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Alkalinity Relationships in Water Chemistry
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Table 1 — Mineral acidity* vs pH value H+, ppm as CaCO3
pH
2–3 4–5 6–7 8–9 10–11 12–13 14–16 17–20 21–25 26–30 31–40 41–50
4.3 4.0 3.9 3.8 3.7 3.6 3.5 3.4 3.3 3.2 3.1 3.0
*Mineral acidity is reported as the H+ ion.
Another significant alkalinity measure is “P alkalinity,” which exists at pH's above the phenolphthalein end-point range of pH 8.2–8.4.
In general, the alkalinity of most natural water supplies is caused by dissolved bicarbonate salts. The following equations show how rain, picking up CO2 from the atmosphere and from the respiration of soil organisms, dissolves magnesium and calcium from a common mineral, dolomite, to produce hardness and alkalinity in ground water: H2O + 2CO2 + MgO → Mg (HCO3)2
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Alkalinity is the presence of alkaline (acid neutralizing) minerals in water. By definition, total alkalinity — also called “M alkalinity” — is that which produces a pH above the methyl orange (M) endpoint of about 4.2–4.4, and which reacts with mineral acids to produce a neutral salt at the M endpoint. Also by definition, then, alkalinity ceases to exist at pH 4.2–4.4, and further reduction of pH produces free mineral acidity. The concentration of acidity is measured by pH, partly influenced by the level of total dissolved solids according to Table 1.
Figure 1 — Approximate relationship of carbon dioxide, alkalinity, and pH value
H2O + CO2 + CaCO3 → Ca (HCO3)2
There remains a balance between excess CO2 and bicarbonate ions, which is measured by pH value, as shown in Figure 1. Theoretically, a pH of 7.0 represents a neutral system, with higher pH being alkaline and lower pH acid. Obviously, in water chemistry the expression “neutral pH” has little or no meaning, since even at a pH of 5, alkalinity is present. To properly define a water condition, pH should be expressed accurately.
In the region above pH 8.2–8.4, the “P” endpoint, it is convenient to use a “shorthand” device to easily calculate the balance between HCO3, CO3, and OH based on P and M alkalinities. These expressions are as follows: Below pH 9.8–10.0 (where P Alk. is less than 1/2 M Alk.): CO3 HCO3 OH
= 2 x P Alk. = M – CO3 = M – 2P = Zero
Above pH 9.8–10.0 (where P Alk. exceeds 1/2 M Alk.):
When the pH exceeds 8.2–8.4, the free CO2 disappears and the CO3 = 2 (M – P) bicarbonate begins to convert to OH = 2P – M the carbonate ion. This progresses HCO3 = Zero to a pH of about 9.8–10, at which point all of the CO2 - originating alkalinity is essentially in the form of carbonate.
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These approximations are very useful, but they may be subject to interferences especially in contaminated waters where ammonia may be high, for example. In some cases, the carbonate is precipitated first by addition of BaCl2, and subsequent titration to the P endpoint gives hydrate alkalinity alone more accurately than can be calculated from usual P and M relationships. Waste waters may contain ions in addition to HCO3 and CO3 which are alkaline, such as bisulfides, sulfides, and phosphates. When dealing with such waters, M and P titrations are inadequate to determine HCO3 – CO3 relationships, and acid evolution of CO2 must be resorted to. Table 2 — Caustic alkalinity vs pH OH, ppm as CaCO3
pH
2–3 4–5 6–7 8–9 10–11 12–13 14–16 17–20 21–25 26–30 31–40 41–50
9.7 10.0 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 11.0
Table 3 — Approximate relationships of P, M, and pH (not corrected for TDS or temperature) P Alk., % of total alkalinity
Approx. pH
10 15 10
8.2–8.4* 8.7–8.9* 9.0–9.2*
15 20 25
9.3–9.4* 9.5–9.6* 9.6–9.7*
30 35 50
9.7–9.8* 9.8–9.9* 9.9–10.0
*Assuming zero CO2. For pH values below 8.2 *in presence of CO2 , see Table 2.
When free hydroxyl ion appears, above pH 9.8–10.0, the concentration can be approximated from Table 2, subject to some variation caused by the level of total dissolved solids. Below pH 10, the pH may be approximated by the ratio of P alkalinity to M alkalinity, as shown by Table 3. These alkalinity relationships are extremely important in water chemistry, since the most prominent water problems are deposits and corrosion, and these are closely related to the instability of each specific water caused by the tendency of CaCO3 to dissolve in or precipitate from it. In the early days of water chemistry, the “marble test” was used as a measure of a water supply's stability. A sample of water shaken with finely ground marble
and then filtered was analyzed for hardness and alkalinity before and after limestone treatment. If it had a deposit-forming tendency, the hardness and alkalinity would drop; if it were an aggressive (corrosive) water, these values would increase. Langelier developed an index based on solubility products and dissociation constants which very ingeniously related alkalinity, pH, and calcium hardness and determined the pH at which saturation should occur at various temperatures. The Langelier Index in a simplified form (uncorrected for concentrations of total dissolved solids) is shown by Figure 2.
Figure 2 — Simplified Langelier Index
In titrating a mixture of OH and CO3, the following would apply:
Using this graph, assume a water supply with a calcium hardness of 240 ppm, an alkalinity of 190 ppm, and pH 6.8. The saturation pH (pHs) is found to be 7.3. The Langelier Index is —
1. At the P endpoint, all OH and 1/2CO3 would be reacted. 2. At the M endpoint, all OH and all CO3 would be reacted, or,
pH – pHs = 6.8 – 7.3 = –0.5
The Langelier Index assumes that a positive value shows the water to be scale forming (CaCO3 will probably drop out), and a negative value indicates corrosive tendencies. (This is an oversimplification, since the concentration of dissolved oxygen has a pronounced effect.) Working from these data, Ryznar evaluated the Langelier Index against actual field experiences with corrosive and scale-forming waters in municipal systems. He developed his Stability Index, whereby SI = 2 pHs – pH
and in this framework an index over 6 was found to be corrosive and below 6, scaling. A final consideration is the importance of buffer effect in alkaline waters. This can be a critical factor where careful control of pH may be necessary in treating either a raw water supply or a wastewater. As an example of this, compare the neutralization of NaOH to the neutraliza-
P = 1/2CO3 + OH; 2P = CO3 + 2OH M = CO3 + OH; M = CO3 + OH Figure 3 — Neutralization of alkaline water with H2SO4 (assume 50 ppm M alkalinity)
tion of Na2CO3, as shown in Figure 3. It is obvious that it is virtually impossible to control the pH of the NaOH neutralization at pH 7, since there is a vertical drop between pH 9 and 4.3. As a corollary to this, it is considerably easier to control the pH of an acidic waste with Na2CO3 than with NaOH, provided the CO2 generation can be controlled without excessive foaming. Figure 3 provides the basis for the P–M rules of thumb for calculating HCO3– CO3– OH relationships expressed earlier. On the NaOH neutralization curve — P = M = OH
while on the Na2CO3 curve P = 1/2 M = 1/2 CO3
Subtracting, 2P – M = OH Since M is total alkalinity, CO3 = (M – OH) = [M – (2P – M)] = 2 (M – P)
In summary, the relationships of the various forms of alkalinity in water are fundamental to any evaluation of problems in water systems. These basic relationships can be used to control such diverse operations as corrosion control, lime softening, and pH correction.
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