Question

Which of the following are correct formulas for ionic compounds? For those that are not, give the correct formula. (a) \(\mathrm{AlCl}_{2}\) (b) \(\mathrm{KF}_{2}\) (c) \(\mathrm{Ga}_{2} \mathrm{O}_{3}\) (d) \(\mathrm{MgS}\)

Short answer

(a) Incorrect: \(\mathrm{AlCl}_{3}\); (b) Incorrect: \(\mathrm{KF}\); (c) Correct; (d) Correct.

Step-by-step solution

Understanding Ionic Compounds

Ionic compounds are formed by the combination of cations (positive ions) and anions (negative ions). Each compound must be electrically neutral, meaning the total positive charge must equal the total negative charge. We will analyze each formula to ensure this neutrality.

Analyzing \\( \mathrm{AlCl}_{2} \\\\)

For aluminum chloride, aluminum (\(\mathrm{Al}\)) forms a +3 charge, and chloride (\(\mathrm{Cl}\)) forms a -1 charge. To balance the charges: \( \mathrm{Al} \) requires 3 \( \mathrm{Cl}^- \) ions to make the compound neutral: Correct formula: \( \mathrm{AlCl}_{3} \).

Analyzing \\( \mathrm{KF}_{2} \\\\)

Potassium (\(\mathrm{K}\)) forms a +1 charge, and fluoride (\(\mathrm{F}\)) forms a -1 charge. The correct ratio is one \(\mathrm{K}^+\) to one \(\mathrm{F}^-\), not two \(\mathrm{F}^-\). Correct formula: \( \mathrm{KF} \).

Analyzing \\( \mathrm{Ga}_{2} \mathrm{O}_{3} \\\\)

Gallium (\(\mathrm{Ga}\)) typically forms a +3 charge, while oxide (\(\mathrm{O}\)) forms a -2 charge. The given formula \(\mathrm{Ga}_{2} \mathrm{O}_{3}\) contains two \(\mathrm{Ga}^{3+}\) ions (total +6) and three \(\mathrm{O}^{2-}\) ions (total -6), correctly balancing the total charges.The formula \(\mathrm{Ga}_{2} \mathrm{O}_{3}\) is correct.

Analyzing \\( \mathrm{MgS} \\\\)

Magnesium (\(\mathrm{Mg}\)) forms a +2 charge, and sulfur (\(\mathrm{S}\)) also forms a -2 charge. The charges are already balanced with one \(\mathrm{Mg}^{2+}\) and one \(\mathrm{S}^{2-}\).The formula \(\mathrm{MgS}\) is correct.

Key concepts

Chemical Formulas

Chemical formulas are representations of the composition of chemical compounds. For ionic compounds, these formulas are derived from the charges of the ions involved.
Ions are atoms or molecules that have a net electric charge due to the loss or gain of one or more electrons.
In ionic compounds, the cation is always written first, followed by the anion.

• For example, in aluminum chloride (\( \mathrm{AlCl}_{3} \)), aluminum (\( \mathrm{Al}^{3+} \)) is the cation and chloride (\( \mathrm{Cl}^{-} \)) is the anion.
• The subscript numbers indicate how many of each ion are required to achieve a neutral compound.

Chemical formulas must reflect the simplest ratio of ions needed to balance these charges.

Charge Balance

Charge balance in ionic compounds ensures that the total positive and negative charges are equal, resulting in an electrically neutral compound.
This step is crucial to correctly formatting chemical formulas.
If we consider stepwise improvements in approaching charge balance:

• Identify the charge of the cation and the anion involved.
• Determine the ratio of ions needed to achieve neutrality.
• Re-examine possible adjustments if initial analysis shows imbalance.
• Use these ratios to construct the chemical formula, ensuring whole numbers.

For instance, in potassium fluoride, recognizing the +1 charge for potassium and \(-1\) for fluoride guides us to form \( \mathrm{KF} \).

Cations and Anions

Cations and anions, as integral components of ionic compounds, play distinct roles based on their electrical charges.
Cations are ions with a positive charge, formed when an atom loses electrons.
Anions carry a negative charge, resulting from the gain of electrons.

• Typical cations include:
  • Magnesium (\( \mathrm{Mg}^{2+} \))
  • Potassium (\( \mathrm{K}^{+} \))
  • Aluminum (\( \mathrm{Al}^{3+} \))
• Common anions include:
  • Chloride (\( \mathrm{Cl}^{-} \))
  • Fluoride (\( \mathrm{F}^{-} \))
  • Oxide (\( \mathrm{O}^{2-} \))

Understanding the propensity of atoms to form certain charges is vital in predicting the resulting ionic compounds.

Electroneutrality

Electroneutrality is a principle stating that, in stable ionic compounds, the sum of the positive charges must equal the sum of the negative charges.
This balance is essential for the stability of the compound.
Let's break down how electroneutrality guides the creation of formulas:

• For the compound to remain stable, no excess of positive or negative charge should exist.
• This means careful adjustment of the number of cations and anions until neutrality is reached.
• Electroneutrality often requires multiples of ions, like in \( \mathrm{AlCl}_{3} \) where three chloride ions balance one aluminum ion.
• A correct understanding ensures that a formula like \( \mathrm{MgS} \) holds, reflecting accurate charges offset.

Maintaining electroneutrality minimizes internal charge repulsions and maximizes stability.