Question

Predict the chemical formulas of the compounds formed by (b) \(\mathrm{Fe}^{3+}\) and the following pairs of ions: (a) \(\mathrm{Cr}^{3+}\) and \(\mathrm{Br}^{-}\), \(\mathrm{O}^{2-},(\mathrm{c}) \mathrm{Hg}_{2}^{2+}\) and \(\mathrm{CO}_{3}^{2-},(\mathrm{d}) \mathrm{Ca}^{2+}\) and \(\mathrm{ClO}_{3}^{-},(\mathrm{e}) \mathrm{NH}_{4}^{+}\) and \(\mathrm{PO}_{4}{ }^{3-}\).

Short answer

The chemical formulas of the compounds formed by the given pairs of ions are: (a) \(\mathrm{CrBr_3}\) (b) \(\mathrm{Fe_2O_3}\) (c) \(\mathrm{Hg_2CO_3}\) (d) \(\mathrm{Ca(ClO_3)_2}\) (e) \(\mathrm{(NH_4)_3PO_4}\)

Step-by-step solution

Pair (a): \(\mathrm{Cr}^{3+}\) and \(\mathrm{Br}^{-}\)

Since both Cr and Br have equal but opposite charges, they will combine in a 1:1 ratio. The chemical formula for the compound formed by \(\mathrm{Cr}^{3+}\) and \(\mathrm{Br}^{-}\) is \(\mathrm{CrBr_3}\).

Pair (b): \(\mathrm{Fe}^{3+}\) and \(\mathrm{O}^{2-}\)

In this pair, since the charges on Fe and O ions are not equal, we will need to find the least common multiple (LCM) of their absolute charge values, which is 6. Thus, the ratio of \(\mathrm{Fe}^{3+}\) to \(\mathrm{O}^{2-}\) should be 2:3 to achieve charge balance. The chemical formula for the compound formed is \(\mathrm{Fe_2O_3}\).

Pair (c): \(\mathrm{Hg}_{2}^{2+}\) and \(\mathrm{CO}_{3}^{2-}\)

In this pair, the charges on \(\mathrm{Hg}_{2}^{2+}\) and \(\mathrm{CO}_3^{2-}\) are equal but opposite. Therefore, they will combine in a 1:1 ratio. The chemical formula for the compound formed is \(\mathrm{Hg_2CO_3}\).

Pair (d): \(\mathrm{Ca}^{2+}\) and\(\mathrm{ClO}_{3}^{-}\)

Here, the positive charge on \(\mathrm{Ca}^{2+}\) is twice the negative charge on \(\mathrm{ClO}_3^{-}\). Therefore, we need two \(\mathrm{ClO}_3^{-}\) ions to balance the positive charge of one \(\mathrm{Ca}^{2+}\) ion. The chemical formula for the compound formed will be \(\mathrm{Ca(ClO_3)_2}\).

Pair (e): \(\mathrm{NH}_{4}^{+}\) and \(\mathrm{PO}_{4}^{3-}\)

In this case, the positive charge on \(\mathrm{NH}_4^+\) is three times smaller than the negative charge on \(\mathrm{PO}_4^{3-}\). Hence, we require three \(\mathrm{NH}_4^+\) ions to balance the negative charge of one \(\mathrm{PO}_4^{3-}\) ion. The chemical formula for the compound formed is \(\mathrm{(NH_4)_3PO_4}\).

Key concepts

Ion Charges

When discussing ion charges, we're looking at the electrical charge that an ion carries. Ions are atoms or molecules that have gained or lost one or more electrons, resulting in a net positive or negative charge.

• A positive charge, indicated by a plus sign (e.g., \(\mathrm{Fe}^{3+}\)), means an ion has lost electrons.
• A negative charge, indicated by a minus sign (e.g., \(\mathrm{O}^{2-}\)), means an ion has gained electrons.

Understanding the charge of ions is crucial in predicting how different ions will combine to form chemical compounds. The charges must balance out to form stable compounds, which leads us into the concept of ionic bonding.

Chemical Compounds

Chemical compounds are substances formed when two or more elements are chemically bonded together. Each compound has a specific formula that shows the types and numbers of atoms present.

• The formula gives a clear indication of the proportion of atoms of each element involved in the compound.
• For example, \(\mathrm{CrBr_3}\) indicates one chromium ion and three bromine ions are part of the compound.

Identifying the correct chemical compounds involves understanding the charges of each ion and ensuring they combine in a way that their overall electric charge is neutral. This charge balance is vital for the formation of stable compounds.

Ionic Bonding

Ionic bonding is the process through which ions with opposite charges attract each other to form a stable compound.

• This type of bond is typically formed between metals and nonmetals.
• Metals, such as \(\mathrm{Fe}^{3+}\) or \(\mathrm{Ca}^{2+}\), generally form positive ions by losing electrons.
• Nonmetals form negative ions, as seen with \(\mathrm{Br}^{-}\) or \(\mathrm{O}^{2-}\), by gaining electrons.

The key to ionic bonding is the transfer of electrons from one atom to another, resulting in a neutral compound. These interactions are crucial in predicting the structure and formula of ionic compounds.

Charge Balance

In chemical compounds formed through ionic bonding, maintaining charge balance is essential for stability. Charge balance means that the total positive charge from the cations (positively charged ions) equals the total negative charge from the anions (negatively charged ions).

• This ensures that the compound has no net charge.
• For instance, in \(\mathrm{Fe_2O_3}\), two \(\mathrm{Fe}^{3+}\) ions have a total charge of +6, which balances the total -6 charge from three \(\mathrm{O}^{2-}\) ions.
• Another example is \(\mathrm{(NH_4)_3PO_4}\), where three \(\mathrm{NH}_4^+\) ions' total charge of +3 equals the -3 charge of one \(\mathrm{PO}_4^{3-}\) ion.

Ensuring charge balance helps us accurately determine the correct chemical formula for a compound.

Compound Prediction

Predicting chemical compounds with accuracy is a mix of understanding ion charges, evaluating potential ionic bond pairings, and maintaining charge balance.

• Start by identifying the charges of each ion involved.
• Determine the ratio of ions needed to achieve zero net charge.
• Use the common multiple method for ions of different charges to find how many of each ion are needed.
• Write the chemical formula indicating these ratios, ensuring it's the simplest expression of their proportions.

By following these steps, such as in finding \(\mathrm{Ca(ClO_3)_2}\), where one \(\mathrm{Ca}^{2+}\) ion balances with two \(\mathrm{ClO}_{3}^{-}\) ions, you'll be able to predict compounds effectively and accurately.