Problem 97 - Chemistry The Central Science

Question

Predict which member of each pair produces the more acidic aqueous solution: (a) \(\mathrm{K}^{+}\) or \(\mathrm{Cu}^{2+},(\mathbf{b}) \mathrm{Fe}^{2+}\) or \(\mathrm{Fe}^{3+}\) , (c) \(\mathrm{Al}^{3+}\) or \(\mathrm{Ga}^{3+}\) .

Step-by-Step Solution

Answer

In conclusion, the more acidic cations in each pair are: (a) \(\mathrm{Cu^{2+}}\) is more acidic than \(\mathrm{K^{+}}\), (b) \(\mathrm{Fe^{3+}}\) is more acidic than \(\mathrm{Fe^{2+}}\), and (c) \(\mathrm{Al^{3+}}\) is more acidic than \(\mathrm{Ga^{3+}}\).

Step 1: Analyze the charge of the ions

All else being equal, cations with a higher positive charge are generally stronger Lewis acids (more acidic) because of their greater attraction for electrons. In this case: a) \(\mathrm{K}^{+}\) has a +1 charge, while \(\mathrm{Cu}^{2+}\) has a +2 charge. b) Both ions are from the same element \(\mathrm{Fe}\), but they have different charges: \(\mathrm{Fe}^{2+}\) (2+ charge) and \(\mathrm{Fe}^{3+}\) (3+ charge).

Step 2: Analyze the size of the ions

The size of the ion also plays a role in acidity. Generally, smaller ions are more acidic than larger ions with the same charge. This is because smaller ions have a higher charge density, which allows them to attract electrons more easily. We will now analyze the size of the ions in part (c): c) \(\mathrm{Al}^{3+}\) and \(\mathrm{Ga}^{3+}\) are both from Group 13 on the periodic table, but \(\mathrm{Al}\) is above \(\mathrm{Ga}\) in the same group. As we move down a group in the periodic table, the atomic size increases, making \(\mathrm{Al}^{3+}\) smaller than \(\mathrm{Ga}^{3+}\).

Step 3: Comparing the acidity of the cations

Using the information from Steps 1 and 2, we can now determine which cation in each pair is more acidic: a) \(\mathrm{Cu^{2+}}\) is more acidic than \(\mathrm{K^{+}}\) because it has a higher positive charge (+2) compared to \(\mathrm{K^{+} }\)(+1). b) \(\mathrm{Fe^{3+}}\) is more acidic than \(\mathrm{Fe^{2+}}\) because it has a higher positive charge (+3) compared to \(\mathrm{Fe^{2+}}\) (+2). c) \(\mathrm{Al^{3+}}\) is more acidic than \(\mathrm{Ga^{3+}}\) because it is smaller in size as it's higher in the periodic table (group 13) than \(\mathrm{Ga}\). In conclusion, the more acidic cations in each pair are \(\mathrm{Cu^{2+}}\), \(\mathrm{Fe^{3+}}\), and \(\mathrm{Al^{3+}}\).

Key Concepts

Lewis Acids

Lewis acids are chemical entities that can accept electron pairs. They play a central role in chemistry because they act as the "electron-pair receivers" in reactions. Cations, particularly those with higher positive charges, typically function as Lewis acids. This is because their positive charge creates an attraction to electron pairs, facilitating reactions. When comparing cations, those with higher charges are often more potent Lewis acids as they exhibit greater electron pair acceptance.
For instance:

• Cu²⁺ as opposed to K⁺: With its +2 charge, Cu²⁺ accepts electron pairs more efficiently when compared to the +1 charge of K⁺, making it a stronger Lewis acid.
• Fe³⁺ over Fe²⁺: The additional positive charge in Fe³⁺ makes it even more likely to attract and accept electron pairs, classifying it as a stronger Lewis acid.

Appreciating the behavior of Lewis acids and their interactions enhances a student's understanding of acid-base chemistry and reaction mechanisms.

Ionic Charge and Acidity

The ionic charge of a cation significantly influences its acidity. Generally, a higher positive charge on a cation results in a stronger acid. This is because a higher charge means a greater electric field around the ion, strengthening its ability to attract electron pairs.
Here's a breakdown of how ionic charge affects acidity:

• Cations with a higher charge have increased acidity. The +2 charge on Cu²⁺ over the +1 on K⁺ makes Cu²⁺ the more acidic ion in this pair.
• Similarly, between Fe²⁺ and Fe³⁺, the higher charge of +3 in Fe³⁺ leads to greater acidity because it more strongly pulls in electron pairs.

Thus, understanding the concept of ionic charge is vital in predicting the acidic behavior of cations in solutions.

Periodic Table Trends

The periodic table offers invaluable clues about the acidity of different cations, specifically through understanding size trends among elements. Generally, for cations of the same charge, smaller ions are more acidic due to higher charge density. This refers to how concentrated the positive charge is over a smaller surface area, enhancing its ability to attract electrons.
Let's see how periodic trends help us understand acidity:

• The size trend within a group: As you move down a group in the periodic table, the atomic size increases. Therefore, Al³⁺ is smaller than Ga³⁺, making it more acidic due to higher charge density.

The placement of an element in the periodic table directly affects its size and, consequently, its acidity, serving as a guide to predict behaviors of cations in solution.