Problem 10 - Chemistry The Science in Context

Question

Indicate the substance that contains the smallest cation. (a) \(\mathrm{BaCl}_{2} ;\) (b) \(\mathrm{Al}_{2} \mathrm{O}_{3} ;\) (c) \(\mathrm{Mg}_{3} \mathrm{N}_{2} ;\) (d) SrS

Step-by-Step Solution

Answer

Answer: Al2O3 contains the smallest cation.

Step 1: Identify the Cations in Each Substance

In each given substance, the metal element forms the cation. For the given substances, the cations are: (a) BaCl2 - Ba²⁺ (b) Al2O3 - Al³⁺ (c) Mg3N2 - Mg²⁺ (d) SrS - Sr²⁺ Now that we have identified the cations, we will determine their position in the periodic table to understand their relative sizes.

Step 2: Finding the Positions of the Elements in the Periodic Table

Let's now find the positions of these elements in the periodic table: (a) Ba (Barium) - Group 2, Period 6 (located in the alkaline earth metals group) (b) Al (Aluminium) - Group 13, Period 3 (located in the p-block elements group) (c) Mg (Magnesium) - Group 2, Period 3 (also located in the alkaline earth metals group) (d) Sr (Strontium) - Group 2, Period 5 (also located in the alkaline earth metals group)

Step 3: Comparing the Sizes of Cations Based on Group and Period

As we move from top to bottom in a group and from left to right in a period, we can generally notice a trend in the size of the elements: (a) Ba²⁺ is in Group 2, Period 6 - with higher period number, it will be larger than other elements in Group 2. (b) Al³⁺ is in Group 13, Period 3 - with higher group number, it will be smaller than other elements in Period 3. (c) Mg²⁺ is in Group 2, Period 3 - it will be larger than Al³⁺ within Period 3 but smaller than Ba²⁺ and Sr²⁺ in Group 2. (d) Sr²⁺ is in Group 2, Period 5 - it will be smaller than Ba²⁺ but larger than Mg²⁺ within Group 2.

Step 4: Identifying the Substance with the Smallest Cation

Based on the comparisons made in step 3, we can conclude that Al³⁺ is the smallest cation among the given substances. Therefore, the substance which contains the smallest cation is Al2O3. The answer is (b) \(\mathrm{Al}_{2}\mathrm{O}_{3}\).

Key Concepts

metal cations in compounds

When dealing with chemical compounds, cations are positively charged ions usually formed by metals. In a compound, the metal atoms lose one or more electrons to form cations. Consider the given exercise, where we have compounds like

• BaCl₂ (Barium Chloride)
• Al₂O₃ (Aluminum Oxide)
• Mg₃N₂ (Magnesium Nitride)
• SrS (Strontium Sulfide)

In each case, the metal element forms the cation. For instance, in BaCl₂, barium (Ba) loses two electrons to become Ba²⁺. Similarly, magnesium (Mg) in Mg₃N₂ becomes Mg²⁺ after losing two electrons.

Each of these metal cations, like Al³⁺ in Al₂O₃, plays a significant role in determining the chemical and physical properties of the compound. The ability of these metal atoms to lose electrons and form cations makes them key players in forming stable ionic compounds. These cations also influence the compound's melting point, solubility, and electrical conductivity.

periodic table trends

The periodic table helps us understand the characteristics of elements as they form cations. Elements' positions determine both their size and reactivity.

• As you move from left to right across a period, atoms generally become smaller.
• When you move down a group, the atom size increases due to the addition of more electron shells.

In understanding the size of cations like Ba²⁺, Al³⁺, Mg²⁺, and Sr²⁺, these trends are crucial. Barium (Ba) and Strontium (Sr) are in Group 2 and become larger due to their increased electron shells compared to magnesium (Mg), which is also in Group 2 but higher up on the table.

Aluminum (Al), found in Group 13, forms a smaller than magnesium cation within the same period, as moving from Group 2 to Group 13 effectively decreases the size of the cations, even though there are more electrons.

cation size comparison

Comparing cation sizes involves understanding how metal ions change as they form ions. Because cations lose electrons, they generally decrease in size compared to their neutral atom form due to a decrease in electron-to-electron repulsion. Several factors influence cation size:

• Cation charge: Higher positive charges (more electrons lost) often result in smaller cations, like Al³⁺ being smaller than Mg²⁺ due to its greater positive charge.
• Electron shells: More shells mean larger cations. Barium (Ba²⁺), with more shells than magnesium (Mg²⁺), therefore is larger.

When comparing the cations Ba²⁺, Al³⁺, Mg²⁺, and Sr²⁺, Al³⁺ comes out as the smallest. This is due to it having the highest positive charge, as well as its position on the periodic table, which places it among elements with fewer electron shells. Hence, Al₂O₃ is the substance with the smallest cation among the given options due to these size constraints of Al³⁺.