# The influence of various forms of carbon dioxide in water on its pH value

Ivan Tikhonov

Annotation

*This article discusses the existence of various forms of carbon dioxide in water. The importance of measuring the pH value in determining the ratios of bicarbonates, carbonates and hydrates is shown. The article presents a method for calculating the pH value of water depending on the ratio of various forms of carbon dioxide in water. The developed method is adapted for calculating the pH value of water in the alkaline range. The article presents the results of calculations using this method and it compares the calculated and experimental data.*

It is known that carbon dioxide is found in water in a bound, semi-bound and free form. The bound form includes carbonate ions (CO_{3}^{2-}), semi – bound bicarbonate ions (HCO_{3}^{–}), and free form carbonic acid dissolved (H_{2}CO_{3}) and gaseous (CO_{2}).

The total amount of carbon dioxide in water is defined as the sum of all three forms.

Ʃ_{СО2} =СО_{2} + Н_{2}СО_{3} + НСО_{3}^{–} + СО_{3}^{2- }(1)

The amount (concentration of carbon dioxide forms) is measured in mmol / l. These forms of carbon dioxide are in a certain balance. The percentage of concentrations of various forms of carbon dioxide depends on the pH value of water. Thus, when the pH value of water is 8.37, there is practically no free form of carbon dioxide in the water and, accordingly, only bicarbonate ion exists and a carbonate ion begins to appear (Fig. 1).

The ratio between carbonic acid, carbonates and bicarbonates is established experimentally and depends on the pH value of water (Henderson-Hasselbalch Equation for dissociation of carbon dioxide and bicarbonate):

(2)

(3)

*where,*

*6.352-negative logarithm of the dissociation constant of carbonic acid in water at the 1st stage;*

*10.328-negative logarithm of the dissociation constant of carbonic acid in water at the 2nd stage;*

*СО _{2}, НСО_{3}^{–}, СО_{3}^{2-}, Н_{2}СО_{3 }– concentrations of carbon dioxide, bicarbonate, carbonate, and carbonic acid in moles.*

As can be seen from the graph (Fig.1), changing the amount of one form of carbon dioxide leads to the change in the ratio of the other two forms of carbon dioxide. This changes the pH value of the water.

**Figure 1**

Here it is necessary to explain how the entry form for equations (2) and (3) was obtained.

The equation of acid dissociation in water can be written in general form:

HA<-->H^{+}+A^{–}

*where,*

*HA is an acid, where H ^{+} is the hydrogen ion and A^{–} is the acid anion.*

The equilibrium constant (dissociation) of this chemical reaction can be written as:

This equation can be written as follows taking the hydrogen ion to the left side:

Then write it as a decimal logarithm taken from both sides:

(4)

It is obvious that

At the same time

The dissociation constant or equilibrium constant of the equation of dissolution of carbon dioxide in water for the first stage is equal to K_{1}=4.45 *10^{-7}, for the second stage K_{2}=4.69 * 10^{-11}. Respectively,

Then, the equation (4) is easily converted to equations (2) and (3).

We can say that when carbon dioxide is dissolved in water, the pH of water decreases due to the appearance of a hydrogen ion in the water because the equation (2) is nothing more than a form of writing for the equation of the chemical reaction of carbon dioxide and water. Then the pH value of the water will be set depending on the amount of end products: the hydrogen ion (H^{+}) and bicarbonate (HCO3^{–}), formed as a result of the chemical reaction.

This can be clearly seen in figure 1. If the water, after dissolving the initial amount of carbon dioxide, contains the same amount of carbon dioxide and bicarbonate formed as a result of the chemical reaction of CO2 with water (50% each), the pH value of such water will be 6,352 units of pH.

Let’s consider the following example. C= 0.3 mmol/l of carbon dioxide is dissolved in desalinated water. The pH value of such water can be determined by the formula:

According to figure 1, we determine the percentage of carbon dioxide and bicarbonate in such water. We get about 3.6% of the carbon dioxide gas CO2 reacted with water to form bicarbonate. This suggests that only 3.5 percent of carbon dioxide reacts with desalinated water.

At the same time the amount of the produced hydrogen ion can be calculated as

С_{н}=0,3*0,035=0,0108 mol/l

At the same time the water with a pH value of 4.94 contains

С_{н}=10^{-4,94} *1000=0,011 mol/l.

The values are almost equal. A minor error is determined by the visual detection error of the percentage of carbon dioxide to bicarbonate using figure 1.

An increase in the concentration of carbon dioxide in water leads to a decrease in the proportion of carbon dioxide that reacts with water to form carbonic acid. But due to the overall increase in the concentration of carbon dioxide in water, the pH of such water will decrease to a value of 4.0. Below this value, carbon dioxide is practically not dissolved in water.

Let’s look at an example where water containing carbon dioxide also contains sodium bicarbonate (NaHCO3). In this case, the pH value can be calculated using the equation (2).

The water contains the following concentrations of carbon dioxide and sodium bicarbonate: concentration of С_{CO2}=0.3 mol/l; concentration of C_{н}_{co3}=0.8 mmol/l.

Accordingly, using the equation (2), we can write,

Using figure 1, we determine the proportion of dissociation (interaction of carbon dioxide with water) in the case of bicarbonate in the water. In this case 22 % is carbon dioxide and 78 % is bicarbonate.

At the same time, water with a pH value of 6.96 contains hydrogen

С_{н}=10^{-6,96} *1000=0,00011 mmol/l,

which means that only (0,00011/0,3) *100=0,036% carbon dioxide reacts with water to form carbonic acid. I.e., almost all carbon dioxide is in the water in a gaseous state (or sometimes called the adsorbed state).

The dissociation of carbon dioxide in this case is significantly less (0.036%) at the same concentration of carbon dioxide in water than in the first example (3.5% in the first example), this is due to the fact that the water already contains the product of dissociation of carbonic acid-bicarbonate.

Further, it is necessary to consider in more detail the process of dissolving carbonic acid in water in two stages.

Write down the reaction the equations:

1st stage

СО_{2}+Н_{2}О <--> H^{+}+НСО_{3}^{– }(5)

2nd stage

2НСО_{3}^{–} <--> СО_{3}^{2-} + Н_{2}СО_{3} (СО_{2}+Н_{2}О) (6)

Dissociation in the first stage occurs in accordance with the dissociation constant K_{1}, and the proportion of carbon dioxide that formed carbonic acid in water can be determined by the pH value of such water using the equation (2) or figure (1).

Dissociation of carbon dioxide by the second stage does not occur under normal conditions. The fact is that the bicarbonate formed in the first stage is subjected to dissociation at the second stage. In order for bicarbonate to dissociate to form carbonate and carbonic acid, the carbonic acid must be removed from the process. Then the bicarbonate will form a carbonate. This process is observed, for example, when boiling water contains sodium bicarbonate.

It is obvious that removing carbon dioxide from the water will increase the pH value. This can be seen in figure 1. The more bicarbonate passes into carbonate in accordance with (6), the higher the pH value. I.e., the percentage of bicarbonate in water falls and, accordingly, the percentage of carbonate increases.

This condition using the K_{2} dissociation constant is presented as the equation (3).

To understand the process of increasing the pH value, dissociation by the second stage is more convenient to present in the following form:

СО_{3}^{2-} <--> НСО_{3}^{–} + ОН^{–} (7)

In fact, the equation (7) represents the process of dissociation of carbonates in water. When the carbonate is dissolved in water, two equal shares moles of bicarbonate and hydrate are formed. It is the appearance of hydrate in water that increases the pH value of water, i.e. the ratio of hydrogen-hydrate increases in the direction of hydrate.

We define the equilibrium constant K_{h} for the chemical reaction (7).

(8)

This constant is the constant of hydrolysis of carbonate in water.

K_{w}=1*10^{-14} – ionic product for water.

let’s isolate the hydrate from the equation of the hydrolysis constant (8):

By analogy with the equation (4), we can write:

(9)

where,

then,

(10)

Using the equation (10), we can determine the pH value of water depending on the ratio of carbonates to bicarbonates.

It is obvious that,

i.e.

let’s add the number 14 to the right and left sides of the equation (10). We receive,

As a result, we obtain the equation (3) after transformations using the equation of hydrolysis of carbonates (7) and the constant of hydrolysis, which was originally obtained for the process of dissociation of carbonic acid at the second stage. This circumstance is extremely important and allows us to draw the following conclusion. **The increase in the pH value of water with an increase in the ratio of carbonate-bicarbonate occurs due to the hydrolysis of the formed carbonates to form hydrates and bicarbonates. Just as the pH value decreases when the carbon dioxide – bicarbonate ratio changes, it is due to the interaction of carbon dioxide with water that a hydrogen ion and bicarbonate are formed.**

Understanding that carbonates hydrolyze in water according to the equation (7), the equation (3) can be written as follows:

Since carbonates hydrolyze to form bicarbonate and hydrate in water, the initial amount of carbonate (CO_{3}^{2-}) hydrolyzes to an equal amount in moles into hydrate (OH^{bound}) and bicarbonate (HCO_{3}^{bound}) and the residual amount of the carbonate itself (CO_{3}^{res}). As a result, we can write,

Hydrate (OH^{free}) and bicarbonate (HCO_{3}^{free}), we will call them free, are ions obtained not as a result of hydrolysis of the initial value of the carbonate. Perhaps, they have been introduced into the water by dissolving sodium bicarbonate and caustic soda.

It is obvious that the value of the numerator in the equation (11) is equal to the initial amount of carbonates involved in hydrolysis plus the amount of hydrate put additionally (obtained not as a result of hydrolysis). Although the physical model of such a system will consider the “free” hydrate as a product of hydrolysis of the original carbonate. Accordingly, numerically in moles, the value of the numerator will be equal to the value obtained when determining the alkalinity of such water by phenolphthalein (P).

For this below we consider the structure of titration of a water sample with hydrochloric acid to determine of bicarbonates, carbonates and hydrates. The alkali concentration is measured in mg-ql/l, in strict accordance with the amount of acid that has been consumed for titration.

During the titration of the sample a hydrogen ion (H) of hydrochloric acid converts the sodium hydroxide into sodium chloride and sodium carbonate into the bicarbonate. Accordingly, all of the hydroxyl ion and half of the carbonate ion react with hydrochloric acid in the presence of phenolphthalein. That is, after the discoloration of phenolphthalein only bicarbonates will remain in the water (pH 8.1-8.3), some of which belong to the carbonates and formed as a result of their destruction by hydrochloric acid.

NaOH+HCl ->NaCl+H_{2}O

Na_{2}CO_{3}+HCl ->NaHCO_{3}+NaCl

NaHCO_{3} +HCl ->NaCl+H_{2}O+CO_{2}

The denominator in the equation (11) will be equal to the sum of bicarbonate obtained during hydrolysis (НСО_{3}^{bound}) and bicarbonate obtained not as a result of hydrolysis (НСО_{3}^{free}).

Accordingly, the equation (11) can be written as

Using the equations (11) and (12), I developed a method for determining the pH of water by the alkalinity values for phenolphthalein (P) and methylorangeine (M) obtained from the analysis of water for alkalinity according to ISO 9963-2:1994 Water quality – Determination of alkalinity.

It should be noted that an acceptable simplification is introduced for further calculations: it is further assumed that the alkalinity for methylorange (M) is defined as the total alkalinity minus the alkalinity for phenolphthalein (P) in mol/l.

We can record the alkalinity values for (P) and (M):

We can also write that

The pH value is related to the concentration of hydrate in water according to the equation:

Knowing the values for (P) and (M) in mol/l using equations (11) – (16), we can determine the pH value of water for these values (P) and (M). The Method for determining the pH value is shown in figure 2.

Initially, the data array (ОН_{рН}; рН)^{16} is calculated using the formula (16). To do this, set the pH value from 8.5 to 14 with a certain step. A graphical representation of the solution to the equation (16) is shown in figure 3.

Then the calculation is made in two directions.

**The first direction:**

If the value (P) is greater than (M).

In this case, the concentration of “free” hydrate is defined as

(17)

We set the concentration (OH)^{11} (for calculation by the equation (11)) equal to 0.0001 mol/l.

At the same time,

(18)

In this case, there is no free bicarbonate, HCO_{3}^{free}=0. (In accordance with ISO 9963-2:1994)

Accordingly, the total concentration of bicarbonate is determined only by the concentration of bicarbonate obtained as a result of hydrolysis of carbonate (HCO_{3}^{bound}).

Then, taking into account the condition (15) and substituting ОН^{free} by (17) in the equation (18), we get,

Thus, by setting the total hydrate value (OH)^{11}, we can determine all the values of the variables included in the equation (11).

Then we calculate the value (pH)^{11} by the equation (11). If the value (pH)^{11} coincides with the value (pH)^{16} calculated using the formula (16), then this is the desired pH value. If the pH values do not match, then we set a new value (OH)^{11} with a certain step and repeat the calculation (pH)^{11}. The calculation is performed until the pH values match.

**The second direction:**

If the value (P) is less than (M).

In this case, there is no “free” hydrate in the water and, accordingly, the calculation is carried out, initially setting the value of bicarbonate (HCO_{3})^{11}, it equals to

And then the value (pH)^{12} is calculated using the equation (12). Then the pH values are also compared using the equations (16) and (12).

For example, we calculate the pH value of an aqueous solution of sodium carbonate with a concentration of 10 mmol/l.

The analysis shows that the values of such a solution are equal to P=10 mmol/l and M=10 mmol/l

Next, setting the pH value in the range of 8.5-14 by the equation (16), we determine the value of ОН_{рН}. The graph of the function according to the equation (16) in the range of pH values from 10 to 12 is shown in figure 3.

Then, setting the value (НСО_{3})^{11}, we calculate the pH according to the equation (12). The graph of the function according to the equation (12) in the range of values (НСО_{3})^{11} from 0.000213 to 0.01 (mol/l) is shown in figure 3.

It should be noted here that equations (3) or (11) or (12) have a physical meaning only if the bicarbonate value is at least 0.000213 mol/l.

Figure 3 shows that the intersection point of the two functions gives a single pH value of 11.16. This value can also be obtained using the hydrolysis constant (K_{h}).

It should be noted that this pH value was obtained using concentrations, not activities. Therefore, the calculated pH value differs slightly from the actual pH of a solution of this concentration. Later we will discuss how to get a pH value equal to the actual measured pH value of the solution based on the presented calculations.

**Figure 2 Flowchart for determining the pH value depending on the P and M values**

**Figure 3**

It is obvious that the presence of “free” hydrates or bicarbonates in the water will affect the degree of hydrolysis of the carbonate.

Calculations were made using the developed method based on experiment for a visual representation of the change in the degree of hydrolysis of carbonate. For the experiment, a solution of sodium carbonate with a concentration of 10 mmol/l was taken. Then the solution was forcibly purged with air. As a result, carbon dioxide from the air began to be absorbed by water. In the end, the resulting carbonic acid neutralizes the hydrate into bicarbonate with an increase in the concentration of bicarbonate and a decrease in the concentration of hydrate and carbonate, from which the hydrate is obtained as a result of hydrolysis.

Figure 4 shows the graphs of the dependence of changes in the concentration of bicarbonate, carbonate and hydrate depending on the pH when the solution is purged with air.

As you can see, when 10 mol/l of sodium carbonate is dissolved in water, 1.46 mmol/l of bicarbonate and 1.46 mmol/l of hydrate are formed. Thus, the calculated рН is equal to 11.16. The proportion of dissociated carbonate was 1,46/10=0,146 (14,6%). Figure 1 shows that this proportion also corresponds to a pH of 11.16.

Then the solution is saturated with carbon dioxide. The hydrate that was formed during hydrolysis binds into bicarbonate according to the reaction equation:

Н_{2}СО_{3} +NaOH <--> NaHCO_{3}

At certain intervals, the solution was analyzed for P and M and based on these data, the pH value and concentration of bicarbonates, carbonates and hydrates were calculated.

Figure 4 shows that immediately after the dissolution of sodium carbonate (CO_{3}^{source}) in the solution, hydrate (OH) and bicarbonate (HCO_{3}) were formed in equal proportions. Then the carbon dioxide binds the hydrate into bicarbonate and at the pH value of 10.6, the bicarbonate concentration was 4.4 mmol/l, and the hydrate was 0.4 mmol/l and the carbonate was 7.6 mmol/l. 4,2/2+0,4/2+7,6=10 mmol/l of the source carbonate. At the same time, the alkalinity value for phenolphthalein P was 8 mmol/l, and methylorange M was 12 mmol/l.

It should be noted that the concentration of carbonate and bicarbonate according to ISO 9963-2:1994 will be equal to СО_{3}^{source}=8 mmol/l, НСО_{3}^{source}=4 mmol/l. As you can see this ISO does not take into account the hydrolysis of carbonates in water and determines the amount of carbonates bicarbonates and hydrates without taking into account the hydrolysis process. At the same time quantity of source carbonate for hydrolysis is determined to be true to ISO, but it does not take into account the number resulting from the hydrolysis of bicarbonates and hydroxides, which makes it impossible to calculate the pH of water from pH values above 10.0 to 10.5.

As we can see, at a pH of 10.0, the hydrolysis of carbonates is so insignificant that at a sufficiently high concentration of bicarbonates, this practically does not cause a large error in the calculation of pH by the equation (3).

As an example, let’s consider a well-known buffer solution with a pH value of 10.00 (at 25 ^{0}C), which contains 25 mol/l Na_{2}CO_{3} and 25 mmol/l NaHCO_{3}. It is known that the calculated pH value of such a solution without taking into account the activity coefficients will be 10.328. We calculate the pH of such a solution according to the developed method. Obviously, the alkalinity for phenolphthalein P is 25 mmol/l and for methylorange M 50 mmol/l. The graphical solution of the equations (11) and (16) is shown in figure 5. The calculation using the proposed method shows that the pH value is 10.326, which gives an error of only 0.002 pH units.

If we consider a solution where P is equal to M, then in accordance with ISO 9963-2:1994 in this solution there is no bicarbonate at all and, accordingly, it is not possible to calculate the pH of this solution. This is incorrect, because the solution contains bicarbonate as a product of hydrolysis of carbonate (HCO_{3}^{bound}). Thus, using the proposed method, you can calculate the pH of the solution at any ratio of P to M.

As it can be seen in figure 4, at the pH of 9.4, the amount of bicarbonate was 16 mmol/l, the amount of carbonate 2 mmol/l and the amount of hydrate 0.0025 mmol/l. I.e., the more hydrolysis products in the solution, the lower the degree of hydrolysis is. The amount of carbon dioxide absorbed from the air was 8 mmol/l.

**Figure 4 The dependence of different forms of carbon dioxide and hydrate on the pH value for the case P<=M**

**Figure 5 Graphical solution of equations (11) and (16)**

Figure 6 shows the graphs of the dependence of changes in the concentration of bicarbonate, carbonate and hydrate depending on the pH for the case when the value of P is greater than M.

20 mmol/l of caustic soda and 10 mmol/l of sodium bicarbonate were dissolved in the water. The P value is 20 mmol/l. The M value is 10 mmol/l. As a result of calculating the pH value according to the developed method, the pH equal to 12.02 was obtained. This means that this solution contains 10.04 mmol/l of hydrate (OH) and not 10.0 mmol of hydrate, as prescribed for the determination of carbonate and bicarbonate hydrate by phenolphthalein and methylorange alkalinity, where 0.4 mmol/l is the concentration of “bound” hydrate obtained by hydrolysis of carbonates in the presence of a large amount of hydrate. Accordingly, the solution contains 0.4 mmol/l of “bound” bicarbonate at this pH.

It is obvious that as a result of mixing sodium hydrate and bicarbonate, 10 mol/l of carbonate (CO_{3}^{source}) was formed. Then sodium bicarbonate was added to the water in steps of 2 mmol/l. As a result, the hydrate binds bicarbonate into carbonate and the carbonate increases, which is hydrolyzed to form (CO3, OH, HCO3). There was a constant decrease in the source “free” hydrate (OH^{source}) and an increase in the carbonate (CO_{3}^{source}) and, accordingly, an increase in the share of carbonate hydrolysis with an increase in the “bound” hydrate (OH) and bicarbonate (HCO_{3}).

As a result, after adding 10 mmol/l of sodium bicarbonate to the solution, the value of P and M became 20 mmol/l. As a result, the pH value of the solution is determined only by the concentration of the “bound” hydrate. In this case, 2 mmol/l of bicarbonate were formed during hydrolysis, which corresponds to 10% of the source amount of carbonate (20 mmol/l). As we can see from figure 1, 10% of bicarbonate corresponds to the pH value of 11.3.

F**igure 6 The dependence of various forms of carbon dioxide and hydrate on the pH value for the case P>=M**

This method uses ion concentrations. As a result, the calculated pH values do not match the actual measured pH values. The greater the ionic strength of the solution, the greater the discrepancy between the calculated and measured values. In order for the calculated and measured pH values to coincide, it is necessary to use ion activity in the calculations. It is known that the activity of ions is defined as the multiplication of the concentration of an ion by its activity coefficient.

Figure 7 shows the dependence of the activity coefficients of HCO3 and CO3 ions on the ionic strength. The dependence is based on the solution of the equation

*where,*

*f _{i} – the activity coefficient of the ion,*

*z _{i} – the value of the ion charge,*

*I – ionic strength of the solution, mol/l.*

To obtain a calculated pH value equal to the measured value, we need to use the activity of carbonate and bicarbonate in formula (3). The value of the carbonate in the equation (11) or (12) must be multiplied by the activity coefficient of carbonate, taken at the appropriate ionic strength of the solution and the bicarbonate value is multiplied by the activity coefficient of the bicarbonate. It allows to obtain the same values of calculated and measured pH.

For example, for a solution of 25 mmol/l Na2CO3 and 25 mmol/l NaHCO3, the calculated pH value is 10.328. Multiply the corresponding ions by their activity coefficients.

To do this, we determine the ionic strength of the solution.

*where,*

*С _{i} – ion concentration, mmol/l.*

At this ionic strength, the activity coefficient for carbonate is 0.37, for bicarbonate is0.775. (figure 7)

Then

Thus, the calculated pH value is equal to the one measured at the temperature of 25^{0}C. It should be clearly understood that the calculated values match those measured only at the temperature of 25 ^{0}C.

The effect of the temperature on pH measurement is quite significant, especially at high pH values, and the change in pH from temperature for each solution must be determined individually. The pH-temperature dependence is linear. Therefore, it is sufficient to determine only the slope coefficient. This problem is not discussed in this article.

For example, let’s determine the pH value for a solution of 20 mmol/l NaOH + 10 mmol/l NaHCO3. The calculated pH value for concentrations was determined above – 12.02.

Let’s determine the ionic strength of the solution. In fact, the solution contains (according to ISO 9963-2:1994) 10 mmol/l Na2CO3 and 10 mmol/l NaOH. Then,

I=0.04

The activity coefficients for this ionic strength are equal to:

f_{со}_{3}=0,48

f_{hco3}=0,83

We use the equation (12) for simplification. Taking into account the activity coefficients we get:

The solution has this pH value at 25 C.

I have conducted quite a lot of experiments with solutions containing different ratios of P to M. On average, the calculated and measured pH values had differences of no more than 0.05 units of pH, which is a very good indicator in terms of the existing measurement error. The pH was measured to a value of no more than 12.5, to avoid an alkaline error.

It is worth saying that this technique was developed for the technology of boiler water control of low-and medium-pressure steam boilers. The pH value of the boiler water of the working boiler cannot exceed 12.5. Therefore, I was primarily interested in solutions in the pH range from 8.5 to 12.5. At the time of writing this article (07.02.2020), application no.2020100737 (dated 14.01.2020) for the patent “The method for controlling and adjusting the water-chemical mode of a steam boiler” had been filed. The paten includes this technique as a part of the control of the ingress of hardness salts into the boiler water.

**Figure 7**

I would like to stress one more point. Initially, it was difficult to understand that the P value can be multiplied by the activity coefficient of the carbonate. If the water initially contains only carbonate, then everything is clear. But if there is a “free” hydrate in the water, which is not obtained as a result of hydrolysis of carbonates… Analysis of the physical meaning of the equation (3) suggests that the value of phenolphthalein alkalinity (hydrate and carbonate) provides a quantitative characteristic in determining the pH, and the value of bicarbonate provides a qualitative characteristic. That is, the smaller the value we divide, the greater the value we get, but the resulting pH value cannot be greater than what the phenolphthalein alkalinity potentially contains. If carbon dioxide is removed when bicarbonate is dissolved in water, the resulting carbonate will hydrolyze to form a hydrate. After removing more than half of the carbon dioxide in such water, a “free” hydrate will appear. That is, the phenolphthalein alkalinity will be greater than the methylorange (P=>M). However, this is exactly the hydrate that was formed from the initial amount of bicarbonate. In accordance with figure 1, it turns out that it is the remaining amount of bicarbonate that provides the pH value, while all the rest, represented by the alkalinity by phenolphthalein, is assumed to be in the form of carbonate.

Let’s conduct a simple experiment. 10 mmol/l of caustic soda was dissolved in deionized water. The measured pH value of this solution was 11.86. The ionic strength of the solution is 0.01. The activity coefficients for this ionic strength are equal to:

f_{со3}=0,659

f_{hco}_{3}=0,9

Respectively,

As you can see, we get a pH value that is completely determined by the concentration of hydrates in the solution, without taking into account the activity coefficient, when substituting bicarbonates in the equation (3) for the value of the carbonates hydrolysis constant (the minimum value at which the equation (3) has a physical meaning of 0.000213 or for mmol 0.213). I.e., if 10 mmol/l of NaOH were dissolved in deionized water.

In this case, taking into account the activity coefficients, we get:

As you can see, even in the absence of carbonates in the water, using this calculation method with certain assumptions (the minimum concentration of bicarbonate is 0.213 mmol/l) allows you to get the calculated pH value equal to the measured one.

Interestingly, the NaOH activity coefficient in water at an ionic strength of 0.01 is 0.9. The measured pH value of the solution with a concentration of 10 mmol/l (I=0.01) at 25 ^{0}C is 11.86. This assumes that when measuring pH, the NaOH activity coefficient will not be defined as the hydrate activity coefficient. For example, for this concentration of caustic soda (0.01 mol/l), the hydrate activity coefficient will be 0.724, not 0.9.

Or

*where,*

*С _{ОН} – hydrate activity, mmol/l.*

Experiments at different hydrate concentrations and different ionic strength confirm the possibility of using the equation (3), taking into account the minimum bicarbonate concentration of 0.000213 mol/l, in calculating the pH value when at least caustic soda is dissolved in water and using the activity coefficients for carbonate and bicarbonate.

**Conclusions:**

- The method for calculating the pH value of water containing carbonates has been developed. The developed method allows us to calculate the pH value of water based on the values of phenolphthalein and methylorange The calculation algorithm is presented.
- The possibility of the existence of hydrates and bicarbonates in water, which are not taken into account when analyzing water for alkalinity according to ISO 9963-2:1994, is shown.
- The effect of the ionic strength of the solution on the pH value is shown.
- The possibility of using the developed method for the purpose of controlling the water-chemical mode of a steam boiler is indicated. (patent application no. 2020100737 (dated 14.01.2020) “The method for controlling and adjusting the water-chemical mode of a steam boiler”).