Hydrochloric acid ( \(\mathrm{HCl})\) is sold as a concentrated aqueous solution \((12.0 \mathrm{~mol} / \mathrm{L})\). If the density of the solution is \(1.18 \mathrm{~g} / \mathrm{mL}\), determine the molality of the solution.

Chemical concentration refers to the amount of a substance (solute) present in a given volume of solution. In this exercise, we are working with hydrochloric acid \((\text{HCl})\), where the concentration is given as 12.0 mol/L. This means there are 12 moles of \(\text{HCl}\) per liter of solution. Chemical concentration is a critical concept in chemistry because it helps us understand the strength of a solution. The higher the concentration, the more solute is present in the solution. To find the molality, we'll use this concentration in further steps. Knowing how to convert between different units of concentration is essential for solving problems in chemistry.

The density of a solution is a measure of its mass per unit volume. In this problem, the density is given as 1.18 g/mL. This means that each milliliter (mL) of the solution weighs 1.18 grams. Density is a physical property that relates to how compact a substance is. To calculate the mass of a given volume of the solution, like 1 liter (1000 mL), we multiply the density by the volume.
Using the formula: \[ \text{Mass of solution} = \text{Density} \times \text{Volume} \] we find the mass of the solution to be 1180 grams. This step is important as it provides the total mass we need for further calculations.

Molality is a way to express the concentration of a solution. It is defined as the number of moles of solute per kilogram of solvent. Unlike molarity, molality does not depend on the temperature or pressure of the solution since it's based on mass. To find molality, we first need the moles of solute (12 moles of \(\text{HCl}\)) and the mass of the solvent (water) in kilograms.
From the problem:
\(\text{Mass of water} = \text{Mass of solution} - \text{Mass of HCl} = 1180 \text{ grams} - 437.52 \text{ grams} = 742.48 \text{ grams}\).
Converting grams to kilograms:
\(\text{Mass of water (kg)} = 742.48 \text{ grams} \times \frac{1 \text{ kg}}{1000 \text{ grams}} = 0.74248 \text{kg}\). Finally, using the molality formula:
\(\text{molality} = \frac{12.0 \text{ mol}}{0.74248 \text{ kg}} = 16.16 \text{ mol/kg} \).

The molar mass of a substance is the mass of one mole of that substance. It is usually expressed in grams per mole (g/mol). For hydrochloric acid \((\text{HCl})\), the molar mass is given as 36.46 g/mol. This value is crucial for converting between moles and grams of \(\text{HCl}\).
To calculate the mass of \(\text{HCl}\) in 1 liter of solution:
\(\text{Mass of HCl} = \text{Moles of HCl} \times \text{Molar mass of HCl} = 12.0 \text{ mol} \times 36.46 \text{ g/mol} = 437.52 \text{ grams} \).
Understanding molar mass is essential for working with chemical quantities since it connects the macroscopic scale (grams) with the microscopic scale (moles). This step ensures we have the accurate mass of \(\text{HCl}\) to proceed with the molality calculation.