Final answer:
The equivalent water hardness for a 0.1M calcium chloride solution expressed in mg CaCO3 per liter is 10,009 mg/L. This value greatly exceeds the provided options a) through d), indicating a possible error in the question or the need for further clarification.
Step-by-step explanation:
To calculate the equivalent water hardness in mg CaCO₃ for a calcium chloride solution containing 0.1M CaCl₂, we need to consider the relationship between the molarity of CaCl₂ and the concentration of CaCO₃. Every mole of CaCl₂ in solution provides one mole of Ca²⁺ ions, which can correspond to one mole of CaCO₃ since they both have one mole of calcium per mole of compound. The molar mass of CaCO₃ is 100.09 g/mol.
To find the equivalent mass of CaCO₃ for the given molarity of CaCl₂ (0.1M), we perform the following calculations:
(0.1 mol/L CaCl₂) × (100.09 g/mol CaCO₃) = 10.009 g/L CaCO₃
Since hardness is given in mg/L and 10.009 g/L is equivalent to 10,009 mg/L, the correct answer for the hardness of 0.1M CaCl₂ solution in terms of CaCO₃ is 10,009 mg/L, which is not listed in the options a) through d). Thus, it seems there might be an error in the given options or the question may need clarification.