Problem 9 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following order is correct for the size of \(\mathrm{Fe}^{3+}, \mathrm{Fe}\) and \(\mathrm{Fe}^{2+} ?\) (a) \(\mathrm{Fe}^{3+}<\mathrm{Fe}^{2+}<\mathrm{Fe}\) (b) \(\mathrm{Fe}<\mathrm{Fe}^{3+}<\mathrm{Fe}^{2+}\) (c) \(\mathrm{Fe}<\mathrm{Fe}^{2+}<\mathrm{Fe}^{3+}\) (d) \(\mathrm{Fe}^{2+}<\mathrm{Fe}^{3+}<\mathrm{Fe}\)

Step-by-Step Solution

Answer

(a) \(\mathrm{Fe}^{3+}<\mathrm{Fe}^{2+}<\mathrm{Fe}\) is the correct order.

Step 1: Understand Atomic and Ionic Size

Understand that atomic size generally increases as you move down a group and decreases as you move across a period in the periodic table. Ionic size is influenced by the charge: cations (positive ions) like \(\mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+}\) are smaller than their neutral atom \(\mathrm{Fe}\) because they have lost electrons, resulting in a reduced electron cloud and increased effective nuclear charge per electron.

Step 2: Determine Neutral Atom Size

The size of a neutral iron atom \(\mathrm{Fe}\) without any charge is bigger than that of any of its ions. This is because it contains more electrons compared to its cations, leading to greater electron-electron repulsion resulting in a larger radius.

Step 3: Order ions based on Charge

Compare \(\mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+}\): - \(\mathrm{Fe}^{3+}\) has lost three electrons compared to a neutral Fe atom, leading to higher effective nuclear charge per electron, thus smaller size. - \(\mathrm{Fe}^{2+}\) has lost two electrons, so it is bigger than \(\mathrm{Fe}^{3+}\) but smaller than \(\mathrm{Fe}\).

Step 4: Apply the Arranged Order

Arrange the sizes using the observations: The correct order is \(\mathrm{Fe}^{3+}<\mathrm{Fe}^{2+}<\mathrm{Fe}\) where the most positively charged ion (\(\mathrm{Fe}^{3+}\)) is smallest, followed by \(\mathrm{Fe}^{2+}\), and the neutral atom (\(\mathrm{Fe}\)) is the largest.

Key Concepts

Cation Size

Understanding the size of cations compared to their neutral atoms is important in predicting the properties of elements and compounds. A cation is an ion that carries a positive charge because it has lost one or more electrons. This loss of electrons leads to a smaller ionic radius than the neutral atom. The decrease in size happens because:

• There is less electron-electron repulsion in a cation than in the neutral atom, allowing the remaining electrons to be drawn closer to the nucleus.
• A higher positive charge results in a greater pull by the nucleus on the electron cloud, leading to a smaller size.

When you compare different cations of the same element, the cation with the higher positive charge will generally be smaller. For example, -

- - has a more significant positive charge than - , so it is smaller in size.

Effective Nuclear Charge

The effective nuclear charge (ENC) is the net positive charge experienced by an electron in a multi-electron atom. This concept is crucial in understanding why cations are smaller than their corresponding neutral atoms. When electrons are removed to form cations, the ENC per electron increases because:

• The number of protons in the nucleus remains the same.
• The number of electrons decreases, leading to a reduction in electron shielding or repulsion.

Therefore, each remaining electron feels a stronger attraction to the nucleus, resulting in a smaller ionic radius. With iron, for example, - - - - This phenomenon explains why - the size hierarchy observed in cations. -

Electron Configuration of Iron

Iron is an element with versatile chemistry, partly due to its complex electron configuration. The neutral iron atom has the electronic configuration \[ \]. When iron loses electrons, it forms cations, and this electron configuration changes.- In - - - changes to - when forming Each electron removal alters the magnetic and chemical properties of the atom or ion significantly, affecting size and reactivity. These changes in electron configuration demonstrate the flexibility and range of chemically possible states for iron, making it a vital element in both biological and industrial processes. Understanding these principles helps in anticipating the behavior of iron in various chemical reactions.