\(\mathrm{N}_{2} \mathrm{O}\) is called dinitrogen monoxide, whereas, \(\mathrm{Na}_{2} \mathrm{O}\) is called sodium oxide, not disodium oxide. Explain why, and also explain how the name sodium oxide still lets us know that there are two sodium atoms in the formula.

The given compounds are: 1. Dinitrogen monoxide: \(\mathrm{N}_{2} \mathrm{O}\) 2. Sodium oxide: \(\mathrm{Na}_{2} \mathrm{O}\)

Covalent compounds, which are formed between non-metal atoms, have a specific naming convention involving prefixes to indicate the number of atoms of each element present in the molecule. In the case of dinitrogen monoxide (\(\mathrm{N}_{2} \mathrm{O}\)), both nitrogen and oxygen are non-metals, so we use the prefixes "di-" for two nitrogen atoms and "mono-" for one oxygen atom, resulting in the name "dinitrogen monoxide."

Ionic compounds are formed between metal and non-metal atoms, and they do not use numeric prefixes in their names. This is because the ratio of atoms in these compounds is determined by the charges on their ions, which follow the principle of charge neutrality - the net charge of the compound is zero. In the case of sodium oxide (\(\mathrm{Na}_{2} \mathrm{O}\)), there is a metal (sodium) and a non-metal (oxygen) present. Therefore, it must be named following the ionic compound convention, which is simply "sodium oxide."

The name sodium oxide does not explicitly say there are two sodium atoms, but we can infer this from the charges on the ions. Sodium is an alkali metal in Group 1, which means it forms a +1 charge when it becomes an ion (\(\mathrm{Na}^{+}\)). Oxygen is a Group 16 non-metal, which means it forms a -2 charge when it becomes an ion (\(\mathrm{O}^{2-}\)). To achieve charge neutrality in the compound, we need two sodium ions for each oxygen ion (\(2 \times \mathrm{Na}^{+}\) and \(1 \times \mathrm{O}^{2-}\)), resulting in the formula \(\mathrm{Na}_{2} \mathrm{O}\). In conclusion, dinitrogen monoxide is named with prefixes because it is a covalent compound, while sodium oxide follows the ionic compound naming convention, which does not use prefixes. The name sodium oxide still lets us know there are two sodium atoms because the charges on the ions imply that they combine in a 2:1 ratio to maintain charge neutrality.