As we have seen, the pH needs to be adjusted to the optimum for optimal coagulation. In general, there are two directions in which this can happen. If the pH is high, then it needs to be adjusted in the downward direction and if it is low, it needs to be adjusted in the upward direction. To adjust in the downward direction, an acid is needed. The cheapest way to do this is to use carbon dioxide. To adjust in the upward direction, a base is needed and the cheapest way to do this is to use lime. In Chapter 11, the following formula was derived:

where

[Acadd]geq _ gram equivalents per liter of acid needed [Acur]geq _ current alkalinity pH(0 _ destination pH pHcur _ current pH

Ya _ fractional dissociation of the hydrogen ion from acid used

Carbon dioxide will be used as the source of acidity in the derivation below. To determine the equivalent mass of carbon dioxide, the species it is reacting with must be known. Whatever alkalinity species are present, it is expected that carbon dioxide will react with them until the end point is reached. Since the hydroxyl ion is always present no matter what stage of pH any solution is in, the OH- is the very ion that will take carbon dioxide to this end point; thus, it determines the equivalent mass of carbon dioxide.

Therefore, proceed as follows:

This reaction represents one of the alkalinity reactions that carbon dioxide must neutralize before it can provide the needed hydrogen ion concentration that lowers the pH. These hydrogen ions, it provides from the H+ of the H2CO3 it will eventually become as follows:

From Equation (12.79), the equivalent mass of carbon dioxide is CO2/2 = 22. We must make this also as its equivalent mass in Equation (12.80), if the two equations are to be compatible. Let MC^pH be the kilograms of carbon dioxide added to lower the pH from pHcur to pH(0 and V be the corresponding cubic meters of water treated. Then, r 10-pH,° _10-pHcar 1

M CO2pH = 22j [Acadd]geq = [Acur]geq + --^-V (12.81)

Now, consider the situation where pHcur is less than pHo. In this case, a base is needed. As in the case of alkalinity, a natural water will always have acidity. Until it is all consumed, this acidity will resist the change in pH when alkalinity is added to the water. Let the current total acidity be [Acur]geq in gram equivalents per liter. Also, let the total alkalinity be [Afldd]geq in gram equivalents per liter.^

Assuming no acidity present, the total base to be added is 10 cur - 10 gram moles per liter of the equivalent hydrogen ions. But since there is always acidity present, the total alkalinity to be added must include the amount for neutralizing the natural acidity, [AciM(]geq = [Accur]geq. Thus, the total alkalinity to be added,

where <—b is the fractional dissociation of the hydroxide ion from the base supplied. For strong bases, <—b is unity; for weak bases, it may be calculated from equilibrium constants.

To obtain the equivalent mass of the lime, consider that it must neutralize the acidity first before raising the pH. Thus,

Thus, the equivalent mass of lime is CaO/2 = 28.05.

Let MCaOpH be the kilograms of lime to be added to raise the pH from pHcur to pH(0 and V be the corresponding cubic meters of volume treated. Then,

McaOph = 28.05 [Aadd]geq V = 28.05Î [Accur]geq + 10-—10- V (12.84)

In Chapter 13, we will calculate some values of — and —,. Healthy Chemistry For Optimal Health

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