A hard-water sample contains \(0.0085 \%\) Ca by mass (in the form of \(\mathrm{Ca}^{2+}\) ions). What mass of water in grams contains \(1.2 \mathrm{~g}\) of \(\mathrm{Ca}\) ? ( \(1.2 \mathrm{~g}\) of \(\mathrm{Ca}\) is the recommended daily allowance of calcium for 19- to 24-year-olds.)

Understanding chemical concentration is essential in chemistry, as it describes how much of a substance is present within a mixture. In the context of water quality, like in the hard-water sample from our exercise, chemical concentration refers to the amount of a particular element or compound, such as calcium, dissolved in water. The concentration is usually expressed in units of mass per volume or as a percentage.

Converting the percentage of a compound to a more usable form, such as a decimal, enables calculations and comparisons. For instance, we started with a concentration of calcium stated as 0.0085%, which converts to the decimal 0.000085 for further calculations. This step is fundamental in accurately determining quantities in chemical solutions and is an essential skill in chemistry lab practices.

The term 'mass percent' is a way of expressing a concentration that compares the mass of a solute to the total mass of the solution. It is calculated using the formula: mass percent = (mass of solute / mass of solution) x 100%. In our exercise, mass percent represents the amount of calcium in the water sample.

This concept is pivotal because it provides a simple metric to understand the proportionate amount of a substance within a mixture. For practical purposes, it allows for easy adjustments to concentrations. For example, health guidelines might use mass percent to recommend the amount of a nutrient, such as calcium, that should be consumed in our daily diet.

Calcium is a vital mineral for the human body, having roles in bone health, muscle function, and nerve signaling. The daily allowance of calcium suggests the optimal amount of calcium one should consume to maintain good health. For 19- to 24-year-olds, the recommended daily allowance (RDA) is typically around 1.2 grams.

It's important for dietary planning and public health guidelines to ensure sufficient calcium uptake, especially considering its limited presence in certain water supplies. When calculating the mass of water necessary to supply the RDA of calcium, as seen in our problem, understanding the chemical concentration of calcium in that water allows us to estimate how much water would be needed to meet this nutritional requirement.

Stoichiometry is the section of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. In the case of our exercise, stoichiometry involves the proportion of calcium ions in water, determining the mass of water needed to obtain a specific mass of calcium.

The stoichiometric calculation bridges the chemical concentration (expressed as mass percent here) with the desired quantity of an element or compound. By applying the stoichiometric principles, we can solve practical problems, such as ensuring the right amount of an element is consumed according to the daily allowance recommendations. Stoichiometry requires a clear understanding of the mole concept, molar masses, and Avogadro's number, but in this exercise, we focused on the mass relationships to find our solution.