(a) Calculate the mass of \(\mathrm{CaCl}_{2}-6 \mathrm{H}_{2} \mathrm{O}\) needed to prepare a \(0.10 \mathrm{~m} \mathrm{CaCl}_{2}(\mathrm{aq})\) solution, using \(2.50 \mathrm{~g}\) of water. (b) What mass of \(\mathrm{NiSO}_{4} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) must be dissolved in \(500 \mathrm{~g}\) of water to produce a \(0.22 \mathrm{~m}\) \(\mathrm{NiSO}_{4}(\mathrm{aq})\) solution?

Understanding the concept of molar mass is crucial when tackling problems in chemistry, especially when making solutions. Simply put, the molar mass is the weight of one mole of a substance, usually expressed in grams per mole (g/mol). It's calculated by adding up the atomic masses of each atom in a molecule. For hydrated compounds like CaCl2·6H2O, you must include the weight of the water molecules bonded to the compound. This is essential in stoichiometry, as it provides a definitive relationship between the mass of a substance and the amount of particles (moles) it contains.

To find the molar mass, you look up the atomic masses on the periodic table and perform a sum: for CaCl2·6H2O, you would add the mass of one calcium atom, two chlorine atoms, and the collective mass of 12 hydrogen and 6 oxygen atoms. Doing these calculations precisely allows for accurate preparation of solutions, as seen in our exercise where we calculate the mass needed for a specific molality of a solution.

Preparing a chemical solution might remind you a bit of cooking, following a recipe to get the expected results. But in the chemistry kitchen, accuracy is everything. Solution preparation involves dissolving solute in a solvent to achieve a desired concentration. The measure of concentration we're focusing on here is 'molality', which is moles of solute per kilogram of solvent, not to be confused with ‘molarity’, which is moles per liter of solution.

To prepare a solution with a specific molality, as in our exercise, you first need to calculate the appropriate mass of solute using the molality formula and molar mass. Accurate measurements of the solute and solvent are imperative for the reliable outcomes. For learners, remembering to convert mass to the correct units (kilograms for molality) is a frequent pain point – focus on getting those conversions right for success in solution preparation.

Stoichiometry is the roadmap of chemistry, guiding you through the quantitative relationships between reactants and products in chemical reactions. It's also vital for preparing solutions, as shown in our previous examples. When calculating the amount of a compound needed to achieve a desired molality, you are using stoichiometric principles.

The use of balanced equations, molar ratios, and conversions between mass and moles are all part of stoichiometry's domain. Understanding this theoretical framework helps you predict the outcomes of reactions and create precise solutions. It's a balancing act, ensuring that the mass of the solute and the volume or mass of the solvent align perfectly with the stoichiometric calculations. Think of stoichiometry as the GPS for navigating the molar highways of chemistry.

Hydrated compounds are a bit like sponges, holding onto water molecules within their crystal structure. These waters of hydration must be accounted for in stoichiometric calculations and when preparing solutions. For instance, CaCl2·6H2O has six water molecules for every formula unit of calcium chloride, and every one of them adds to the mass you need to weigh out.

Remember, when you're asked for the mass of a hydrated compound needed for a solution, you’re not only considering the compound itself but also the bound water. This is why accurately calculating the molar mass of hydrated compounds is key. Miss out on the waters, and your solution's concentration won't match your expectations – a classic stumbling block in chemistry that reinforces the need for meticulous calculation and preparation.