Determine the molarity for each of the following solutions: (a) 0.444 mol of \(\mathrm{CoCl}_{2}\) in 0.654 L of solution. (b) \(98.0 \mathrm{g}\) of phosphoric acid, \(\mathrm{H}_{3} \mathrm{PO}_{4},\) in \(1.00 \mathrm{L}\) of solution. (c) \(0.2074 \mathrm{g}\) of calcium hydroxide, \(\mathrm{Ca}(\mathrm{OH})_{2},\) in \(40.00 \mathrm{mL}\) of solution. (d) \(10.5 \mathrm{kg}\) of \(\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}\) in \(18.60 \mathrm{L}\) of solution. (e) \(7.0 \times 10^{-3}\) mol of \(I_{2}\) in \(100.0 \mathrm{mL}\) of solution. (f) \(1.8 \times 10^{4} \mathrm{mg}\) of \(\mathrm{HCl}\) in \(0.075 \mathrm{L}\) of solution.

Solution concentration is a measure of the amount of solute that is dissolved in a solvent. It is a crucial concept in chemistry, as it helps us understand the strength of a solution. One common unit of concentration is molarity, denoted as M, which is defined as moles of solute per liter of solution. To calculate molarity, simply take the number of moles of a solute and divide it by the volume of solution in liters.

Understanding molarity allows chemists and students to prepare solutions with precise characteristics, crucial for reactions and experiments. When dealing with diluted or small volumes, it is also helpful to be aware of conversions between milliliters and liters, since molarity calculations require the volume to be in liters. In typical problems, you might encounter various units of mass (grams, kilograms, milligrams) and volume (milliliters, liters), so it’s essential to convert these to moles and liters respectively, before calculating molarity.

The conversion from moles to liters is a fundamental skill in chemistry, particularly when discussing gases at standard temperature and pressure or when dealing with solution concentration. However, in the context of molarity, we are often given the moles of a substance and need to consider the volume in liters of the solution to find the concentration.

It is important to note that the volume of the solvent (water, for example) is different from the volume of the solution as a whole. If we start with a certain volume of water and add solute to it, the final volume (volume of the complete solution) can be different than the initial volume of water alone. Molarity problems usually provide the final solution volume, which is the value to use in your calculations. By accurately converting volume units and understanding the distinction between solvent and solution, you can ensure the correct molarity calculation.

The chemical formula of a compound tells us the types and quantities of atoms that are bonded together to form that compound. For instance, the chemical formula \(\mathrm{CoCl}_{2}\) represents a compound made of one cobalt (Co) atom and two chloride (Cl) atoms.

Understanding a chemical formula is crucial when calculating the molarity of a solution, as it allows us to determine the compound's molar mass by adding together the atomic masses of each element as listed in the periodic table. Moreover, a chemical formula can also provide insights into the properties of the substance, such as its reactivity and how it might interact with other chemicals. This understanding is critical when preparing solutions for reactions and can affect the solubility, concentration, and behavior of the substance in the solution.

Molar mass is the mass of one mole of a given substance, expressed in grams per mole (g/mol). It is calculated by adding the atomic masses of all atoms in a molecule. The atomic masses can be found on the periodic table, and they must be used precisely as required to ensure accurate calculations.

When converting mass to moles or vice versa, knowing the molar mass is essential. In the context of molarity calculations, molar mass enables us to convert between grams of solute and moles of solute. Take for example phosphoric acid, \(\mathrm{H}_3\mathrm{PO}_4\), with a molar mass calculated as 3(1.01) + 30.97 + 4(16.00) = 97.99 g/mol. This means that 97.99 grams of phosphoric acid is equivalent to one mole. Using molar mass in this way allows us to start with a mass of a substance and find out how many moles we have, which is a crucial step in calculating the molarity of a solution.