Problem 23 - A Complete Resource Book in Chemistry for JEE Main

Question

If \(\mathrm{T}\) is the intensity of absorbed light and ' \(\mathrm{C}\) is the concentration of \(\mathrm{AB}\) for the photochemical process \(\mathrm{AB}+\mathrm{hv} \longrightarrow \mathrm{AB} \bullet\), the rate of formation of \(\mathrm{AB}\) ' is directly proportional to (a) \(\mathrm{C}\) (b) I (c) \(\mathrm{I}^{2}\) (d) C.I

Step-by-Step Solution

Answer

The rate of formation of AB' is directly proportional to both C and I, so the correct option is (d) C.I.

Step 1: Understand the Reaction Mechanism

For the given photochemical process, when light (hv) is absorbed by the substance AB, it results in the formation of AB'. This is a typical photochemical reaction where the incident light provides the energy needed for the reaction to occur.

Step 2: Relate Rate of Formation to Intensity and Concentration

The rate of formation of AB' in a photochemical reaction is directly related to the number of photons absorbed. The number of photons absorbed depends on the intensity of light, I, that interacts with a given concentration of AB, C.

Step 3: Identify the Rate Proportionality

In many simple photochemical reactions, the rate of reaction can be described as being proportional to both the intensity of light (I) and the concentration of the reactant (C), written as Rate ∝ C.I.

Step 4: Choose the Correct Option

From the options provided, option (d) C.I represents this relationship: the rate of formation of AB' is directly proportional to both the concentration of AB and the intensity of the absorbed light.

Key Concepts

Intensity of Absorbed Light

In photochemical reactions, the intensity of absorbed light plays a crucial role in determining the rate of the reaction. The intensity, often denoted by \(I\), refers to the amount of energy transmitted through the light per unit area. High intensity means more photons, which can interact with the reactants, leading to increased reaction rates.
Understanding this concept helps clarify why reactions that are exposed to stronger light sources tend to proceed at a faster pace. This is because more photons are available to be absorbed, triggering the reaction to continue with greater frequency.

• High intensity = More photons = Faster reaction rate
• Intensity directly influences the availability of photons for the reaction

It's essential to note that not all light will be absorbed, but only those photons that match the energy required for the specific transition involved in the reaction.

Concentration Dependency

The rate of a photochemical reaction is also affected by the concentration of the reactant, here represented as \(C\) for the molecule AB. The concentration refers to how many molecules of reactant are present in a given volume. Higher concentrations typically lead to more frequent interactions between photons and molecules.
When there are more reactant molecules available, the probability of each photon finding a target to interact with increases, accelerating the reaction rate.
This is why increasing the concentration could potentially enhance the speed of a photochemical reaction.

• More molecules = Increased probability of photon interaction
• Concentration influences reaction rate by dictating molecule availability for photon absorption

Rate Proportionality

In many photochemical processes, the reaction rate can be mathematically described by the term "rate proportionality." This means that the rate at which a product is formed in a reaction is proportional to certain factors. For a typical photochemical reaction, this relationship is represented as Rate ∝ C.I.
This equation suggests that both the concentration of the reactant (C) and the intensity of absorbed light (I) together determine the reaction rate. This relationship is essential for predicting how changes in light intensity or reactant concentration will affect the reaction.

• Rate ∝ C.I defines how both concentration and intensity impact the reaction speed
• Both factors play a role in how quickly and efficiently the reaction progresses

Photon Interaction

Photons, as particles of light, are integral to photochemical reactions. When light is absorbed by a reactant molecule, the photons provide the energy necessary to enable reactions that would not occur otherwise.
Photons, carrying distinct packets of energy, interact with reactant molecules when the energy of the photons matches the energy required for the reaction. This process leads to an energized state of the reactant, resulting in the formation of reaction products.

• Photons carry energy critical for the reaction
• Their interaction triggers the reaction initiation

The efficiency of this interaction directly affects how much of the product is formed, making photon interaction a pivotal concept in understanding photochemical reactions.

Reaction Mechanism

Understanding the reaction mechanism is critical in deciphering photochemical processes. The mechanism explains the step-by-step sequence in which reactants turn into products, notably involving the initial absorption of photons.
In the given reaction, AB absorbs a photon, which excites it to a higher energy state, forming AB'. This state is often an essential intermediate in the overall reaction process.

• Light absorption leads to excitation and subsequent reaction
• Mechanisms show the transition steps from reactants to products

Recognizing the mechanism helps predict the reaction behavior, facilitating better control and optimization of conditions for desired outcomes.