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

Molarity

Molarity is a unit of concentration defined as the number of moles of a substance present in one liter of solution. It is a fundamental concept in chemistry that allows the conversion from a measured mass or volume of a solute into the amount of substance per unit volume, which is crucial for quantitative analysis and chemical reactions.

Unit Conversion (mg to Moles)

Converting a mass given in milligrams to moles involves using the molar mass of the substance. By dividing the mass in mg (converted to grams) by the molar mass (in g/mol), one can determine the number of moles present. This conversion is essential when dealing with measurements at a scale where substances are represented in small masses but chemical formulas require mole-based calculations.

Stoichiometry of Calcium Carbonate

Stoichiometry is the relation between the quantities of reactants and products in a chemical reaction. In this context, calcium carbonate (CaCO?) is used to represent water hardness, and it dissociates to yield calcium ions (Ca²?) in a 1:1 molar ratio. Understanding this stoichiometric relationship is key to calculating the molar concentration of Ca²? from the given mass of CaCO?.

Water Hardness

Water hardness is a measure of the concentration of divalent metal ions, primarily calcium (Ca²?) and magnesium (Mg²?), but is commonly represented as an equivalent amount of calcium carbonate (CaCO?) in parts per million (mg/L). This standardization facilitates consistent water quality assessments and comparisons across different water samples.

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