Question

Which is correct increasing order of their tendency of the given elements to form \(M^{3}\) ion? (a) \(\mathrm{Bi}>\mathrm{Sb}>\mathrm{As}>\mathrm{P}>\mathrm{N}\) \(2 e^{\circ}\) (b) \(\mathrm{Bi}<\mathrm{Sb}<\mathrm{As}<\mathrm{P}<\mathrm{N}\) (c) \(\quad \mathrm{N}<\mathrm{P}<\mathrm{Sb}<\mathrm{Bi}<\mathrm{As}\) (d) \(\mathrm{Bi}>\mathrm{Sb} \sim \mathrm{N} \sim \mathrm{P}>\mathrm{As}\)

Short answer

\(\mathrm{N}<\mathrm{P}<\mathrm{As}<\mathrm{Sb}<\mathrm{Bi}\) - Option (b) presents the correct increasing order, if we consider the periodic trend that going down a group makes it easier for atoms to lose electrons.

Step-by-step solution

Understand the periodic trends

To determine the increasing order of the tendency of elements to form a M^3+ ion, we need to understand periodic trends. As we move across a period from left to right, the effective nuclear charge increases, which makes it harder for elements to lose electrons. However, as we move down a group, the outer electrons are further from the nucleus and more shielded by inner electrons, making it easier for atoms to lose electrons and form cations.

Apply periodic trends to the given elements

The given elements are from the group 15 of the periodic table (pnictogens). Their tendencies to form a M^3+ ion will depend on how easily they can lose 3 electrons. Going down the group from N to Bi, it should become easier for atoms to lose electrons due to increased size and shielding. Nitrogen, being the smallest and having high electronegativity, is least likely to form a M^3+ ion, while Bismuth, being the largest and having the lowest electronegativity, will form a M^3+ ion most readily.

Choose the correct order

Based on the above explanation, option (b) \(\mathrm{Bi}<\mathrm{Sb}<\mathrm{As}<\mathrm{P}<\mathrm{N}\) presents the correct increasing order of tendency to form a M^3+ ion, which is opposite of what is expected. Moving down the group from N to Bi, the size and shielding increase, which should make it easier for atoms to lose electrons, thus the correct order should be exactly the opposite of option (b).

Key concepts

Periodic Trends

Periodic trends are patterns in the properties of elements across the periodic table. One key trend is atomic size, which generally increases as you move down a group and decreases as you move from left to right across a period. Another trend is ionization energy, the energy required to remove an electron from an atom, which generally increases as you move up a group and from left to right across a period.

For students, a useful way to remember these trends is to picture the periodic table as a slope, where atomic size is like a ball that rolls down the slope (increasing) as you move down a group, but when sweeping across a period, the slope climbs up, and the size of the ball (atomic radius) decreases.

Effective Nuclear Charge

Effective nuclear charge (Z_eff) refers to the net positive charge experienced by an electron in a multi-electron atom. The actual nuclear charge (the number of protons in the nucleus) is shielded by the electrons in inner orbits, which means that outer electrons do not feel the full charge of the nucleus.

• Z_eff increases as you move across a period because more protons in the nucleus result in a stronger pull on the electrons.
• As you move down a group, added electron shells increase the shielding effect, causing Z_eff to increase but at a slower rate compared to the increase across a period.

Visualizing Z_eff

Imagine a group of people (inner electrons) crowded around a celebrity (the nucleus); the fans further out in the crowd (outer electrons) experience less of the celebrity's presence due to the bustle of the crowd in between.

Cation Formation

Cation formation occurs when an atom loses one or more electrons, resulting in a positively charged ion. This process depends on the ionization energy and the tendency of an element to achieve a stable electronic configuration.

For atoms in Group 15 (the pnictogens), forming a M³⁺ ion means losing three electrons, which can be quite energetic for elements like nitrogen with its strong hold on its electrons due to its lower atomic size and higher effective nuclear charge. As you move down the group to bismuth, the atomic size increases with additional inner electron shells, the electrons are not held as tightly, and cation formation becomes more favorable.

Electronegativity

Electronegativity is a measure of an atom's ability to attract and hold onto electrons within a chemical bond. The trend in electronegativity within the periodic table follows a distinctive pattern: it increases as one moves from left to right across a period and decreases as one moves down a group.

In the context of cation formation, high electronegativity indicates a reluctance to give up electrons, whereas low electronegativity denotes a greater willingness to release electrons and form positive ions. Thus, for the pnictogens, nitrogen, which has high electronegativity, has the least tendency to form an M³⁺ ion, while bismuth, with much lower electronegativity, readily forms M³⁺ ions.

Pnictogens

Pnictogens are the elements found in group 15 of the periodic table, and they include nitrogen (N), phosphorus (P), arsenic (As), antimony (Sb), and bismuth (Bi). These elements exhibit varying properties, including their state of matter at room temperature and their chemical reactivity.

What is important for our context is their varying tendency to form M³⁺ ions. Nitrogen, being the smallest pnictogen with the highest electronegativity, is the least likely to form a M³⁺ ion. Conversely, bismuth is the largest and has the lowest electronegativity, so it most readily forms M³⁺ ions. This trend is due to the periodic and group trends that affect various properties such as atomic size, ionization energy, and Z_eff.