Problem 146 - Introductory Chemistry Atoms First

Question

Why is the formula for calcium sulfide \(\mathrm{CaS}\) and not \(\mathrm{Ca}_{2} \mathrm{~S} ?\)

Step-by-Step Solution

Answer

The formula for calcium sulfide is CaS because the valencies of calcium (+2) and sulfur (-2) balance each other without the need for a subscript. This is determined by understanding valency and elements' combining capacity. Calcium loses 2 electrons and sulfur gains 2 electrons, resulting in a stable compound with electrical neutrality.

Step 1: Understanding Valency

Valency is the measure of an element's combining capacity with other elements to form compounds. It's determined by the number of electrons an element can gain, lose, or share in order to achieve a stable electronic configuration (a full outer shell of electrons).

Step 2: Identifying the Valency of Calcium and Sulfur

Calcium (Ca) belongs to Group 2 of the periodic table, which means it has 2 valence electrons. Calcium's valency is +2, since it prefers to lose these 2 electrons to achieve a stable electronic configuration with a full outer shell. Sulfur (S) belongs to Group 16 of the periodic table, which means it has 6 valence electrons. Sulfur requires 2 more electrons to achieve a stable electronic configuration, so its valency is -2.

Step 3: Applying the Valency Rule to Form the Compound

When elements combine to form a compound, their valencies should be balanced to maintain electrical neutrality in the compound. To do this, we can use the 'cross-over rule' or simply swap the valency numbers of the elements. Calcium (Ca) has a valency of +2, while sulfur (S) has a valency of -2. When we cross over the valencies, we use the absolute value of the valency and write the compound as: Calcium Sulfide: Ca (with subscript 2) S (with subscript 2) However, since the valency numbers (2) are the same, we can simplify this by removing the subscripts 2: Calcium Sulfide: CaS

Step 4: Conclusion

The formula for calcium sulfide is CaS and not Ca₂S because the valencies of calcium and sulfur balance each other without the need for a subscript in their chemical formula. By understanding the concept of valency and combining capacity, we can determine the correct formula for compounds.

Key Concepts

Understanding Chemical Formula

A chemical formula is a concise way of expressing information about the atoms that constitute a particular chemical compound. It provides insights into the elemental composition of the compound at the atomic level. In the case of calcium sulfide, its proper chemical formula is the result of balancing the charges from the constituent elements, calcium (Ca) and sulfur (S).
To represent the compound, each element's symbol is used along with subscripts indicating the number of each type of atom in the compound. For calcium sulfide, the formula is written as \( \text{CaS} \). This indicates that for every calcium atom, there is one sulfur atom, balancing out their respective charges.

Using the Periodic Table

The periodic table is an essential tool for chemists, providing valuable information about the elements. Each element is characterized by its atomic number, which is the number of protons in its nucleus.
Knowing an element’s position on the periodic table helps to determine its properties, such as valency, which influences how it will bond with other elements. For example:

• Calcium is in Group 2, suggesting it is an alkaline earth metal with a valency of +2.
• Sulfur is in Group 16, indicating it is a nonmetal with a valency of -2.

These groups provide a visual guide to an element's properties and typical chemical behavior.

Exploring Electron Configuration

Electron configuration reveals the distribution of electrons in an atom's orbitals. Understanding this arrangement helps in predicting and explaining an atom's chemical properties and its tendency to form bonds. The electrons are organized into energy levels or shells.
For calcium, which has 20 electrons, the configuration is \( 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 \). Calcium strives to lose the 2 electrons in its outermost shell (4s) to reach a stable configuration equivalent to the noble gas argon.
Similarly, sulfur, with 16 electrons, has the configuration \( 1s^2 2s^2 2p^6 3s^2 3p^4 \). It needs to acquire 2 additional electrons to achieve the electron configuration of argon, making it energetically favorable to accept electrons.

Essentials of Compound Formation

Compound formation involves the combination of elements to create a new substance with unique properties. Key factors in this process include valency and electrical neutrality.
In the formation of calcium sulfide, calcium donates its two electrons to sulfur, which needs two electrons to fill its valence shell. This electron exchange results in calcium giving up its valence electrons to achieve a noble gas configuration, while sulfur completes its outer shell, forming an ionic bond.

• This exchange maintains electrical neutrality, as the positive charge of the two lost electrons balances with the negative charge of the two gained electrons.
• The resulting compound, calcium sulfide (\(\text{CaS}\)), reflects equal numbers of positive and negative charges, ensuring a stable compound formation.