Problem 17 - Chemistry and Chemical Reactivity

Question

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

Step-by-Step Solution

Answer

Correct formulas: (b) KF, (c) Ga₂O₃, (d) MgS. Corrected formula for (a) is AlCl₃.

Step 1: Understanding Ionic Compounds

Ionic compounds consist of a combination of cations (positively charged ions) and anions (negatively charged ions). The formula of an ionic compound reflects the smallest whole-number ratio of the ions involved, ensuring overall charge neutrality.

Step 2: Check Formula for AlCl₂

The aluminum cation ext{Al}^{3+} and the chloride anion ext{Cl}^{-} combine to form aluminum chloride. Since each Al cation has a charge of +3 and each Cl anion has a charge of -1, three Cl anions are needed to balance the charge of one Al cation: ext{AlCl}_{3}. Thus, ext{AlCl}_{2} is incorrect, and the correct formula is ext{AlCl}_{3}.

Step 3: Check Formula for Ga₂O₃

The gallium cation ext{Ga}^{3+} and the oxide anion ext{O}^{2-} combine to form gallium oxide. Since gallium has a +3 charge and oxygen has a -2 charge, two Ga cations and three O anions are needed for charge balance, resulting in ext{Ga}_{2} ext{O}_{3}. Therefore, ext{Ga}_{2} ext{O}_{3} is the correct formula.

Step 4: Check Formula for KF₂

The potassium cation ext{K}^{+} and the fluoride anion ext{F}^{-} combine to form potassium fluoride. Since both ions are singly charged, they combine in a 1:1 ratio, which makes the correct formula ext{KF}. Hence, ext{KF}_{2} is incorrect, and the correct formula is ext{KF}.

Step 5: Check Formula for MgS

The magnesium cation ext{Mg}^{2+} and the sulfide anion ext{S}^{2-} combine to form magnesium sulfide. Each ion has a charge of ±2, so they combine in a 1:1 ratio for charge balance, resulting in the correct formula ext{MgS}. Therefore, ext{MgS} is correct.

Key Concepts

Charge Neutrality

In ionic compounds, the principle of charge neutrality is vital. This principle ensures that the overall charge of an ionic compound is zero. Meaning, the total positive charge from the cations must equal the total negative charge from the anions.

• For example, if you have a cation with a charge of +2, you'll need either two anions of -1 or one anion of -2 to balance the positive charge.
• The need for balance means ionic compounds are stable when the charges cancel out completely.

Charge neutrality is the reason why formulas like \(\mathrm{AlCl}_2\) are incorrect. This formula does not reflect equal total charges, since \(\mathrm{Al}^{3+}\) needs three \(\mathrm{Cl}^{-}\) ions to balance the positive charge, making \(\mathrm{AlCl}_3\) the correct formula.

Cations and Anions

Understanding the role of cations and anions in chemistry is key. Cations are positively charged ions, while anions are negatively charged.

• Cations are formed when an atom loses electrons, and the most common cations include \(\mathrm{Na}^+\), \(\mathrm{Ca}^{2+}\), and \(\mathrm{Al}^{3+}\).
• Anions, on the other hand, form when an atom gains electrons, with examples such as \(\mathrm{Cl}^-\), \(\mathrm{O}^{2-}\), and \(\mathrm{S}^{2-}\).

The correct formulas for ionic compounds depend on these ions; in the compound \(\mathrm{MgS}\), \(\mathrm{Mg}^{2+}\) (a cation) pairs with \(\mathrm{S}^{2-}\) (an anion) to achieve a neutral charge.

Chemical Formulas

Chemical formulas convey crucial information about the composition of a compound. They show the types of atoms and their proportions.

• In an ionic compound, the formula is written with the cation first followed by the anion.
• The subscripts in a chemical formula indicate the number of each type of ion needed to maintain charge neutrality.

For instance, the formula \(\mathrm{Ga}_2\mathrm{O}_3\) indicates two gallium ions (\(\mathrm{Ga}^{3+}\)) and three oxide ions (\(\mathrm{O}^{2-}\)) that combine to form a balanced ionic compound. The subscripts reveal how many ions are present.

Balancing Charges

Balancing charges in ionic compounds involves adjusting the ratio of ions so that the charges cancel out and the compound is stable.

• The key is to ensure that the total positive charge from the cations equals the total negative charge from the anions.
• Formulating a compound involves identifying the charges of the ions involved and determining the correct ratio.

Consider \(\mathrm{KF}\): the potassium ion \(\mathrm{K}^+\) balances perfectly with the fluoride ion \(\mathrm{F}^-\), since both have charges of \(+1\) and \(-1\) respectively. If the formula were \(\mathrm{KF}_2\), the charges would not balance, making it incorrect.