A solution is made by dissolving \(18.4 \mathrm{~g}\) of \(\mathrm{HCl}\) in \(662 \mathrm{~mL}\) of water. Calculate the \(\mathrm{pH}\) of the solution. (Assume that the volume remains constant.)

Molarity is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute divided by the volume of the solution in liters (L). The formula for calculating molarity (M) is \[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \].

When solving chemistry problems, understanding molarity is fundamental because it relates the amount of the substance dissolved to the total volume of the solution, allowing us to deduce how concentrated or dilute a solution is. In our example, by dividing the moles of hydrochloric acid (HCl) by the volume of the solution, we can calculate the molarity, which is essential for finding the pH level of the solution.

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is a physical property that is used to convert the mass of a substance to the amount of substance in moles. The molar mass of a compound is calculated by summing up the standard atomic weights of the atoms in its chemical formula.

In this exercise, the molar mass of HCl (\(36.5 \text{ g/mol}\)) provides the conversion factor from the given mass of HCl (\(18.4 \text{ g}\)) to moles. Knowing the molar mass is crucial for accurately determining the number of moles, which plays an integral part in calculating molarity, and ultimately, the pH of the solution.

The pH of a solution is a logarithmic measure of the hydrogen ion concentration (\[H^+\]). The mathematical expression for pH is \[ \text{pH} = -\log[\text{H}^+] \], where the logarithm used is the base-10 logarithm. Logarithms help in converting multiplicative relationships into additive ones, making it easier to handle a wide range of ion concentrations.

pH is crucial in determining whether a solution is acidic or basic. A lower pH value indicates a higher concentration of hydrogen ions, meaning the solution is more acidic. For instance, figuring out the negative log of the molarity of HCl allows us to turn the concentration value into a pH value that easily categorizes the acidity of the solution, as demonstrated in our problem.