Question

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

Short answer

The nonbonding electron-pair domain in NH₃ is smaller as compared to the one in PH₃. This is due to the greater electronegativity and smaller atomic orbitals of nitrogen in NH₃, which attracts the electron pair more effectively and contracts the size of the nonbonding domain.

Step-by-step solution

Identify the electron-pair domains

First, we need to draw the Lewis structure for both NH₃ and PH₃ molecules. In NH₃, nitrogen (N) has 5 valence electrons and hydrogen (H) has 1 valence electron, making a total of 8 valence electrons. In the Lewis structure, nitrogen is the central atom and needs to form three single bonds with three hydrogen atoms, leaving one lone pair of electrons (nonbonding electron-pair domain) on nitrogen. Similarly, in PH₃, phosphorus (P) has 5 valence electrons and hydrogen (H) has 1 valence electron, making a total of 8 valence electrons. In the Lewis structure, phosphorus is the central atom and needs to form three single bonds with three hydrogen atoms, leaving one lone pair of electrons (nonbonding electron-pair domain) on phosphorus.

Compare the size of nonbonding electron-pair domains

Nonbonding electron-pair domains are regions where the electron pair is not involved in any bond formation. The size of the nonbonding electron-pair domain depends on the electronegativity of the central atom and the size of its atomic orbitals. In our case, the electronegativity of nitrogen (3.04) is greater than that of phosphorus (2.19). So, the nitrogen in NH₃ attracts the electron pair more effectively, and consequently, the nonbonding electron-pair domain is more contracted and smaller in size as compared to the one in PH₃. On the other hand, the atomic orbitals of phosphorus are larger than that of nitrogen due to its increased size and the presence of more shells. Thus, the electron cloud is more dispersed for PH₃ and the size of the nonbonding electron-pair domain is greater for PH₃ than NH₃.

Conclusion

After comparing the electronegativity and size of atomic orbitals, we can conclude that the nonbonding electron-pair domain in NH₃ will be smaller in size than the corresponding one in PH₃ due to the greater electronegativity and smaller atomic orbitals of nitrogen.

Key concepts

Lewis structure

Understanding Lewis structures is crucial in predicting molecular shapes and reactivity. Lewis structures are diagrams that show the bonding between atoms and the lone pairs of electrons that may exist in the molecule. In drawing a Lewis structure:

• Determine the total number of valence electrons for the molecule.
• Use a pair of electrons to form a bond between each pair of bound atoms.
• Distribute the remaining electrons to satisfy the octet rule, which means that atoms share electrons until they each have eight electrons in their valence shell.

For example, using the molecule NH₃: - Nitrogen has five valence electrons; each hydrogen has one. - This gives a total of eight valence electrons. - We place nitrogen in the center, establishing three single bonds with hydrogen, resulting in one lone pair of electrons on nitrogen.

Electronegativity

Electronegativity is a measure of the tendency of an atom to attract a bonding pair of electrons. Generally, electronegativity values increase across a period and decrease down a group in the periodic table. This concept is critical when comparing two different molecules. For instance, nitrogen (N) in NH₃ has a higher electronegativity value (3.04) than phosphorus (P) in PH₃ (2.19). This implies that nitrogen can attract the nonbonding pair of electrons more strongly, leading to a more compact and contracted electron cloud around nitrogen than around phosphorus. As a result, nonbonding domains (lone pairs) are smaller in NH₃ compared to PH₃.

Atomic orbitals

Atomic orbitals represent regions in an atom where the probability of finding electrons is highest. They are described by quantum numbers and have different shapes, such as s, p, d, and f orbitals. In the context of molecules like NH₃ and PH₃, the size and shape of atomic orbitals can significantly affect the properties of the molecules: - Nitrogen uses its smaller 2p orbitals to form bonds and hold the lone pair tightly in NH₃. - Phosphorus, which is larger, uses its 3p orbitals, resulting in a looser hold on the lone pair in PH₃. Due to the larger orbitals of phosphorus, the nonbonding electron pair in PH₃ is more spread out, while in NH₃, it is more compact due to the smaller size of nitrogen's orbitals.

NH₃

Ammonia, with the chemical formula NH₃, is a simple nitrogen hydride. Its structure features nitrogen atom at the center with three hydrogen atoms bonded to it and one lone pair of electrons. The presence of the lone pair affects its molecular geometry: - The molecule adopts a trigonal pyramidal shape due to the lone pair, which repels the bonded electrons, influencing the angle between hydrogen atoms. - NH₃ is a polar molecule, owing to the difference in electronegativity and the geometry caused by the lone pair. This polarity contributes to hydrogen bonding, giving NH₃ higher boiling and melting points compared to other similar-sized molecules without hydrogen bonds.

PH₃

Phosphine, designated as PH₃, is structurally similar to ammonia, with phosphorus as the central atom bonded to three hydrogen atoms, plus one lone pair of electrons. The main difference from NH₃ arises from the difference in electronegativity and orbital sizes: - PH₃ is also trigonal pyramidal, but due to phosphorus' lower electronegativity and larger orbitals, the lone pair is more spread out. - Consequently, PH₃ is less polar than NH₃, leading to weaker forces between its molecules. As a result, phosphine's boiling point is lower than ammonia's. It is less soluble in water and generally characterized by its lack of hydrogen bonding capabilities.