Question

If RDS is Ist step of propagation, then correct order of rate of reaction for \(\mathrm{X}_{2}\) is (A) \(\mathrm{F}_{2}>\mathrm{Cl}_{2}>\mathrm{Br}_{2}>\mathrm{I}_{2}\) (B) \(\mathrm{Br}_{2}>\mathrm{I}_{2}>\mathrm{Cl}_{2}>\mathrm{F}_{2}\) (C) \(\mathrm{Cl}_{2}>\mathrm{Br}_{2}>\mathrm{F}_{2}>\mathrm{I}_{2}\) (D) \(\mathrm{Cl}_{2}>\mathrm{F}_{2}>\mathrm{Br}_{2}>\mathrm{I}_{2}\)

Short answer

The correct order of rate of reaction for X2 is (A) \(\mathrm{F}_{2}>\mathrm{Cl}_{2}>\mathrm{Br}_{2}>\mathrm{I}_{2}\).

Step-by-step solution

Expression of the rate law

In order to compare the reaction rates of the different halogens, we need to express the rate law in terms of the concentration of the halogen molecule X2. For a bimolecular reaction, the rate law can be expressed in the following general form: \[ Rate = k[X_2]^m \] where k is the rate constant, m is the order of the reaction, and [X2] is the concentration of the halogen molecule.

Analysis of bond strengths and polarity

The bond dissociation energies of the halogens are as follows: \[ D(\mathrm{F}_{2})= 155 \,\mathrm{kJ/mol} \] \[ D(\mathrm{Cl}_{2})= 243 \,\mathrm{kJ/mol} \] \[ D(\mathrm{Br}_{2})= 193 \,\mathrm{kJ/mol} \] \[ D(\mathrm{I}_{2})= 151 \,\mathrm{kJ/mol} \] In general, a lower bond dissociation energy corresponds to a more reactive bond. However, we must also consider the polarity of the molecules involved, as this can influence the overall reactivity. Since F2, Cl2, Br2, and I2 are symmetrical diatomic molecules, they are nonpolar.

Determining the correct order of rate of reaction

Taking both bond dissociation energies and molecule polarity into consideration, the general trend of reactivity for halogens in RDS propagation steps is: \[ \mathrm{F}_{2}> \mathrm{Cl}_{2}> \mathrm{Br}_{2}> \mathrm{I}_{2} \] Therefore, the correct order of rate of reaction for X2 is: (A) \(\mathrm{F}_{2}>\mathrm{Cl}_{2}>\mathrm{Br}_{2}>\mathrm{I}_{2}\)

Key concepts

Rate Law

Understanding the rate law is crucial when studying chemical reactions, particularly those involving halogens. In a rate law equation, the rate of reaction is usually expressed in terms of the concentration of reactants.

For a bimolecular reaction, the general form of the rate law is: \[ Rate = k[X_2]^m \] Where:

• \(Rate\): Represents the speed at which the reaction proceeds.
• \(k\): Is the rate constant, a unique value specific to each reaction that takes into account factors like temperature and pressure.
• \([X_2]\): Denotes the concentration of the halogen molecule.
• \(m\): Is the reaction order, which usually is determined experimentally and indicates how the rate is affected by the concentration of reactants.

The rate law helps in predicting how changes in the concentration of the reactants will affect the reaction rate. It is essential in comparing the reactivity of various substances, like different halogens, by understanding their behavior in chemical processes.

Bond Dissociation Energy

Bond dissociation energy (BDE) is an invaluable concept when understanding the reactivity of molecules, especially halogens. BDE is defined as the energy required to break a bond in a molecule, resulting in the formation of neutral atoms.

The BDEs for the halogen diatomic molecules are quite revealing:

• \(D(\mathrm{F}_2) = 155\,\mathrm{kJ/mol}\)
• \(D(\mathrm{Cl}_2) = 243\,\mathrm{kJ/mol}\)
• \(D(\mathrm{Br}_2) = 193\,\mathrm{kJ/mol}\)
• \(D(\mathrm{I}_2) = 151 \,\mathrm{kJ/mol}\)

Typically, a lower BDE indicates a weaker bond, which means the molecule can more readily participate in reactions. However, it's not just about breaking the bond; we also need to consider the stability of the resulting species and other factors that may enhance or reduce reactivity.

Although \(\mathrm{I}_2\) has a low BDE, its larger atomic radius reduces its reactivity compared to \(\mathrm{F}_2\), which, although having a slightly higher BDE, is highly reactive due to the electronegativity of fluorine.

Halogen Reactivity

Halogen reactivity is an engaging topic, particularly when discussing how these elements participate in chemical reactions. Halogens—fluorine, chlorine, bromine, and iodine—are elements in Group 17 of the periodic table, known for their high reactivity.

Key factors influencing the reactivity of halogens include:

• Electronegativity: Fluorine, being the most electronegative element, is highly reactive, as it has the strongest tendency to attract electrons.
• Bond Dissociation Energy: Lower bond dissociation energy makes it easier for the molecule to break apart and participate in reactions, though it isn't the only factor.
• Atomic Size and Molecular Polarity: Larger atoms like iodine tend to be less reactive compared to smaller atoms like fluorine and chlorine.

The halogen reactivity trend generally follows: \[ \mathrm{F}_2 > \mathrm{Cl}_2 > \mathrm{Br}_2 > \mathrm{I}_2 \] This order reflects how readily these elements can engage in chemical reactions, largely driven by their electronegativity and the energy associated with breaking their molecular bonds. Understanding these aspects can help predict and explain the behavior of halogens in various chemical processes.