Question

Determine the molarity of a \(40.0 \%\) solution of \(\mathrm{HCl}\) which has a density of \(1.20 \mathrm{~g} / \mathrm{ml}\).

Short answer

The molarity of the 40.0% HCl solution with a density of 1.20 g/ml is 13.15 M.

Step-by-step solution

1. Convert percentage concentration to mass concentration

Given the percentage concentration of HCl as 40.0%, we can convert it to mass concentration by multiplying the density of the solution by the percentage: \( mass\ concentration = \)(percentage concentration) × (density of the solution)

2. Calculate the mass of solute in 1 liter of solution

First, we need to convert the density from g/ml to g/L. Since there are 1000 ml in 1 liter: \( density = 1.20\ g/ml * 1000\ ml/L = 1200\ g/L\) Then, we will multiply the density by the mass concentration to find the mass of HCl in 1 liter of solution: \( mass\ of\ HCl = mass\ concentration * density = 1200\ g/L * 0.4 = 480\ g/L\)

3. Calculate the moles of solute in 1 liter of solution

To find the moles of HCl in 1 liter of solution, we'll divide the mass of HCl by its molar mass. The molar mass of HCl is approximately 1 g/mol for hydrogen and 35.5 g/mol for chlorine, totaling 36.5 g/mol: \( moles\ of\ HCl = \frac{mass\ of\ HCl}{molar\ mass\ of\ HCl} = \frac{480\ g}{36.5\ g/mol} = 13.15\ mol\)

4. Calculate the molarity of the solution

To find the molarity of the solution, we'll divide the moles of HCl by the volume of the solution in liters: \( molarity\ of\ HCl = \frac{moles\ of\ HCl}{volume\ of\ solution} = \frac{13.15\ mol}{1\ L} = 13.15\ M\) The molarity of the 40.0% HCl solution with a density of 1.20 g/ml is 13.15 M.

Key concepts

Solution Concentration

Understanding the concentration of a solution is essential when working in chemistry. The concentration can be expressed in various ways, but one common method is using molarity. Molarity is defined as the number of moles of solute per liter of solution. It provides a measure of the solute concentration in terms of the amount of substance in a given volume. To calculate molarity, you need to know the number of moles of solute and the volume of the solution. In the context of the exercise, the student had to first determine the mass concentration of hydrochloric acid (HCl), which was given as a percentage. The step-by-step solution involved converting that percentage into a mass using the density of the solution and then the mass into moles.

It's important to recognize that the density plays a crucial role here, as it converts the volume of the solution into mass, which is then used along with the percentage concentration to find the mass of HCl. Once you have the mass and the molar mass of the solute (HCl, in this case), the solution's molarity is just a step away. This is useful not only for academic exercises but also for practical applications in laboratory settings where precise chemical reactions are crucial.

Molar Mass

The molar mass is a fundamental concept in chemistry, relating to both stoichiometry and solution concentration calculations. It represents the mass of one mole of a substance and is expressed in grams per mole (g/mol). To find molar mass, sum the atomic masses of all the atoms in a molecule of the substance. For example, the molar mass of hydrochloric acid (HCl) is calculated by adding the atomic masses of hydrogen (H) and chlorine (Cl), which are approximately 1 g/mol and 35.5 g/mol, respectively, giving us 36.5 g/mol for HCl.

Understanding molar mass allows students to convert between the mass of a substance and the amount in moles, a crucial step in solving molarity problems like the one in our textbook exercise. This conversion is vital when dealing with reactants and products in chemical reactions, making it an indispensable tool in acid-base chemistry and other areas of chemical study.

Acid-Base Chemistry

Acid-base chemistry is a branch of chemical science that studies the properties, behavior, and reactions of acids and bases. It plays a significant role in various chemical processes, from industrial manufacturing to biological systems. In an academic setting, understanding the concepts of acid-base chemistry allows students to predict the outcomes of reactions and understand the behavior of substances in different solutions.

The molarity of an acid or base is particularly relevant in reactions where neutralization or pH changes are involved. Acids like HCl dissociate in water to produce hydronium ions (H3O+), which contribute to the acid's properties. When we talk about the concentration of acids or bases in a solution, we're often referring to their molar concentration, which indicates the strength of the acid or base in the solution. Clearly understanding molarity, molar mass, and their applications in acid-base chemistry enables students to grasp more complex chemical concepts and carry out quantitative analyses of chemical reactions.