Question

Predict which member of each pair produces the more acidic aqueous solution: (a) \(\mathrm{K}^{4}\) or \(\mathrm{Cu}^{2+}\), (b) \(\mathrm{Fe}^{2+}\) or \(\mathrm{Fe}^{3+}\), (c) \(\mathrm{Al}^{3+}\) or \(\mathrm{Ga}^{3+}\). Explain.

Short answer

In each pair, the ions that produce more acidic aqueous solutions are: (a) \(K^{4+}\), (b) \(Fe^{3+}\), and (c) \(Al^{3+}\). This is due to their higher charges (or smaller atomic radius in the case of Al^3+ and Ga^3+), which make them more likely to donate protons to the surrounding water molecules, resulting in more acidic solutions.

Step-by-step solution

Identify the solution's acidity based on the ion's charge

An acidic solution has a pH below 7. The higher the positive charge of an ion, the more the ion will attract water molecules and the more likely it will be to donate protons to the surrounding water molecules. Therefore, a higher charge means a more acidic solution.

Compare the charges and sizes of the ions

In each pair, we need to compare the charges and sizes of the ions to determine which ion is more likely to donate a proton and produce an acidic solution. Let's look at each pair individually. (a) K^4+ and Cu^2+: • K^4+ has a charge of +4; • Cu^2+ has a charge of +2. (b) Fe^2+ and Fe^3+: • Fe^2+ has a charge of +2; • Fe^3+ has a charge of +3. (c) Al^3+ and Ga^3+: • Both Al^3+ and Ga^3+ have a charge of +3. • Al is in the third period and Ga is in the fourth period of the periodic table, which means that Ga^3+ has a larger atomic radius than Al^3+.

Determine which ion is more likely to donate a proton

Now, let's determine which ion in each pair is more likely to produce a more acidic solution by donating a proton. (a) K^4+ has a higher charge than Cu^2+, so it is more likely to produce a more acidic solution because it will be more likely to donate protons to the surrounding water molecules. (b) Fe^3+ has a higher charge than Fe^2+, so it will produce a more acidic solution. (c) Both Al^3+ and Ga^3+ have the same charge. However, Al^3+ has a smaller atomic radius than Ga^3+, which means that its positive charge is more concentrated and will attract more water molecules. This concentration will make it more likely to donate protons to the surrounding water molecules, making it a more acidic solution. In conclusion, the members of each pair that produce more acidic aqueous solutions are: (a) K^4+; (b) Fe^3+; (c) Al^3+.

Key concepts

pH Level

The concept of pH is a central topic in chemistry, particularly when discussing the acidity of solutions. The pH scale measures how acidic or basic a solution is, and it ranges from 0 to 14. A pH below 7 indicates an acidic solution, 7 is neutral, and above 7 is basic. The lower the pH value, the higher the acidity.

When ions are dissolved in water, they can affect the pH of the solution by either donating protons (hydrogen ions, H+) to the water, which makes the solution more acidic, or accepting protons, making it more basic. This process is fundamental to understanding the differences in acidity among various solutions. In the given exercise, we analyze different ions and predict which ones would yield a more acidic solution by focusing on their propensity to donate protons to water.

The pH level is influenced by the ion’s charge; higher positive charges usually suggest stronger attraction to water molecules and a greater ability to donate protons, resulting in a more acidic solution. This relationship between ion charge and pH level is crucial for students to grasp, as it underpins many reactions and behaviors in aqueous chemistry.

Ion Charge

Ion charge is pivotal in determining the acidity of aqueous solutions. Ions are atoms or molecules that have lost or gained electrons, thus acquiring a charge. Positively charged ions, called cations, and negatively charged ions, called anions, have different potentials to impact the pH of a solution.

In the context of the exercise, we are concerned with cations and their charges. The general rule of thumb is that the greater the positive charge of the ion, the stronger its interaction with water molecules will be. Due to an increased attraction, these ions will more readily donate protons (H+) to water, thus increasing the hydrogen ion concentration and lowering the pH, which indicates a more acidic solution.

This concept is vital for solving problems that involve predicting acidity in aqueous solutions. For example, comparing the charges of K^4+ and Cu^2+, we infer that K^4+ will more significantly influence the acidity of the solution due to its higher positive charge. Understanding how ion charge affects solution acidity is essential for students who are studying aqueous chemistry and acid-base reactions.

Atomic Radius

Atomic radius refers to the size of an atom, typically measured from the nucleus to the outer boundary of the electron cloud. In any consideration of solution acidity, particularly when comparing two ions with identical charges, the atomic radius becomes an important factor.

Returning to the exercise, when comparing Al^3+ and Ga^3+, we note that they have the same charge but different atomic radii because they are elements from different periods on the periodic table. A smaller atomic radius means that the ion's charge density is higher, resulting in a stronger electrostatic pull on surrounding water molecules. Therefore, an ion with a smaller atomic radius and the same charge as a larger ion will more likely attract water closely enough to donate protons, leading to a more acidic solution.

If an ion has a smaller atomic radius, its ability to impact the pH level increases. This is especially true when we compare ion pairs with similar charges – the ion with the smaller atomic radius will usually produce the more acidic solution. This concept helps explain why Al^3+, with a smaller atomic radius compared to Ga^3+, is predicted to form a more acidic solution in an aqueous environment.