Describe the formation of solid potassium sulfide \(\left(\mathrm{K}_{2} \mathrm{~S}\right)\) from large numbers of potassium and sulfur atoms.

To understand how potassium sulfide forms, we first need to look at the ions involved. Potassium (K) atoms and sulfur (S) atoms participate in this reaction. Potassium is a metal and tends to lose electrons, becoming a positively charged ion called a cation. When a potassium atom loses one electron, it forms a \( \text{K}^{+} \) ion. This loss of one electron helps potassium achieve a stable electron configuration.

On the other hand, sulfur is a non-metal and gains electrons. Sulfur atoms need two additional electrons to become stable, forming a negatively charged ion called an anion. When a sulfur atom gains two electrons, it forms a \( \text{S}^{2-} \) ion. So, the first step in forming potassium sulfide is the creation of these \( \text{K}^{+} \) and \( \text{S}^{2-} \) ions.

Next, let's balance the charges. In any compound, the total positive charge must balance the total negative charge. Potassium forms a \( \text{K}^{+} \) ion with a +1 charge, while sulfur forms an \( \text{S}^{2-} \) ion with a -2 charge. To balance these charges in potassium sulfide, we need two \( \text{K}^{+} \) ions to pair with one \( \text{S}^{2-} \) ion.

This relationship is key because two \( \text{K}^{+} \) ions, each with a +1 charge, sum to a +2 total charge. This +2 charge exactly balances the -2 charge from one \( \text{S}^{2-} \) ion. Therefore, for every sulfur ion, two potassium ions are required to achieve electrical neutrality.

In the solid state, ions are arranged in a highly ordered structure. This arrangement is known as a crystal lattice. In the case of potassium sulfide, each \( \text{S}^{2-} \) ion is surrounded by \( \text{K}^{+} \) ions. This structure maximizes the attractive forces between the oppositely charged ions and minimizes the repulsive forces between similarly charged ions.

The crystal lattice structure provides stability to the compound. This orderly 3D arrangement of ions is why potassium sulfide forms a solid, rather than remaining as separate ions floating around.

Once the charges are balanced and the structure is formed, the next important step is to determine the chemical makeup of the compound. The empirical formula is the simplest whole-number ratio of ions in the compound. For potassium sulfide, two potassium ions balance one sulfur ion, leading to the empirical formula \( \text{K}_{2}\text{S} \).

This empirical formula tells us the simplest ratio of elements in potassium sulfide: for every sulfur ion, there are two potassium ions. This ratio is crucial for understanding the composition and properties of the compound.