Question

A typical solution used in general chemistry laboratories is \(3.0 M\) HCl. Describe, in detail, the composition of \(2.0 \mathrm{~L}\) of a \(3.0 \mathrm{M}\) \(\mathrm{HCl}\) solution. How would \(2.0 \mathrm{~L}\) of a \(3.0 \mathrm{M} \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) solution differ from the same quantity of the \(\mathrm{HCl}\) solution?

Short answer

In short, both the \(2.0 \mathrm{~L}\) of the \(3.0 \mathrm{~M}\) \(\mathrm{HCl}\) solution and the \(2.0 \mathrm{~L}\) of the \(3.0 \mathrm{~M} \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) solution have the same volume, molarity, and contain \(6.0 \mathrm{~mol}\) of solute. However, they differ in their composition; the \(\mathrm{HCl}\) solution contains hydrogen ions (\(\mathrm{H^{+}}\)) and chloride ions (\(\mathrm{Cl^{-}}\)), while the \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) solution contains hydrogen ions (\(\mathrm{H^{+}}\)) and acetate ions (\(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}^{-}_{2}\)). Moreover, \(\mathrm{HCl}\) is a strong acid that completely dissociates in water, while \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) is a weak acid that partially dissociates in water, leading to a lower pH value for the \(\mathrm{HCl}\) solution compared to the \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) solution.

Step-by-step solution

Calculate moles of solute

To calculate the number of moles of solute (n) in each solution, we will use the formula: Molarity (M) = \(\frac{\text{moles of solute}}{\text{Liters of solution}}\) For the \(3.0 \mathrm{~M}\) \(\mathrm{HCl}\) solution: n(HCl) = Molarity × Volume of solution n(HCl) = \(3.0 \mathrm{~M}\) × \(2.0 \mathrm{~L}\) = \(6.0\mathrm{~mol}\) For the \(3.0 \mathrm{~M}\) \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) solution: n(HC2H3O2) = Molarity × Volume of solution n(HC2H3O2) = \(3.0 \mathrm{~M}\) × \(2.0 \mathrm{~L}\) = \(6.0 \mathrm{~mol}\)

Describe the composition of each solution

Now that we know the number of moles of solute in each solution, we can describe the composition: The \(2.0 \mathrm{~L}\) of the \(3.0 \mathrm{~M}\) \(\mathrm{HCl}\) solution contains \(6.0 \mathrm{~mol}\) of \(\mathrm{HCl}\). In this solution, each molecule of \(\mathrm{HCl}\) dissociates into hydrogen ions (\(\mathrm{H^{+}}\)) and chloride ions (\(\mathrm{Cl^{-}}\)) in water. The \(2.0 \mathrm{~L}\) of the \(3.0 \mathrm{~M} \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) solution contains \(6.0 \mathrm{~mol}\) of \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\). In this solution, each molecule of \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) dissociates into hydrogen ions (\(\mathrm{H^{+}}\)) and acetate ions (\(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}^{-}_{2}\)) in water.

Compare the two solutions

From the information obtained in Steps 1 and 2, both solutions have the same volume and molarity, and they both contain \(6.0 \mathrm{~mol}\) of solute. However, the composition of the solute in each solution differs. While the \(\mathrm{HCl}\) solution contains hydrogen ions (H+) and chloride ions (Cl-), the \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) solution contains hydrogen ions (H+) and acetate ions (C2H3O2-). Another key difference is that \(\mathrm{HCl}\) is a strong acid, meaning it will completely dissociate in water, while \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) is a weak acid, meaning it will only partially dissociate in water. Therefore, the \(3.0 \mathrm{~M}\) \(\mathrm{HCl}\) solution will exhibit a higher concentration of hydrogen ions and thus a lower pH value compared to the \(3.0 \mathrm{~M} \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) solution.

Key concepts

Solution Composition

Understanding the composition of a solution is fundamental in chemistry. In the context of the exercise, the composition refers to the types and amounts of substances present in a mixture. A solution is made up of two parts: the solute, which is the substance dissolved, and the solvent, which is the substance in which the solute is dissolved, typically water in chemical solutions.

When considering a solution of hydrochloric acid (HCl), we are presented with a solution where HCl acts as the solute and water is the solvent. The given concentration of HCl is 3.0 molar (M), which translates to 3.0 moles of HCl in every liter of solution. Thus, 2.0 liters of this solution contain a total of 6.0 moles of HCl. Solute composition is critical for predicting the properties of the solution, which includes conductivity, reactivity, and pH.

Moles of Solute

The quantity of a substance in a solution is often measured in moles, a standard unit in chemistry for counting particles. The mole is connected to the molecular weight of a substance and offers a bridge between the microscopic world of atoms and molecules and the macroscopic world of grams and liters.

For our exercise, molarity calculation uses the formula: M = \(\frac{n}{V}\), where M is the molarity, n is the number of moles of solute, and V is the volume of solution in liters. In a 3.0 M solution of acetic acid (HC2H3O2), for example, determining the number of moles of solute involves multiplying the molarity by the volume of the solution. With a volume of 2.0 L, the solution contains 6.0 moles of acetic acid.

Acid Dissociation

Acid dissociation is a critical concept that determines the behavior and strength of an acid in a solution. It describes the separation of an acid into ions when dissolved in water. A strong acid, such as HCl, dissociates completely in water, releasing a predictable and high concentration of hydrogen ions (H+). This complete dissociation contributes to the acid's high reactivity and corrosiveness.

On the contrary, a weak acid like acetic acid (HC2H3O2) only partly dissociates in water, leading to a lower concentration of hydrogen ions. This partial dissociation is due to the acid's lower tendency to release H+ ions, which affects various properties of the solution, including its electrical conductivity and pH. Notably, the extent of acid dissociation is often represented by the acid dissociation constant (Ka), which is a key value when studying acid-base reactions.

pH Value

The pH value is an essential property of a solution, providing a measure of acidity or basicity. The pH is logarithmically based and inversely related to the concentration of hydrogen ions in a solution: a high concentration of hydrogen ions corresponds to a low pH value, making the solution more acidic, whereas a low concentration of hydrogen ions corresponds to a high pH value, indicating a more basic or alkaline solution.

For our study on HCl and HC2H3O2 solutions, the difference in dissociation leads to a significant pH difference. Since the HCl solution completely dissociates to release more H+ ions, it will have a lower pH value compared to the weakly dissociating acetic acid solution. Therefore, the pH value serves as an indirect indicator of molecule dissociation and acid strength, which is quintessential in the understanding of chemical behaviors of acids and bases.