Question

For the following pairs of ions, use the concept that a chemical compound must have a net charge of zero to predict the formula of the simplest compound that the ions are most likely to form. a. \(\mathrm{Fe}^{3+}\) and \(\mathrm{P}^{3-}\) b. \(\mathrm{Fe}^{3+}\) and \(\mathrm{S}^{2-}\) c. \(\mathrm{Fe}^{3+}\) and \(\mathrm{Cl}^{-}\) d. \(\mathrm{Mg}^{2+}\) and \(\mathrm{Cl}^{-}\) e. \(\mathrm{Mg}^{2+}\) and \(\mathrm{O}^{2-}\) f. \(\mathrm{Mg}^{2+}\) and \(\mathrm{N}^{3-}\) g. \(\mathrm{Na}^{+}\) and \(\mathrm{P}^{3-}\) h. \(\mathrm{Na}^{+}\) and \(\mathrm{S}^{2-}\)

Short answer

a. \(\mathrm{FeP}\) b. \(\mathrm{Fe}_{2}\mathrm{S}_{3}\) c. \(\mathrm{FeCl}_{3}\) d. \(\mathrm{MgCl}_{2}\) e. \(\mathrm{MgO}\) f. \(\mathrm{Mg}_{3}\mathrm{N}_{2}\) g. \(\mathrm{Na}_{3}\mathrm{P}\) h. \(\mathrm{Na}_{2}\mathrm{S}\)

Step-by-step solution

Since both ions have the same magnitude of charge, but opposite in sign, one iron ion will balance the charge of one phosphorus ion. Therefore, the compound formula will be \(\mathrm{FeP}\). b. \(\mathrm{Fe}^{3+}\) and \(\mathrm{S}^{2-}\) #Step 1: Find the least common multiple of the charges#

In order to balance the charges, we need to find the least common multiple (LCM) between the magnitudes of the charges (3 and 2). The LCM of these charges is 6. #Step 2: Determine the number of ions needed to balance charges#

In order to balance 6 units of positive charge from \(\mathrm{Fe}^{3+}\), we'll need two \(\mathrm{Fe}^{3+}\) ions and three \(\mathrm{S}^{2-}\) ions. #Step 3: Write the compound formula#

The compound formula will be \(\mathrm{Fe}_{2}\mathrm{S}_{3}\). c. \(\mathrm{Fe}^{3+}\) and \(\mathrm{Cl}^{-}\) #Step 1: Balance charges for cation and anion#

In order to balance the +3 charge of one \(\mathrm{Fe}^{3+}\) ion, we'll need three \(\mathrm{Cl}^{-}\) ions. #Step 2: Write the compound formula#

The resulting compound formula is \(\mathrm{FeCl}_{3}\). d. \(\mathrm{Mg}^{2+}\) and \(\mathrm{Cl}^{-}\) #Step 1: Balance charges for cation and anion#

One \(\mathrm{Mg}^{2+}\) ion will need two \(\mathrm{Cl}^{-}\) ions to balance the charge. #Step 2: Write the compound formula#

The resulting compound formula is \(\mathrm{MgCl}_{2}\). e. \(\mathrm{Mg}^{2+}\) and \(\mathrm{O}^{2-}\) #Step 1: Balance charges#

Since both ions have the same magnitude of charge, but opposite in sign, one magnesium ion will balance the charge of one oxygen ion. Therefore, the compound formula will be \(\mathrm{MgO}\). f. \(\mathrm{Mg}^{2+}\) and \(\mathrm{N}^{3-}\) #Step 1: Find the least common multiple of the charges#

The LCM of the magnitudes of these charges (2 and 3) is 6. #Step 2: Determine the number of ions needed to balance charges#

To balance 6 units of positive charge, we will need three \(\mathrm{Mg}^{2+}\) ions and two \(\mathrm{N}^{3-}\) ions. #Step 3: Write the compound formula#

The compound formula will be \(\mathrm{Mg}_{3}\mathrm{N}_{2}\). g. \(\mathrm{Na}^{+}\) and \(\mathrm{P}^{3-}\) #Step 1: Balance charges for cation and anion#

In order to balance the -3 charge of one \(\mathrm{P}^{3-}\) ion, we'll need three \(\mathrm{Na}^{+}\) ions. #Step 2: Write the compound formula#

The resulting compound formula is \(\mathrm{Na}_{3}\mathrm{P}\). h. \(\mathrm{Na}^{+}\) and \(\mathrm{S}^{2-}\) #Step 1: Balance charges for cation and anion#

In order to balance the -2 charge of one \(\mathrm{S}^{2-}\) ion, we'll need two \(\mathrm{Na}^{+}\) ions. #Step 2: Write the compound formula#

The resulting compound formula is \(\mathrm{Na}_{2}\mathrm{S}\).

Key concepts

Ionic Compounds

Ionic compounds are formed when atoms transfer electrons between each other, resulting in ions. These ions have oppositely charged attractions. For example, when a metal atom transfers electrons to a non-metal atom, the metal becomes positively charged (a cation), and the non-metal becomes negatively charged (an anion).
This transfer creates a bond through electrostatic interaction, holding the ions together in a compound. The classic examples include sodium chloride (NaCl), where sodium transfers one electron to chlorine, resulting in a stable ionic compound.
With two ions of opposite charges, ionic compounds always aim to balance these charges to reach a net neutral state. This means the total positive charge and negative charge must cancel each other out. Knowing how to write the chemical formula requires understanding the charges of the given ions.

Charge Balance

For an ionic compound to be stable, the total positive charges must equal the total negative charges. This is essential because a neutral compound has no net charge. Imagine a seesaw that must be perfectly balanced for the compound to be stable.
If you are given ions like \(\mathrm{Fe}^{3+}\) and \(\mathrm{Cl}^{-}\), the question is: How do they balance? Each \(\mathrm{Fe}^{3+}\) ion provides a +3 charge, while each \(\mathrm{Cl}^{-}\) provides a -1 charge. To balance, you need three chloride ions for every iron ion, resulting in the formula \(\mathrm{FeCl}_{3}\).This balance is fundamental in predicting the correct formula for ionic compounds.

Valency

Valency is the combining capacity of an element, often determined by the number of electrons an atom can donate, accept, or share. In ionic compounds, valency corresponds to the ion's charge. For instance, magnesium (\(\mathrm{Mg}^{2+}\)) has a valency of +2, meaning it can lose two electrons.
Understanding valency is crucial to combining the right number of atoms to form a neutral compound. Say, for example, you have \(\mathrm{Mg}^{2+}\) and \(\mathrm{Cl}^{-}\); knowing their valencies helps you predict the compound \(\mathrm{MgCl}_{2}\). Here, the valency (or charge) tells you that two chloride ions are needed to balance one magnesium ion for a stable compound.

Least Common Multiple

The least common multiple (LCM) is a useful math tool, particularly when dealing with ionic compounds. It helps determine how many of each ion are needed to balance the charges in cases where the ions have different charges.
Let's consider \(\mathrm{Fe}^{3+}\) and \(\mathrm{S}^{2-}\). The charges, +3 and -2, don't immediately cancel out.Here, the LCM of 3 and 2 is 6, meaning a total charge of 6 from both ions is needed.So, two \(\mathrm{Fe}^{3+}\) ions provide +6 charge, and three \(\mathrm{S}^{2-}\) ions provide -6 charge. Thus, the formula \(\mathrm{Fe}_{2}\mathrm{S}_{3}\) balances the charges perfectly, making it electrically neutral.Mastery of LCM ensures precision when writing the chemical formulas for ionic compounds.