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Answer :
Final answer:
The correct option is a) 33.1 mg/L The total hardness as CaCO3 of a water sample with Ca2+ and Mg2+ each at 33.1 mg/L is calculated to be 109.9867 mg/L. However, this does not match any of the provided options, indicating a possible mistake. Total alkalinity cannot be determined without more information.
Explanation:
The question asks about the total alkalinity and total hardness in mg/L as CaCO3 in a water sample containing Ca2+ and Mg2+ ions at a concentration of 33.1 mg/L each. Since the hardness depends on the concentration of calcium and magnesium ions, we need to convert their concentrations to equivalents in terms of CaCO3.
To convert the concentrations to as CaCO3, we use the equivalent weight of CaCO3 which is 50.04 g/mol. The molecular weight of Ca2+ is approximately 40.08 g/mol so each mg of Ca2+ corresponds to 50.04/40.08 = 1.247 mg of CaCO3. Similarly, the molecular weight of Mg2+ is 24.31 g/mol, hence each mg of Mg2+ corresponds to 50.04/24.31 = 2.058 mg of CaCO3. Now we can calculate:Total hardness as CaCO3 = (1.247 x 33.1 mg/L of Ca2+) + (2.058 x 33.1 mg/L of Mg2+) = 109.9867 mg/L, which does not match any of the options provided.Therefore, there seems to be a mistake in the provided options or in the original question. The alkalinity of the water is not provided in the question, and therefore cannot be answered without additional information.
The total alkalinity in a water sample can be determined by measuring the concentration of HCO3- and CO32- ions present. The total hardness, on the other hand, can be determined by measuring the concentration of Ca2+ and Mg2+ ions present. In this case, the water sample has a concentration of 33.1 mg/L for both Ca2+ and Mg2+ ions. Since both ions contribute to the total hardness, the total hardness in mg/L as CaCO3 would be twice the concentration of either ion. Therefore, the total hardness is 66.2 mg/L as CaCO3 (option b).
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