In aqueous solution, the addition of CaO involves the following reaction:
But the product formed, Ca(OH)2 is under the following solubility equilibrium:
Then , we can calculate the solubility of the product formed in a saturated solution of Ca(OH)2 according to the following table:
Notice that the expression of KSP in terms of the solubility can be written as:
Solving for solubility:
Substituting known values:
This is the solubility of Ca(OH)2 in water. Also, is the equilibrium concentration of Ca+2 ions coming from the addition of CaO to the water. Due to the 1:1 stoichiometry between CaO and Ca+2 ions, we can establish a value of 0.0111M as the molar concentration of CaO required in water.
From the units of molarity as concentration unit:
In one hour, the water treatment plant needs to treat an average of 8600 cubic meters of water. Converting this discharge into liters units:
If we multiply this discharge by the concentration required of CaO, we will have the molar quantity of CaO required per hour (nCaO):
To calculate the quantity of CaO require in one day we will apply the following conversion factor:
Notice that we are simplifying units in every conversion factor.
In one year we will have:
The molecular weight of CaO is:
The mass of CaO required per year is given by the product:
Substituting data:
The tons of CaO needed per year are calculated using the following conversion factor:
The answer is
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