Question

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

Short answer

In a 2.0 L, 3.0 M HCl solution, there are 6 moles of HCl, which is a strong acid that dissociates completely in water, forming more H⁺ ions. In a 2.0 L, 3.0 M HC₂H₃O₂ solution, there are also 6 moles of solute, but with acetic acid (vinegar), which only partially dissociates, producing fewer H⁺ ions and making it less acidic than the HCl solution.

Step-by-step solution

Calculate the moles of solute in each solution

Since the molarity of a solution is defined as the moles of solute per liter of solution, we can calculate the moles of solute in a given volume by multiplying the molarity by the volume. For the 2.0 L of 3.0 M HCl solution, we will perform the following calculation: Moles of HCl = Molarity × Volume Moles of HCl = 3.0 M × 2.0 L Moles of HCl = \(6.0 \ mol \) Similarly, for the 2.0 L of 3.0 M HC₂H₃O₂ solution, we will perform the following calculation: Moles of HC₂H₃O₂ = Molarity × Volume Moles of HC₂H₃O₂ = 3.0 M × 2.0 L Moles of HC₂H₃O₂ = \(6.0 \ mol \)

Compare the composition of the two solutions

Now that we've calculated the moles of solute in each solution, let's compare the composition of the two solutions: 1. Both solutions have the same volume (2.0 L) and molarity (3.0 M), which means they have the same number of moles of solute in them (6 moles). 2. The main difference between the two solutions is the type of solute present in them. In the HCl solution, the solute is HCl, which is a strong acid that dissociates completely in water, forming H⁺ ions (protons) and Cl⁻ ions. Conversely, in the HC₂H₃O₂ solution, the solute is acetic acid (vinegar), which is a weak acid that partially dissociates in water, forming H⁺ ions (protons) and acetate ions (CH₃COO⁻). This means that the HCl solution has more H⁺ ions and is therefore more acidic than the HC₂H₃O₂ solution. To summarize, 2.0 L of a 3.0 M HCl solution contains 6 moles of HCl and is more acidic, while 2.0 L of a 3.0 M HC₂H₃O₂ solution contains 6 moles of HC₂H₃O₂ and is less acidic.

Key concepts

Moles of Solute

Understanding the concept of moles of solute is essential in chemistry, especially when preparing solutions. In essence, a mole is a unit that measures the amount of substance. It corresponds to Avogadro's number, which is approximately \(6.022 \times 10^{23}\).

When we talk about the moles of solute in a solution, we are referring to the number of moles of the dissolved substance. For example, say we have a 3.0 M (molar) hydrochloric acid (HCl) solution. If we have 2.0 liters of this solution, calculating the moles of solute, which in this case is HCl, involves multiplying the molarity by the volume of the solution:

• Moles of HCl = Molarity \(\times\) Volume
• Moles of HCl = 3.0 M \(\times\) 2.0 L
• Moles of HCl = \(6.0 \ mol\)

This calculation helps us understand that there are 6 moles of HCl dissolved in 2 liters of a 3.0 M HCl solution. It's a straightforward but critical step for preparing solutions with exact concentrations in chemical laboratories.

Acid Dissociation in Water

Acid dissociation in water is a reaction in which an acid releases hydrogen ions, \(H^+\), into the solution, increasing its acidity. The measure of an acid's ability to donate a hydrogen ion is called its dissociation constant, \(K_a\).

Complete vs. Partial Dissociation

When strong acids like hydrochloric acid (HCl) dissolve in water, they dissociate completely into their constituent ions. This means that every molecule of HCl splits into a hydrogen ion \(H^+\) (often referred to as a proton) and a chloride ion \(Cl^-\).

• HCl → \(H^+\) + \(Cl^-\)

On the other hand, weak acids like acetic acid (HC₂H₃O₂) dissociate partially. In water, some acetic acid molecules donate their hydrogen ions, while others remain intact.

• HC₂H₃O₂ \(\rightleftharpoons\) \(H^+\) + CH₃COO⁻

This incomplete dissociation is represented with an equilibrium arrow, indicating a reversible reaction. As a result, a solution of acetic acid will have fewer free hydrogen ions compared to an equal concentration of hydrochloric acid, making it less acidic.

Comparison of Acid Strength

Acid strength is a key concept in chemistry that reflects the extent of acid dissociation in water. Strong acids, like HCl, are known for their almost complete dissociation, which leads to a higher concentration of \(H^+\) ions. In contrast, weak acids, such as acetic acid (HC₂H₃O₂), only partially dissociate, resulting in fewer \(H^+\) ions.

From a practical point of view, when comparing the strength of acids, we look at their dissociation constants and the pH of their solutions:

• A strong acid like HCl has a large dissociation constant and results in a low pH when dissolved in water, indicating high acidity.
• A weak acid like HC₂H₃O₂ has a smaller dissociation constant and a higher pH, denoting lower acidity.

Understanding the differences in acid strength is vital, as it influences reaction rates, equilibrium positions, and buffering capacities in various chemical processes. A typical 3.0 M solution of HCl, due to its complete dissociation, will be more acidic and possess a lower pH than a 3.0 M solution of HC₂H₃O₂, which has more undissociated molecules.