Question

The relative order of reactivity of \(\mathrm{F}^{-}, \mathrm{Cl}^{-}, \mathrm{Br}\) and \(\mathrm{I}\) is/ are (a) \(\mathrm{F}^{-}<\mathrm{Cl}^{-}<\mathrm{Br}<\mathrm{I}^{-}\)in polar solvent (b) \(\mathrm{F}^{-}>\mathrm{Cl}^{->} \mathrm{Br}>\mathrm{I}^{-}\)in non polar solvent (c) \(\mathrm{F}^{-}<\mathrm{Cl}^{-}<\mathrm{Br}<\mathrm{I}^{-}\)in non polar solvent (d) \(\mathrm{F}^{-}>\mathrm{Cl}^{-}>\mathrm{Br}>\mathrm{I}^{-}\)in polar solvent

Short answer

(d) \( \mathrm{F}^{-} > \mathrm{Cl}^{-} > \mathrm{Br}^{-} > \mathrm{I}^{-} \) in polar solvent and (b) \( \mathrm{F}^{-} > \mathrm{Cl}^{-} > \mathrm{Br}^{-} > \mathrm{I}^{-} \) in non-polar solvent.

Step-by-step solution

Understanding Reactivity in Solvents

Reactivity of anions like \( \mathrm{F}^{-}, \mathrm{Cl}^{-}, \mathrm{Br}^{-}, \) and \( \mathrm{I}^{-} \) is influenced by the solvent. In polar solvents, solvation stabilizes smaller anions more effectively due to stronger ion-dipole interactions, whereas larger anions are less stabilized.

Analyzing Reactivity in Polar Solvent

In polar solvents, smaller ions like \( \mathrm{F}^{-} \) are more stable and therefore less reactive due to strong solvation. Larger ions like \( \mathrm{I}^{-} \) are less solvated and hence more reactive. Therefore, the order of reactivity is \( \mathrm{F}^{-}<\mathrm{Cl}^{-}<\mathrm{Br}^{-}<\mathrm{I}^{-} \).

Analyzing Reactivity in Non-polar Solvent

In non-polar solvents, solvation effects are minimal, and reactivity is determined by polarizability. Larger ions, like \( \mathrm{I}^{-} \), which are more polarizable, are more reactive. Hence, the reactivity order is \( \mathrm{F}^{-} > \mathrm{Cl}^{-} > \mathrm{Br}^{-} > \mathrm{I}^{-} \).

Comparing with Given Options

By comparing with the given options: (a) and (c) describe reactivity in polar solvent which is incorrect, as they reverse the actual order. (b) represents reactivity in non-polar solvents correctly. (d) correctly represents reactivity in polar solvents.

Key concepts

Polar Solvent Effects

Polar solvents are known for their ability to stabilize ions through solvation. This happens because polar solvents, like water, have molecules with partial charges. These partial charges create ion-dipole interactions with ions dissolved in the solution. In the context of halide ions, such as \( \mathrm{F}^{-}, \mathrm{Cl}^{-}, \mathrm{Br}^{-}, \mathrm{I}^{-} \), smaller anions like \( \mathrm{F}^{-} \) experience stronger ion-dipole interactions.
This means that in a polar solvent:

• Smaller anions are more solvated due to compact size.
• Greater stability is achieved by stronger solvation.

This stronger stabilization implies lesser reactivity in a polar solvent as the anions are more tightly held and less likely to participate in reactions. Therefore, smaller halide ions are more stable and less reactive in polar solvents, producing the reactivity order: \( \mathrm{F}^{-}<\mathrm{Cl}^{-}<\mathrm{Br}^{-}<\mathrm{I}^{-} \).

Non-Polar Solvent Effects

Non-polar solvents, such as hexane, lack the ionic character or partial charges present in polar solvents. As a result, they do not stabilize anions through solvation. In these solvents, other factors like ion polarizability become dominant in influencing reactivity.
Without significant solvent interactions:

• Reactivity depends significantly on the intrinsic properties of the ions.
• The larger and more polarizable ion will generally be more reactive.

In the case of halide ions, the larger \( \mathrm{I}^{-} \) ion is more polarizable and thus more reactive in non-polar solvents. Consequently, the reactivity order in a non-polar solvent is \( \mathrm{F}^{-} > \mathrm{Cl}^{-} > \mathrm{Br}^{-} > \mathrm{I}^{-} \).

Anion Stability

Anion stability is greatly influenced by the properties of the surrounding solvent. The size of the ion and the nature of the solvent together define how stable an ion is in a given environment.
Small Anions:

• In polar solvents, smaller anions like \( \mathrm{F}^{-} \) are more effectively stabilized.
• Stronger solvation results in lower reactivity due to higher stability.

Large Anions:

• In non-polar environments, larger ions like \( \mathrm{I}^{-} \) are favored regarding reactivity due to minimal stabilization.
• The lack of significant solvation leads to greater intrinsic reactivity.

The environment’s polar nature or lack thereof directly affects the stability of an anion and, consequently, its reactivity potential.

Ion Polarizability

Ion polarizability refers to the ease with which the electron cloud around an ion can be distorted. This property is predominantly a function of ion size. Larger ions are more polarizable because their outer electrons are held less tightly by the nucleus.
Influence on Reactivity:

• In non-polar solvents, where solvation effects are weak, polarizability becomes critical.
• Highly polarizable ions, typically larger ones, are more reactive as they can easily distort and participate in chemical processes.

This is why in non-polar solvents, \( \mathrm{I}^{-} \) is more reactive than \( \mathrm{F}^{-} \), despite being less stable in polar environments. Therefore, in non-polar solvents, the order of reactivity aligns with polarizability: \( \mathrm{F}^{-} > \mathrm{Cl}^{-} > \mathrm{Br}^{-} > \mathrm{I}^{-} \).