The hardness of water (hardness count) is usually expressed...

The hardness of water (hardness count) is usually expressed in parts per million (by mass) of $\mathrm{CaCO}_{3},$ which is equivalent to milligrams of $\mathrm{CaCO}_{3}$ per liter of water. What is the molar concentration of $\mathrm{Ca}^{2+}$ ions in a water sample with a hardness count of 175 $\mathrm{mg} \mathrm{CaCO}_{3} \mathrm{L}$ ?

Key Concepts

Stoichiometry of Dissolution Reactions

Stoichiometry involves using the mole ratios from a balanced chemical equation to relate quantities of reactants and products. In water hardness analysis, calcium carbonate (CaCO3) is used as a reference compound, and it dissociates to produce calcium ions in a one-to-one molar ratio. This stoichiometric relationship allows for the conversion of calcium carbonate concentration to the molar concentration of Ca2+ ions.

Molar Mass Calculation

The molar mass of a compound is the sum of the atomic masses of all the atoms in its chemical formula. It serves as the conversion factor between the mass of a substance and the number of moles. For purposes such as converting milligrams per liter of CaCO3 to moles per liter, knowing the molar mass of CaCO3 is essential.

Unit Conversion and Molar Concentration

Molar concentration, or molarity, is the number of moles of a substance per liter of solution. Converting from a mass concentration (like mg/L) to molarity requires the use of the compound’s molar mass to translate the mass into moles, ensuring that the concentration is expressed in a consistent and meaningful unit for chemical reactions.

Water Hardness Measurement

Water hardness is a measure of the concentration of divalent metal ions, primarily calcium (Ca2+) and magnesium (Mg2+), in water. It is typically expressed as equivalent amounts of calcium carbonate (CaCO3) because CaCO3 is a standard reference used to assess water quality and predict scaling and soap consumption issues.

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