Would you expect the nonbonding electron-pair domain in \(\mathrm{NH}_{3}\) to be greater or less in size than for the corresponding one in \(\mathrm{PH}_{3}\) ? Explain.

Nonbonding electron-pair domain is the region in a molecule where an electron pair is not involved in bonding between atoms. It is also called the lone pair of electrons. The size of the nonbonding electron-pair domain is influenced by the atom's size and the electron repulsion among the electron pairs. In our case, we need to compare the size of the nonbonding electron-pair domain in NH3 and PH3.

To make a comparison between NH3 and PH3, we first need to know the electron configuration of the central atoms, nitrogen (N) and phosphorus (P). Nitrogen has an electron configuration of \(1s^{2}2s^{2}2p^{3}\), with 5 valence electrons. Phosphorus has an electron configuration of \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{3}\), with 5 valence electrons as well.

Both molecules, NH3 and PH3, have a central atom (N and P) surrounded by three hydrogen atoms and one nonbonding electron-pair domain (lone pair). Due to this lone pair, the molecular geometry of both molecules is trigonal pyramidal.

Now, we need to compare the size of the nonbonding electron-pair domain in NH3 and PH3. The size of the nonbonding electron-pair domain depends on the size of the central atom and electron repulsion among electron pairs. Phosphorus is larger in size than nitrogen because it is located in the third period of the periodic table, while nitrogen is in the second period. As a result, the electron cloud in PH3 is more spread out, and the nonbonding electron-pair domain in PH3 will be larger than in NH3. The electron repulsion among electron pairs is another factor that affects the size of the nonbonding electron-pair domain. In NH3, the nitrogen atom has a high electronegativity, which means that it attracts the electrons in the bond more towards itself, thus causing more repulsion between the lone pair and the bonding pairs. In PH3, the electronegativity of phosphorus is lower, and consequently, the repulsion between the lone pair and bonding pairs is also lower. Considering both factors, we can conclude that:

The nonbonding electron-pair domain in PH3 is greater in size than the corresponding one in NH3. This is due to the larger size of the phosphorus atom compared to nitrogen and the lower electron repulsion between the lone pair and bonding pairs in PH3.