

It should be noted that the electrical conductivity of water, i.e. the ability of water to carry an electric charge (electrons), is determined by ions and it is called the ionic electrical conductivity. If you put 2 electrodes in water and include them in a circuit with a current source, the flow of current in the water between the two electrodes will be determined by the movement of ions from one electrode to another. Obviously, different ions will have different ability to move or, as they say, ions have different mobility. Basically, the mobility is determined by the conditions of interaction of ions with the solvent (water). Visually, this process can be represented quite simply. If sodium chloride is dissolved in water, cation of sodium with a positive charge and anions of chloride with a negative charge are formed. The cation and anion interact with water molecules, i. e. they are hydrated by water. Ions having a charge attract the dipolar water molecules. The ability of different ions to hold hydrate shells is different. Common sense suggests that the greater the valence of the ion and the greater its atomic mass, the greater the ability to retain the hydrate shell of the ion is. Sodium cation in hydrate shell carries out electron transfer in water from one electrode to another. In this case, sodium is monovalent and accordingly carries only one electron. Chloride ion also carries only one electron. If calcium chloride is dissolved in water, the divalent calcium ion in the hydrate shell can carry 2 electrons. Accordingly, the sodium ion carries one electron and the calcium ion carries 2 electrons at a time. It turns out that the ability of the calcium ion to carry an electric charge should be twice as large as the sodium ion. In fact, it is.

Table 1 shows the values of specific equivalent of conductivity (ion mobility) in Ohm^-1 *cm²/g-eq at 25 ⁰C. Table 1 shows that the mobility of calcium and sodium ions, with their infinite dilution in water (no effect of the ionic strength of the solution), are almost equal (59.5 and 50.11). Thus, the mobility of the equivalent amount of calcium in relation to sodium will be 59.5*2= 119 and the mobility of the sodium will remain 50,11. It turns out that a certain amount of calcium moles can carry more than twice the electric charge than the same amount of sodium moles. This rule is observed for ions of any valence.

Table 1

Ion	The equivalent conductivity at infinite dilution	Equivalent electrical conductivity of ions at concentrations (mol/l)
		0,0005	0,005	0,05	0,1
1/2 Сa	59,5	49	44,2	35,2	32
1/2Mg	53,06	43	39	31	28
Na	50,11	42,8	41,3	37	36,4
Cl	76,34	64,4	62,5	57,9	55,8
1/2 SO4	80	65	58,7	45	40
HCO3	41,5

It can be noted that the greater the molar mass of the ion and the greater its valence, the greater its mobility decreases with increasing ion concentration in water. The loss of mobility of ions with the increase of their concentration in the solution can be compared to a person who crosses the area where there are no people, and a person who crosses the area in which there is a crowd of people. Figuratively speaking, when there are no people in the area, heavy multivalent ions have an advantage over monovalent ions when crossing the area. When there is “a crowd of people” in the area, a multivalent ion is like a big man with outstretched arms who is much more inhibited by other people than a small man with one outstretched hand. At the same time, half of the people go in one direction, and the other half in the opposite direction.

Figure 1 shows graphs of changes in ion mobility in water depending on their concentration. In fact, it is a graphical representation of table 1. It can be seen that the greatest drop in mobility belongs to the heaviest bivalent sulfate ion, then the same decrease in mobility belongs to bivalent calcium and magnesium ions and the least loss of mobility belongs to monovalent sodium and chloride ions.

Figure 1 The drop of ion mobility with increasing solution concentration

Thus, knowing the value of water conductivity, we can determine the concentration of ions in the water. But here the question arises. How can we reliably determine the salinity of water (the total mass of water ions referred to 1 liter) if the water contains not one specific salt, but several salts?

For a very approximate determination of the salt content of water with electrical conductivity, a simplification is used, which assumes that all salts in the water are presented in the form of sodium chloride. Sodium chloride dissolved in water has a coefficient of conversion of electrical conductivity in the salt content of 0.5-0.55 depending on the value of the salt content of water. If the salt content of water is below 1 ppt, then a conversion factor of 0.5 is used. The greater the salinity of the water, the higher the conversion factor is. The conversion factor will be equal to 0.57 at 16 ppt of NaCl.

Thus, for fresh water, surface and ground, it is assumed that the all salts are sodium chloride and the measured conductivity is multiplied by 0.5-0.55.

In fact, almost all fresh surface water and most groundwater are composed mainly of salts of carbonate and non-carbonate hardness. The direct proportion of sodium chloride in surface waters is rarely more than 10-20 % of the total ion composition.

Under these conditions, the use of conversion factor 0.5-0.55 leads to a significant error in the determination of salinity (ppm). Of course, it is fundamentally possible to determine whether the water is drinking water or not and, for example, whether the desalination plant works. But the error will be about 25-30%. This does not allow reliable determination of the total salt content of water based on electrical conductivity. Therefore, you must analyze all the ions included in the water source.

For example. The most accessible and simple analysis of water from a surface source are carried out on hardness, alkalinity and electrical conductivity. The analysis is presented in table 2.

Table 2

hardness (Ca, Mg)	mq-eq/l	3,2
alkalinity (HCO3)	mq-eq/l	2,1
electrical conductivity	μS/cm	451

As a result, focusing on the salt content of water by conductivity, the following salt content value is calculated S=451*0.5=225.5 ppm (0.5 is the conversion factor for NaCl). The concentration of calcium bicarbonate (Ca(HCO3)2) is equal to 2,1/2*162=170.3 ppm, where, 162 – molar mass of calcium bicarbonate (g/mol).

If we assume that the rest of the salt in the water is represented by calcium chloride (CaCl2), we obtain CaCl2=((3,2-2,1)/2)*111=61,05 ppm. (111 – molar mass of calcium chloride).

Total: 170,3+61,05= 231,35 ppm.

Formally, the salt contents are almost equal to each other.

In fact, a full analysis of the water showed that the water contained 60 ppm of sulphates and 15 ppm of sodium. The total salinity of water is calculated according to the ionic composition turned out to be 312 ppm. It turns out that the value of the salt content of the conductivity in the water determines only part of the salts when using a conversion factor of 0.5-0.55.

The error in conductivity measurements was almost 30 %. For water of this composition, the conversion factor of electrical conductivity into salt content should be – 0.69. This value is significantly different from the generally accepted 0.5-0.55.

Next, we will make simple calculations of the electrical conductivity of water, the composition of which is presented in tables 2, 3 and are compared to the value of the measured conductivity with the help of conductometer – 451 μS/cm.

For the calculation we use the source data [1].

The electrical conductivity of water with the molar concentration in it of a particular salt type can be determined with the formula:

     (1)

where,

μ-conductivity salt, µS/cm,

C-salt concentration, mol/l,

μ₀ – electrical conductivity of the salt at infinite dilution,

a, b – coefficients different for each type of salt are taken according to [1].

The electrical conductivity values of water to calcium chloride were determined with the formula (1). For calcium bicarbonate, the conversion of salt content into electrical conductivity was made on the basis of graphs [1]. The calculation results are presented in table 3.

Table 3

Salt	С, mol/l	μ0	а	b	С,  ppm	n (С/ μ)	μ, μS /cm	Cl, SO4, НСО3, ppm
СаSO4	0,0007				95,2	0,58	164,1	67,0
CaCl2	0,00038	124,5	1,37	1,2	42,18	0,44	95,8	26,0
Ca(HCO3)2	0,00105				170,3	0,81	208,5	128,1
Total 1					311,68	0,665	468,4
MgSO4	0,0007				84	0,56	150,0
MgCl2	0,00038				36,1	0,43	84,0
Total 2							459,2
Softened water
Na2SO4	0,0007				99,4	0,55	180,7
NaCl	0,00076				44,5	0,48	92,7
NaHCO3	0,0021				176,4	0,88	200,5
Total  3					320,3	0,69	473,9

The table shows the concentration of the corresponding salt in mol/l which was obtained from the analysis. Then, the values of salts concentration in water in ppm were obtained by multiplying by the molar mass. Further, the electrical conductivity of the water solution of each salt was calculated on the basis of formula (1) and graphs [1]. Then the conversion factor of electrical conductivity into salinity (n) was calculated by dividing the salinity by electrical conductivity.

It was assumed that the source water contains only calcium as cations. As a result of the calculation, the value of water conductivity (468.4 µs/cm) was obtained. This is more than the measured conductivity value of 451.0 µsm/cm. When taking into account magnesium salts, or rather their share, the calculated electrical conductivity was 459.2 µs/cm. The salt content of water is 311 ppm, and the conversion factor is 0.665. As we can see the real conversion factor is much more than 0.5.

Analyzing table 3, it turns out that the main influence on the conversion factor of electrical conductivity in the salt content has anionic composition. First of all, it happens because of the concentration of bicarbonate (due to the large conversion factor (n = 0.85-1.0)). It can be said that for carbonate, calcium-magnesium waters the conversion factor of electrical conductivity into salt content should be in the range of 0.6-0.75. And only for chloride and sulfate waters (at any cationic composition) the conversion factor will be 0.5-0.55.

We only need to know the conductivity, hardness and alkalinity (HCO3) of water for the approximate determination of the coefficient of conversion of electrical conductivity into salinity.

The following formula can be used to calculate approximate conversion factor of electrical conductivity into the salt content of water (carbonate-calcium water):

 ,

where,

n_HCO3 – the conversion factor for calcium bicarbonate, n_HCO3=0,86;

n_SO4,Cl – the conversion factor for calcium sulfate; n_SO4,Cl=0,53;

q_HCO3 – the proportion of the bicarbonate from the sum of all the anions in g-eq;

q_SO4,Cl – the proportion of the sum of sulfate and chloride from all anions.

Example.

There is water of carbonate-calcium type. Water conductivity – 550 µsm/cm; water hardness – 4.5 mg-eq/l; water alkalinity – 2.7 mg-eq/l.

The absence of monovalent ions in water is assumed. Accordingly, the concentration of anions in water is assumed to be 4.5 mg-eq/l. Then,

q_HCO3=2,7/4,5=0,6

q_SO4,Cl=1-0,6=0,4

n=(0.86*0.6+0.53*0.4)-0.05=0.678

Accordingly, the salinity of water is equal to

S=550*0.678=373 ppm

The real conversion factor for this water is 0.665.

The error when using this formula for carbonate – calcium waters is not more than 0.05.

The second part of this article is devoted to the issue of changing the salinity of water in the process of its softening.

To understand how the salinity and conductivity of softened water change, let’s look at the data in table 4.

Table 4

Salt	mmol/l	ppm	n	µsm/cm	The reference book[2]
Ca(HCO3)2	0,5	81	0,78	103,8462	104
СaSO4	0,5	68	0,49	138,7755	139,5
CaCl2	0,5	55,5	0,41	135,3659	135,85
Mg(HCO3)2	0,5	72,5	0,74	97,97297	97,5
MgSO4	0,5	60	0,45	133,3333	133
MgCl2	0,5	47,5	0,37	128,3784	129,35
NaHCO3	1	84	0,89	94,38202	94,6
Na2SO4	0,5	71	0,54	131,4815	130,1
NaCl	1	58,5	0,46	127,1739	126,45

Table 4 presents the data for calculating the conversion factor of each salt.

The conversion method is as follows:

1. According to the reference book [2], molar electrical conductivity of ions in water is determined at infinite dilution. Example. The electrical conductivity of calcium at infinite dilution is 59.5 µs/cm, bicarbonate is 44.1. Then, 59.5+44.5=104 µs/cm. Use such calculations for all salts. The calculation results are recorded in the last column of the table.
2. We set the molar concentration of salts, so that the concentrations of all salts are equivalently equal, i. e. for divalent salts – 0.5 mmol/l, for monovalent – 1 mmol/l. The values are in the first column.
3. Multiplying by the molar mass of each salt, we obtain the salt concentration in ppm (the third column).
4. The value from the third column divide by the value from the last column and thus the conversion factor (n) for each salt is obtained (the fourth column).
5. The value (n) is rounded off to two decimal places and multiplied by the value of column 3 (the fifth column).

As we can see, the electrical conductivity of any equivalent concentrations of salts of the same anion decreases with decreasing charge and atomic mass of the cation. For example, the electrical conductivity of calcium bicarbonate is the highest in comparison with magnesium and sodium bicarbonate. Calcium is divalent and has the largest mass. This is followed by magnesium bicarbonate. And the smallest electrical conductivity of bicarbonate salts belongs to monovalent sodium bicarbonate. And this is despite the fact that in equivalent concentrations moles of sodium are twice greater than calcium or magnesium.

The same sequence is observed for other anions. For clarity, in table 4 the salts with different anions are shown in different italics.

It turns out that with the infinite dilution of the solution, the divalent ions transfer more electric charge. But experiments confirm that softened water, which contains only sodium salts in concentrations equivalent to the original calcium and magnesium salts, almost always has a higher electrical conductivity This is due to the fact that in real solutions hydrated ions collide with each other, as it has been figuratively said “pass through the area in which there is the crowd of people” or other ions. In this case, there is a significant decrease in the transfer of electric charge by divalent ions. Even at a concentration of several ppm, a significant drop in the electrical conductivity of divalent ions is observed.

In order to demonstrate this, I conducted several experiments on the softening of hard water.

Four solutions were prepared. Two CaCl2 solutions with electrical conductivity of 1168 µs/cm and 339 µs/cm. Two MgSO4 solutions with electrical conductivity of 1169 µs/cm and 355 µs/cm. Then, the softening of all solutions was carried out and the measurement of the electrical conductivity of the treated solutions was taken. For softening an ion exchange column with cationite was used and for measuring electrical conductivity a verified conductometer with an error of not more than 1.5% of the measured value was used.

The results of the experiment are shown in table 5, 6.

Table 5

The original solution of CaCl2
The conductivity of the original solution CaCl2	The conductivity of the softened solution 2NaCl	The conversion factor (n)		Salinity, ppm
		for CaCl2	for    2NaCl	for CaCl2	for   2NaCl
1168	1158	0,47	0,5	549	579
339	332	0,445	0,48	151	159

Table 6

The original solution of MgSO4
The conductivity of the original solution MgSO4	The conductivity of the softened solution Na2SO4	The conversion factor (n)		Salinity, ppm
		for MgSO4	for Na2SO4	for MgSO4	for Na2SO4
1169	1527	0,7	0,64	819	977
355	412	0,56	0,575	198	237

Table 4 shows that the electrical conductivity of the original solution of calcium chloride is greater than the electrical conductivity of the resulting softened solution of sodium chloride. Moreover, the difference in the electrical conductivity of the initial and softened water decreases slightly even with an increase in salt content by 4 times. This confirms that monovalent chloride ions slightly lose mobility with the growth of the total number of ions. The conversion factor varies slightly for both calcium chloride and sodium chloride. But since calcium is divalent, it loses more mobility with an increase in salt content and, accordingly, the conversion factor for calcium chloride grows by 0.47-0.445= 0.25. While the conversion factor for sodium chloride grows only by 0.5-0.48=0.2.

Table 6 shows that the electrical conductivity of the original solution of magnesium sulfate is less than the electrical conductivity of the resulting softened solution of sodium sulfate. Moreover, the greater the electrical conductivity (salinity) of the solution, the greater the difference between the electrical conductivity of the softened and the source water is. This suggests that heavy divalent ion of sulfate greatly reduces mobility with an increase in the salinity of the water. Thus, the conversion factor (n) grows from 0.56 to 0.7 with an increase in salt content of only 3.5 times.

The experiment confirms the key influence of the salt content and divalent ions on

the cause of the increase in the electrical conductivity of softened water compared to the source water.

I conducted an experiment on softening tap water with hardness of 3.2 mg-eq/l and conductivity 451 µs/cm. The results of the measurements are presented graphically in figure 2.

Figure 2 Dependence of electrical conductivity of softened water on residual hardness of softened water

As it can be seen from the graph, the hardness of the softened water immediately after the start of filtering was 0.05 mg-eq/l and electrical conductivity of 468 µs/cm. Then the conductivity began to fall and at a value of 464 µs / cm the hardness value was 0.1 mg-eq/l. Then a significant drop in electrical conductivity and a significant increase in stiffness began. Moreover, the drop in electrical conductivity is linear in relation to the increase in hardness. It can be said that the water softening took place in the volume of the filter cycle up to the conductivity value of 464 µs/cm, untill the depletion of cationite with sodium ions. After exhaustion of cationite with ions of sodium, the conductivity of the water dropped below 464 µs/cm and hardness of the filtrate was unacceptably increased for the first stage of softening. When cationite lost the ability to exchange ions, the electrical conductivity of the source water became equal to the electrical conductivity of the “softened” water.

Interesting observation. When the water was softened at the very beginning of the filter cycle, when cationite was guaranteed to be saturated with sodium ions, the electrical conductivity of the filtrate was kept at the level of 467 µs/cm. That correspond to hardness of the softened water 0.05 mg-eq/l. Then the filtration rate was significantly increased. The filtration rate was more than 100 m/h. In this case, even saturated cationite did not have time to completely soften the water and the electrical conductivity of the water dropped to 461 µs/cm, which correspond to 0.75 mg-EQ/l hardness. Then the speed was restored to the values of 20-25 m/h. The conductivity increased again to 467 µs/cm. This was done in order to eliminate the possible effect on the electrical conductivity of the filtrate of the possible residues of the regeneration solution and to clearly determine the upper limit of the electrical conductivity of the softened water.

Table 3 shows the calculation data of electrical conductivity of the water containing sodium bicarbonate, sodium chloride and sodium sulfate (softened water for which this experiment was conducted). The molar concentration of sodium bicarbonate will be twice the molar concentration of the original calcium bicarbonate, because 1 mol of calcium carbonate is equivalent to two moles of sodium bicarbonate. The same process is for sodium chloride. But the molar concentration of sodium sulfate will be equal to the molar concentration of calcium sulfate.

According to [1], the values of the conversion factor of salt content into electrical conductivity for sodium salts are determined. Then the electrical conductivity of each salt is calculated. As a result, the sum of the electrical conductivity of all salts of sodium is 473.9 µs/cm.

As a result of the calculation, it was found out that the conductivity of hard water is 459.2 µs/cm, and softened 473.9 µs/cm. The calculated electrical conductivity of the softened water is slightly higher than the calculated electrical conductivity of the hard water. This corresponds to the actual electrical conductivity in figure 2.

Since natural water always contains calcium and magnesium and at least 70 % of the amount of all anions is bicarbonate + sulfate, the electrical conductivity of the softened water in most cases will be higher than the electrical conductivity of the hard water supplied to the softening.

Only if there is no bicarbonate and sulfate in the initial hard water, then after softening of such water, the electrical conductivity of the softened water will be lower than the electrical conductivity of the initial hard water with a salt content of the initial water not more than 1 ppt.

It should be noted that the higher the salt content of the source water and, accordingly, the hardness, the greater the difference in the conductivity of hard and softened water is. The electrical conductivity of the softened water will increase in direct proportion to the increase in hardness and, accordingly, the salt content of the source water. As shown above, monovalent sodium ions compared with bivalent ions of calcium and magnesium will have greater mobility at a higher salt content of water.

We can see that the experimental data confirm the calculated data. The conductivity difference was averaged 15 µs for water with an initial hardness of 3.2 mg-eq/l and conductivity of 459.2 µs/cm.

By analyzing the electrical conductivity of different water before and after softening installations at different sites, I determined certain regularity in the change in the electrical conductivity of the source and softened water. The increase in electrical conductivity of softened water compared to hard water is approximately 15 to 25 µs/cm per 3 mg-eq/l of hardness. Of course, it is necessary to remember that these properties are typical only for fresh, slightly salted, hard, carbonate-sulphate surface and underground water.

Example from my practice. The electrical conductivity of the source water before softening was 1692 µs/cm and the water hardness was 11.5 mg-eq/l. After softening, the conductivity was 1795 µs/cm. The increase of conductivity is up to 103 µs/cm. This value is quite significant and can allow to control the installation of softening even using a fairly cheap conductometer.

Conclusions:

1. The conversion factor of electrical conductivity into salinity (n) depends primarily on the anion composition of the water and the total concentration of ions in the water.
2. The conversion factor should be between 0.6 and 0.75 for waters with a bicarbonate content of 30 % to 80 % or more.
3. The use of conversion factor 0.5-0.55 is justified only for chloride-sulphate water (to a greater extent chloride).
4. The following formula can be used to approximate the conversion factor of electrical conductivity into the salt content of water (carbonate-calcium water):

where,

n_HCO3 – the conversion factor for calcium bicarbonate, n_HCO3=0,86;

n_SO4,Cl – the conversion factor for calcium sulfate; n_SO4,Cl=0,53;

q_HCO3 – the proportion of the bicarbonate from the sum of all the anions in g-eq;

q_SO4,Cl – the proportion of the sum of sulfate and chloride from all anions.

5. The increase in the electrical conductivity of softened water in comparison with the initial hard water, for carbonate-calcium waters, occurs primarily due to the presence of calcium, magnesium and sulfate in the water and the value of the total salinity of the water. The higher the hardness of the source water, the greater the difference between the electrical conductivity of the softened and hard water is.
6. During the process of water softening it is quite possible to carry out continuous automatic control of the process of softening by measurement of electrical conductivity of the initial and softened water. At the same time, the higher the hardness of the source water, the more effective the process of monitoring the conductivity is. For water treatment of steam and hot water boilers the use of this method is justified as additional. For technologies that do not require strict requirements for water hardness, this method of control is quite applicable as the main one. For example, to obtain drinking water or to use softening as a preliminary stage of water treatment (for example, before osmosis).

Reference materials:

1. РД 34.37.302 Методические указания по применению кондуктометрического контроля для ведения водного режима электростанций.
2. Краткий справочник физико-химических величин., Под редакцией А.А. Равделя и А.М. Пономаревой. – 2003 г.