If a hard water solution is saturated with calcium carbonate, what volume of the solution has to evaporate to deposit 1.00 × 10^2 mg of CaCO3, given that one of the main components of hard water is CaCO3, and when hard water evaporates, some of the CaCO3 is left behind as a white mineral deposit?

Verified step by step guidance

1. Identify the molar mass of calcium carbonate (CaCO_3) by adding the atomic masses of calcium (Ca), carbon (C), and oxygen (O).
2. Convert the mass of CaCO_3 (1.00 \(\times\) 10^2 \(\text{ mg}\)) to grams by dividing by 1000.
3. Calculate the number of moles of CaCO_3 using the formula: \(\text{moles}\) = \(\frac{\text{mass in grams}\)}{\(\text{molar mass}\)}.
4. Determine the concentration of CaCO_3 in the saturated solution, which is typically given or can be found in a reference table.
5. Use the concentration to find the volume of solution needed to contain the calculated moles of CaCO_3, using the formula: \(\text{volume}\) = \(\frac{\text{moles}\)}{\(\text{concentration}\)}.

Key Concepts

Saturation and Solubility

Saturation refers to the point at which a solution can no longer dissolve additional solute at a given temperature and pressure. The solubility of a substance, like calcium carbonate (CaCO3), indicates how much of it can dissolve in a specific volume of solvent. Understanding these concepts is crucial for determining how much of the solution must evaporate to reach a point where CaCO3 precipitates out.

Evaporation and Concentration

Evaporation is the process by which liquid turns into vapor, leading to a decrease in the volume of the solution. As water evaporates, the concentration of dissolved substances, such as CaCO3, increases. This concept is essential for calculating how much of the solution must evaporate to achieve the desired concentration that allows for the deposition of a specific mass of CaCO3.

Mass-Volume Relationships

Mass-volume relationships involve understanding how the mass of a solute relates to the volume of the solution in which it is dissolved. In this context, knowing the mass of CaCO3 to be deposited allows for the calculation of the volume of solution that must evaporate, based on the concentration of CaCO3 in the saturated solution. This relationship is fundamental for solving the problem presented.