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Chapter 16: Problem 97

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

Short Answer

Expert verified
(a) Cu虏鈦�, (b) Fe鲁鈦�, (c) Al鲁鈦� produce more acidic solutions.

Step by step solution

01

Understanding Acidity of Aqueous Solutions

The acidity of an aqueous solution containing metal ions is related to the metal ion's ability to polarize and weaken O-H bonds in water molecules, thereby facilitating the release of H鈦� ions. Generally, metal ions with higher charge and smaller radius have a greater polarizing effect and lead to a more acidic solution.
02

Comparing K鈦� and Cu虏鈦� for Acidity

K鈦� is a Group 1 element with a +1 charge and a relatively larger ionic radius. Conversely, Cu虏鈦� has a +2 charge and a smaller ionic radius. The higher charge and smaller size of Cu虏鈦� enable it to polarize water molecules more effectively than K鈦�, thus Cu虏鈦� produces a more acidic aqueous solution.
03

Comparing Fe虏鈦� and Fe鲁鈦� for Acidity

Fe虏鈦� and Fe鲁鈦� are oxidation states of iron. Fe鲁鈦� has a higher charge than Fe虏鈦�, which increases its polarizing power on water molecules. Despite having similar ionic sizes, the higher charge of Fe鲁鈦� makes it more efficient in generating acidity in an aqueous solution.
04

Comparing Al鲁鈦� and Ga鲁鈦� for Acidity

Al鲁鈦� and Ga鲁鈦� both have a +3 charge. Though they have similar charges, the position of the elements in the periodic table indicates that Al鲁鈦� has a smaller atomic radius than Ga鲁鈦�. The smaller size of Al鲁鈦� results in a stronger polarization of water molecules, leading to a more acidic solution.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Metal Ion Polarization
Metal ion polarization refers to the ability of a metal ion to distort the cloud of electrons in surrounding molecules, such as water. This distortion weakens the bonds in the molecule, like the O-H bond in water, and often results in the release of hydrogen ions (H鈦�), making the solution more acidic. When we compare metal ions:
  • Their charge and size play significant roles in how much they can polarize other molecules.
  • Higher charged ions have a greater electric field and thus a stronger polarizing effect.
  • Smaller ions can get closer to other molecules, enhancing their polarizing ability.
To summarize, a metal ion that is small and highly charged can make an aqueous solution very acidic by strongly polarizing the water molecules deteriorating the O-H bonds.
Charge Density
Charge density is an important concept for understanding the behavior of metal ions in solutions. It is defined as the ratio of the charge of an ion to its volume. When predicting the acidity of the solutions, it can help us identify which ions are more likely to polarize water molecules.
  • Higher charge density implies a higher concentration of charge over a smaller area.
  • This results in a stronger electric field around the ion, which can attract and distort the electronic structures of nearby molecules.
  • In essence, ions with high charge density, typically due to high charge and small size, are excellent at polarizing water molecules, leading to increased acidity.
Thus, charge density offers a clear explanation as to why certain metal ions are more successful in creating acidic environments in their aqueous solutions.
Oxidation States
The oxidation state of a metal ion refers to the effective charge of the ion within a compound. It is directly linked to how many electrons the metal has lost or gained through bonding. In the context of metal ions in aqueous solutions:
  • Higher oxidation states mean the metal ion has given up more electrons and usually has a higher positive charge.
  • This increased charge often results in a smaller ionic radius due to greater attraction between the remaining electrons and the nucleus.
  • Consequently, higher oxidation states correlate with increased metal ion polarization power, leading to greater acidity.
Understanding oxidation states helps us predict the tendencies of metal ions to create acidic solutions by looking at their ability to alter the electronic environment of surrounding water molecules.

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Most popular questions from this chapter

Calculate \(\left[\mathrm{OH}^{-}\right]\) and \(\mathrm{pH}\) for each of the following strong base solutions: (a) \(0.182 \mathrm{M} \mathrm{KOH},(\mathbf{b}) 3.165 \mathrm{~g}\) of \(\mathrm{KOH}\) in 500.0 \(\mathrm{mL}\) of solution, (c) \(10.0 \mathrm{~mL}\) of \(0.0105 \mathrm{M} \mathrm{Ca}(\mathrm{OH})_{2}\) diluted to \(500.0 \mathrm{~mL},\) (d) a solution formed by mixing \(20.0 \mathrm{~mL}\) of 0.015 \(M \mathrm{Ba}(\mathrm{OH})_{2}\) with \(40.0 \mathrm{~mL}\) of \(8.2 \times 10^{-3} \mathrm{M} \mathrm{NaOH}\).

An unknown salt is either \(\mathrm{KBr}, \mathrm{NH}_{4} \mathrm{Cl}, \mathrm{KCN},\) or \(\mathrm{K}_{2} \mathrm{CO}_{3} .\) If a \(0.100 M\) solution of the salt is neutral, what is the identity of the salt?

Write the chemical equation and the \(K_{b}\) expression for the reaction of each of the following bases with water: (a) propylamine, \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{NH}_{2} ;\) (b) monohydrogen phosphate ion, \(\mathrm{HPO}_{4}^{2-} ;(\mathbf{c})\) benzoate ion, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2}^{-}\)

Which member of each pair produces the more acidic aqueous solution: (a) \(\mathrm{ZnBr}_{2}\) or \(\mathrm{CdCl}_{2},\) (b) \(\mathrm{CuCl}\) or \(\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}\), (c) \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) or \(\mathrm{NiBr}_{2} ?\)

Calculate the molar concentration of \(\mathrm{OH}^{-}\) in a \(0.050 \mathrm{M}\) solution of ethylamine \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2} ; K_{b}=6.4 \times 10^{-4}\right) .\) Calculate the \(\mathrm{pH}\) of this solution.
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