Commercially available concentrated hydrochloric acid contains \(38 \%\) \(\mathrm{HCl}\) by mass. (a) What is the molarity of this solution? The density is \(1.19 \mathrm{~g} \mathrm{~mL}^{-1}\). (b) What volume of concentrated \(\mathrm{HCl}\) is required to make \(1.00\) litre of \(0.10 \mathrm{M} \mathrm{HCl} ?\)

When talking about the concentration of solutions, we refer to the amount of substance, known as the solute, dissolved in a specific volume of solvent. It is essential for students to comprehend how to express concentration since it is a foundation of stoichiometry in chemistry.

There are various ways to quantify concentration, but a common one is molarity. Molarity, denoted as M, is defined as the number of moles of solute per liter of solution. It's calculated by dividing the number of moles of solute by the volume of the solution in liters.

To apply this in our exercise, we first find the mass of HCl in one liter of solution from its density, then calculate the moles of HCl using its molar mass, and finally divide by the solution's volume to determine the molarity. It's like a recipe, where you measure the ingredients (moles of HCl) and then figure out how much soup (solution) you can make with them. This understanding is critical not only for academic purposes but also for practical applications in laboratories and industries.

Stoichiometry in chemistry is like the mathematics of molecules. It involves calculations that relate the quantities of reactants and products in a chemical reaction. Students need to grasp this concept to handle reactions and understand the relationships within. A fundamental stoichiometric principle is the conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction.

For stoichiometry, molar relationships are key; knowing the number of moles of each reactant and product involved. The balanced chemical equation provides the molar ratio needed to perform calculations. In the context of our exercise, we used the stoichiometry of the HCl solution to calculate the mass, moles, and then molarity, showcasing how stoichiometry is applied beyond just reactions but also to solution preparation.

The dilution equation is a vital concept in chemistry for decreasing the concentration of a solution without altering the amount of solute present. This concept helps in preparing solutions of desired concentrations and is based on the principle that the amount of solute remains the same before and after dilution.

The dilution equation is represented as M₁V₁ = M₂V₂, where M₁ is the initial molarity, V₁ is the volume of the starting solution, M₂ is the final molarity, and V₂ is the final volume. For our exercise, we used this equation to find the volume of concentrated HCl needed to make a more diluted solution. Remember to think of it as watering down paint; you're spreading the color (solute) thinner over a larger volume but the total amount of color remains the same.