Question

Write formulas for the ionic compounds formed from (a) \(\mathrm{K}^{+}\) and nitrate ion, (b) \(\mathrm{Ca}^{2+}\) and acetate ion, (c) ammonium ion and \(\mathrm{Cl}^{-},\) (d) \(\mathrm{Fe}^{3+}\) and carbonate ion, and (e) \(\mathrm{Mg}^{2+}\) and phosphate ion.

Short answer

The formulas for the compounds are (a) KNO3, (b) Ca(C2H3O2)2, (c) NH4Cl, (d) Fe2(CO3)3, and (e) Mg3(PO4)2.

Step-by-step solution

Determine the Charge Balance

The first step in writing the formula for an ionic compound is to ensure that the total positive charge from the cations balances the total negative charge from the anions.

Write the Formulas for the Ionic Compounds

Use the charge of each ion to determine the ratio in which the cations and anions combine to produce a neutral compound. It may be necessary to use more than one of a particular ion to balance the charges.

Use Subscripts to Indicate the Number of Ions

After determining the ratio, use subscripts to show the number of each ion present in the compound. If the ratio is 1:1, no subscript is needed.

Final Formulas

(a) For \(\mathrm{K}^{+}\) and nitrate ion (NO3-), the formula is KNO3. (b) For \(\mathrm{Ca}^{2+}\) and acetate ion (C2H3O2-), the formula is Ca(C2H3O2)2. (c) For ammonium ion (NH4+) and \(\mathrm{Cl}^{-}\), the formula is NH4Cl. (d) For \(\mathrm{Fe}^{3+}\) and carbonate ion (CO3^2-), the formula is Fe2(CO3)3. (e) For \(\mathrm{Mg}^{2+}\) and phosphate ion (PO4^3-), the formula is Mg3(PO4)2.

Key concepts

Charge Balance in Ionic Compounds

Understanding charge balance is pivotal when learning about ionic compounds. An ionic compound is formed from the electrostatic attraction between cations (positively charged ions) and anions (negatively charged ions). For the compound to be stable, the total positive charge must equal the total negative charge. This is sometimes referred to as the 'principle of electrical neutrality'.

For example, to form a neutral compound with potassium (K⁺) and nitrate (NO₃^-), since both ions have a charge of 1 but opposite signs, they combine in a one-to-one ratio to create KNO₃ without the need for additional ions to balance the charge. But for calcium (Ca²⁺) and acetate (C₂H₃O₂^-), you need two acetate ions for every calcium ion to achieve charge balance, resulting in the formula Ca(C₂H₃O₂)₂.

Remember, the goal is to reach the net charge of zero, which is the hallmark of a stable ionic compound.

Determining Ion Ratios

When it comes to writing ionic compound formulas, deciding how many of each ion is needed is key. The ratio is based upon the charges of the ions involved. An easy method is to 'crisscross' the charges of the ions and use them as subscripts for the other ion, omitting the charge sign and reducing to the lowest terms if necessary.

For instance, with magnesium (Mg²⁺) and phosphate (PO₄^3-), you would cross the charges to get Mg_{3(PO4)2, which reflects that three magnesium ions are needed for every two phosphate ions to balance the 2+ and 3- charges. It's essentially a puzzle where you want the sum of positive and negative charges to be zero, and figuring out the ion ratios is how you solve this puzzle.}

Using Subscripts in Chemical Formulas

Once the ion ratios are established, subscripts come into play. Subscripts in chemical formulas indicate how many atoms or ions of a certain element are present in the compound. It's important not to confuse them with coefficients - subscripts refer to the number of atoms within one molecule, while coefficients tell us how many molecules are present.

In the compound Fe₂(CO₃)₃, for example, the subscript '2' next to Fe tells you that there are two iron ions for every three carbonate ions (indicated by the subscript '3' next to CO₃). When no subscript is written, such as in NH₄Cl for ammonium chloride, it's understood to be '1'. This lack of a subscript corresponds to a 1:1 ratio of ions, a simple indication that no more than one of each ion is required to balance the charges. Subscripts are a critical feature of chemical formulas, giving you a count of each ion in the crystal lattice of the ionic compound.