Drug enforcement agents have a variety of chemical tests they can use to identify crystalline substances they may find at a crime scene. Heroin can be detected by treating a sample with a solution of mercury(II) chloride. The heroin will form a rosette of needle-shaped crystals. What is the molarity of \(\mathrm{HgCl}_{2}\) in a stock solution prepared by dissolving \(74.15 \mathrm{~g}\) of \(\mathrm{HgCl}_{2}\) to a final volume of \(250.0 \mathrm{~mL}\) ?

Molarity is a commonly utilized concept in chemistry to describe the concentration of a solution. It is defined as the number of moles of solute per liter of solution. The symbol for molarity is usually an uppercase M. To calculate molarity, you use the formula:
\[ \text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]
In our example, we were given the mass of mercury(II) chloride (HgCl\textsubscript{2}) and the final volume of the solution. Starting by converting the volume from milliliters (mL) to liters (L), we follow through calculating the molar mass, determining the number of moles and then the molarity.

Volume conversion is essential when working with molarity, since molarity is expressed in moles per liter (L). Often, volumes are provided in milliliters (mL), and they need to be converted to liters. The necessary conversion factor is:
\[ 1 \text{ L } = 1000 \text{ mL } \]
So, to convert from mL to L, you divide the number of milliliters by 1000. For instance, in the problem, we converted 250.0 mL to liters:
250.0 mL \times \frac{1 \text{ L }}{1000 \text{ mL }} = 0.2500 L

The molar mass of a compound is the mass in grams of one mole of the compound. To obtain the molar mass, sum the atomic masses of all atoms in the molecule. The atomic mass units (amu) of each element are used for this calculation. Here’s the formula for determining the molar mass:
\[ \text{Molar\ mass} \ (\text{g/mol}) = \sum \text{(Atomic\ mass)} \]
For mercury(II) chloride (HgCl\textsubscript{2}), we use the atomic masses: \text{Hg} = 200.59 \ g/mol\ and \text{Cl} = 35.45 \ g/mol\
The molar mass calculation is:
200.59 \text{ g/mol} + 2(35.45 \text{ g/mol}) = 271.49 \text{ g/mol}
This helps in determining the number of moles using the mass, via the formula:
\[ \text{Moles} = \frac{\text{mass}}{\text{molar mass}} \]

Stoichiometry involves using relationships between reactants and products in a chemical reaction to determine quantities. It allows us to make quantitative predictions about the outcomes of reactions. It is essential for calculating yields, scaling reactions, and understanding reaction mechanics.
In the context of the exercise, stoichiometry bridges the amounts given in grams to the molarity of the solution. It started by using stoichiometry to convert grams of HgCl\textsubscript{2} into moles. The relationship used is:
\[ \text{Moles} = \frac{\text{mass}}{\text{molar mass}} \]
Once we have the number of moles, we use it to find the molarity by dividing it by the volume in liters. This intertwines with stoichiometry principles, completing a full circle from mass, to moles, to molarity.