Question

Complete the table by filling in the formula for the ionic compound formed by each pair of cations and anions, as shown for the first pair. $$ \begin{array}{|l|c|c|c|c|} \hline \text { Ion } & \mathrm{K}^{+} & \mathrm{NH}_{4}{ }^{+} & \mathrm{Mg}^{2+} & \mathrm{Fe}^{3+} \\ \hline \mathrm{Cl}^{-} & \mathrm{KCl} & & & \\ \hline \mathrm{OH}^{-} & & & & \\ \hline \mathrm{CO}_{3}^{2-} & & & & \\ \hline \mathrm{PO}_{4}{ }^{3-} & & & & \\ \hline \end{array} $$

Short answer

The completed table of ionic compounds: $$ \begin{array}{|l|c|c|c|c|} \hline \text { Ion } & \mathrm{K}^{+} & \mathrm{NH}_{4}{ }^{+} & \mathrm{Mg}^{2+} & \mathrm{Fe}^{3+} \\\ \hline \mathrm{Cl}^{-} & \mathrm{KCl} & \mathrm{NH_4Cl} & \mathrm{MgCl}_2 & \mathrm{FeCl}_3 \\\ \hline \mathrm{OH}^{-} & \mathrm{KOH} & \mathrm{NH_4OH} & \mathrm{Mg(OH)}_2 & \mathrm{Fe(OH)}_3 \\\ \hline \mathrm{CO}_{3}^{2-} & \mathrm{K}_2\mathrm{CO}_3 & \mathrm{(NH}_4\mathrm{)}_2\mathrm{CO}_3 & \mathrm{MgCO}_3 & \mathrm{Fe}_2(\mathrm{CO}_3\mathrm{)}_3 \\\ \hline \mathrm{PO}_{4}{ }^{3-} & \mathrm{K}_3\mathrm{PO}_4 & \mathrm{(NH}_4\mathrm{)}_3\mathrm{PO}_4 & \mathrm{Mg}_3(\mathrm{PO}_4\mathrm{)}_2 & \mathrm{FePO}_4 \\\ \hline \end{array} $$

Step-by-step solution

Identify the charges of the given ions

The charges of the cations and anions are given in the table. Let's list them for reference: - \(K^+\) has a charge of +1 - \(NH_4^+\) has a charge of +1 - \(Mg^{2+}\) has a charge of +2 - \(Fe^{3+}\) has a charge of +3 - \(Cl^-\) has a charge of -1 - \(OH^-\) has a charge of -1 - \(CO_3^{2-}\) has a charge of -2 - \(PO_4^{3-}\) has a charge of -3

Combine the cations and anions to form ionic compounds

Now, let's combine the cations and anions from the table, making sure their charges cancel out: a) \(\text{K}^+\) and \(\text{Cl}^-\) form \(\text{KCl}\) (already in the table). b) \(\text{K}^+\) and \(\text{OH}^-\) form \(\text{KOH}\). c) \(\text{K}^+\) and \(\text{CO}_3^{2-}\) form \(\text{K}_2\text{CO}_3\), since we need two potassium ions to balance the charge of one carbonate ion. d) \(\text{K}^+\) and \(\text{PO}_4^{3-}\) form \(\text{K}_3\text{PO}_4\), since we need three potassium ions to balance the charge of one phosphate ion. e) \(\text{NH}_4^+\) and \(\text{Cl}^-\) form \(\text{NH}_4\text{Cl}\). f) \(\text{NH}_4^+\) and \(\text{OH}^-\) form \(\text{NH}_4\text{OH}\). g) \(\text{NH}_4^+\) and \(\text{CO}_3^{2-}\) form \(\text{(NH}_4\text{)}_2\text{CO}_3\), since we need two ammonium ions to balance the charge of one carbonate ion. h) \(\text{NH}_4^+\) and \(\text{PO}_4^{3-}\) form \(\text{(NH}_4\text{)}_3\text{PO}_4\), since we need three ammonium ions to balance the charge of one phosphate ion. i) \(\text{Mg}^{2+}\) and \(\text{Cl}^-\) form \(\text{MgCl}_2\), since we need two chloride ions to balance the charge of one magnesium ion. j) \(\text{Mg}^{2+}\) and \(\text{OH}^-\) form \(\text{Mg(OH)}_2\), since we need two hydroxide ions to balance the charge of one magnesium ion. k) \(\text{Mg}^{2+}\) and \(\text{CO}_3^{2-}\) form \(\text{MgCO}_3\), as their charges are already balanced. l) \(\text{Mg}^{2+}\) and \(\text{PO}_4^{3-}\) form \(\text{Mg}_3(\text{PO}_4\text{)}_2\), as we need three magnesium ions and two phosphate ions to balance the charges. m) \(\text{Fe}^{3+}\) and \(\text{Cl}^-\) form \(\text{FeCl}_3\), since we need three chloride ions to balance the charge of one iron(III) ion. n) \(\text{Fe}^{3+}\) and \(\text{OH}^-\) form \(\text{Fe(OH)}_3\), since we need three hydroxide ions to balance the charge of one iron(III) ion. o) \(\text{Fe}^{3+}\) and \(\text{CO}_3^{2-}\) form \(\text{Fe}_2(\text{CO}_3\text{)}_3\), as we need two iron(III) ions and three carbonate ions to balance the charges. p) \(\text{Fe}^{3+}\) and \(\text{PO}_4^{3-}\) form \(\text{FePO}_4\), as their charges are already balanced. Finally, the completed table looks like this: $$ \begin{array}{|l|c|c|c|c|} \hline \text { Ion } & \mathrm{K}^{+} & \mathrm{NH}_{4}{ }^{+} & \mathrm{Mg}^{2+} & \mathrm{Fe}^{3+} \\\ \hline \mathrm{Cl}^{-} & \mathrm{KCl} & \mathrm{NH_4Cl} & \mathrm{MgCl}_2 & \mathrm{FeCl}_3 \\\ \hline \mathrm{OH}^{-} & \mathrm{KOH} & \mathrm{NH_4OH} & \mathrm{Mg(OH)}_2 & \mathrm{Fe(OH)}_3 \\\ \hline \mathrm{CO}_{3}^{2-} & \mathrm{K}_2\mathrm{CO}_3 & \mathrm{(NH}_4\mathrm{)}_2\mathrm{CO}_3 & \mathrm{MgCO}_3 & \mathrm{Fe}_2(\mathrm{CO}_3\mathrm{)}_3 \\\ \hline \mathrm{PO}_{4}{ }^{3-} & \mathrm{K}_3\mathrm{PO}_4 & \mathrm{(NH}_4\mathrm{)}_3\mathrm{PO}_4 & \mathrm{Mg}_3(\mathrm{PO}_4\mathrm{)}_2 & \mathrm{FePO}_4 \\\ \hline \end{array} $$

Key concepts

Chemical Formulas

Chemical formulas represent the elemental composition of a substance where symbols denote the elements and subscripts show the number of atoms of each element in the compound. In the context of ionic compounds, a chemical formula conveys crucial information about the ions involved and their ratios.

Take, for example, the formula \( \text{KCl} \), which describes a compound composed of potassium (K) and chlorine (Cl), each present in a 1:1 ratio. When dealing with ionic compounds, the formula tells us not just which ions are present but also their proportions necessary to achieve charge neutrality. Hence, understanding how to write and interpret chemical formulas is essential for students to grasp the composition of different ionic compounds.

Cation-Anion Pairing

Cation-anion pairing is integral to forming ionic compounds. Ions are atoms or molecules that carry a charge, with cations being positively charged and anions negatively charged. Ionic compounds arise from the electrostatic attraction between these oppositely charged ions.

Getting to grips with cation-anion pairing involves recognizing that ionic compounds are electrically neutral, so the total positive charge from cations must balance the total negative charge from anions. For instance, when pairing \( \text{NH}_4^+ \) with \( \text{Cl}^- \), each with a charge of +1 and -1 respectively, they combine in a 1:1 ratio to form ammonium chloride \( \text{NH}_4\text{Cl} \). This concept is the cornerstone of understanding how atoms bond to form stable ionic structures.

Charge Balance

Charge balance is the principle that the total charge in an ionic compound must be zero, meaning the sum of positive charges from cations equals the sum of negative charges from anions. This principle guides the formation of chemical formulas for ionic compounds.

In the exercise example, to create a formula for a compound with \( \text{Mg}^{2+} \) and \( \text{CO}_3^{2-} \), we notice that one divalent magnesium ion can neutralize the charge of one divalent carbonate ion, leading to the formula \( \text{MgCO}_3 \). However, for a trivalent ion like \( \text{Fe}^{3+} \) and a trivalent ion like \( \text{PO}_4^{3-} \), a direct 1:1 ratio applies, which gives us the compound \( \text{FePO}_4 \). This balance of charge is not only fundamental to the stability of the compound but also to understanding the stoichiometry of reactions involving ionic species.