Question

Write formula units by combining the cations and anions in each of the following pairs: (a) \(\mathrm{Sr}^{2+}\) and \(\mathrm{As}^{3-}\) (b) \(\mathrm{Ra}^{2+}\) and \(\mathrm{O}^{2-}\) (c) \(\mathrm{Al}^{3+}\) and \(\mathrm{CO}_{3}^{2-}\) (d) \(\mathrm{Cd}^{2+}\) and \(\mathrm{OH}^{-}\)

Short answer

(a) \( \mathrm{Sr}_3\mathrm{As}_2 \), (b) \( \mathrm{RaO} \), (c) \( \mathrm{Al}_2(\mathrm{CO}_3)_3 \), (d) \( \mathrm{Cd(OH)_2} \).

Step-by-step solution

Determine the Charge Balance

To write the formula unit, we need to make sure the total positive charge equals the total negative charge. For the pair \( \mathrm{Sr}^{2+} \) and \( \mathrm{As}^{3-} \), we need to find the smallest amount of each ion that results in a neutral compound.

Find the Least Common Multiple for (a)

The charges are \( +2 \) for \( \mathrm{Sr}^{2+} \) and \( -3 \) for \( \mathrm{As}^{3-} \). The smallest common multiple of 2 and 3 is 6. Therefore, we need 3 \( \mathrm{Sr}^{2+} \) ions (which gives \( 3 \times +2 = +6 \)) and 2 \( \mathrm{As}^{3-} \) ions (which gives \( 2 \times -3 = -6 \)).

Write the Formula for (a)

Thus, the formula unit for combining these ions is \( \mathrm{Sr}_3\mathrm{As}_2 \).

Repeat Steps for (b)

For \( \mathrm{Ra}^{2+} \) and \( \mathrm{O}^{2-} \), both ions have charges of \( 2 \). Thus, one ion of each will balance to form a neutral compound. Write the formula as \( \mathrm{RaO} \).

Repeat Steps for (c)

For \( \mathrm{Al}^{3+} \) and \( \mathrm{CO}_3^{2-} \), we find the least common multiple of 3 and 2 which is 6. Thus, 2 \( \mathrm{Al}^{3+} \) (which gives \( 2 \times 3 = +6 \)) and 3 \( \mathrm{CO}_{3}^{2-} \) (which gives \( 3 \times -2 = -6 \)) are needed. The formula unit is \( \mathrm{Al}_2(\mathrm{CO}_3)_3 \).

Repeat Steps for (d)

For \( \mathrm{Cd}^{2+} \) and \( \mathrm{OH}^{-} \), since \( \mathrm{OH}^{-} \) has a charge of \( -1 \), we need two \( \mathrm{OH}^- \) ions to balance one \( \mathrm{Cd}^{2+} \) ion's charge. Therefore, the formula unit is \( \mathrm{Cd(OH)_2} \).

Key concepts

Ions

Ions are atoms or molecules that have gained or lost one or more electrons, giving them a net electric charge. Most commonly, ions are found as part of compounds. They play a critical role in chemical reactions and the formation of chemical substances.

• Positive ions are called cations, formed when an atom loses electrons.
• Negative ions are known as anions, formed when an atom gains electrons.

Understanding ions is essential in balancing chemical equations and predicting how different substances will interact during a reaction. For example, in our original exercise, understanding that \( \mathrm{Sr}^{2+} \), \( \mathrm{As}^{3-} \), \( \mathrm{Ra}^{2+} \), and other ions have specific charges helps you make these necessary balance and formula calculations.

Charge Balance

The concept of charge balance is crucial when writing chemical formulas. A charge balance ensures that the total positive charge and the total negative charge of ions in a compound are equal. This condition creates a neutral compound.

• You achieve charge balance by determining the correct ratio of cations to anions so that their charges cancel out each other.
• For example, to balance \( \mathrm{Sr}^{2+} \) and \( \mathrm{As}^{3-} \), you need three \( \mathrm{Sr}^{2+} \) ions and two \( \mathrm{As}^{3-} \) ions, resulting in a formula of \( \mathrm{Sr}_3\mathrm{As}_2 \).

Charge balance is what drives the formation of stable compounds and is a fundamental principle in chemistry, especially in the prediction of compounds' properties and behaviors.

Formula Units

A formula unit is the most reduced ratio of ions represented in an ionic compound. It indicates the simplest collection of atoms from which the composition of an ionic compound can be derived.

• Formula units are essential for representing ionic compounds in chemical equations properly.
• For instance, \( \mathrm{RaO} \) is the formula unit for the compound formed from \( \mathrm{Ra}^{2+} \) and \( \mathrm{O}^{2-} \) because both ions balance each other perfectly with one of each ion.

Formula units are different from molecular formulas, as they do not provide information about molecules but instead indicate the ratio of ions in an ionic compound.

Cations and Anions

Cations and anions are the two types of ions that are central to chemical formulas. Understanding their characteristics is vital for any chemistry student. Cations are positively charged ions that generally result from losing electrons. Metals such as strontium (\( \mathrm{Sr}^{2+} \)) and radium (\( \mathrm{Ra}^{2+} \)) act as cations in our exercises.

• Anions, on the other hand, are negatively charged. They result from gaining electrons, such as the \( \mathrm{As}^{3-} \) and \( \mathrm{O}^{2-} \) in our examples.
• A correct understanding of both these ions allows for predicting the structure and formation of ionic compounds, such as \( \mathrm{Cd(OH)_2} \), where one \( \mathrm{Cd}^{2+} \) aligns with two \( \mathrm{OH}^-\) to form a neutral compound.

Cations and anions' distinct features help chemists determine formulas, structures, and even the behavior of compounds in various reactions.