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 \(\mathrm{AB}^{\prime}\) is directly proportional to (a) \(\vec{C}\) (b) I (c) \(\mathrm{I}^{2}\) (d) C.I

Step-by-Step Solution

Answer

The rate is directly proportional to \(\mathrm{C} \cdot \mathrm{I}\).

Step 1: Define Proportionality

The problem states that the rate of formation of \(\mathrm{AB}'\) is directly proportional to certain factors. This implies that as these factors increase, the rate of formation of \(\mathrm{AB}'\) will also increase. To solve the problem, we need to establish what \(\mathrm{AB}'\) is dependent on based on the given photochemical process \(\mathrm{AB} + \mathrm{hv} \longrightarrow \mathrm{AB} \bullet\).

Step 2: Understand Reaction Mechanics

In photochemical reactions like \(\mathrm{AB} + \mathrm{hv} \longrightarrow \mathrm{AB} \bullet\), the light intensity \(\mathrm{I}\) plays a significant role as it's the source of energy driving the reaction forward. Typically, reactions directly proportional to light intensity will have their rate depend linearly on \(\mathrm{I}\).

Step 3: Examine Concentration Effects

The concentration \(\mathrm{C}\) of the reactant \(\mathrm{AB}\) can affect the rate of the photochemical reaction. If more \(\mathrm{AB}\) molecules are present, more reactants can absorb light \(\mathrm{hv}\) and transition into \(\mathrm{AB} \bullet\). Thus, reaction rates are often directly proportional to concentration \(\mathrm{C}\).

Step 4: Combine Factors

Both the light intensity \(\mathrm{I}\) and the concentration \(\mathrm{C}\) influence the chemical reaction. The rate of formation of \(\mathrm{AB}'\) is therefore likely to be directly proportional to the product of these two factors: \(\mathrm{C} * \mathrm{I}\), taking into account the necessity for reactants and sufficient energy input.

Key Concepts

Rate of Reaction

The rate of reaction is a critical concept in understanding photochemical processes. It refers to how quickly a reaction progresses from reactants to products. In the equation presented, \[ \mathrm{AB} + \mathrm{hv} \longrightarrow \mathrm{AB} \bullet, \]the rate of formation of the product \( \mathrm{AB}' \) is central to this reaction.

• In photochemical reactions, the rate is significantly influenced by external factors like light intensity and concentration.
• The rate can be measured by the change in concentration of reactants or products over time.
• In this specific process, the higher the rate, the more products form in a shorter period.

Understanding these influences and how they increase the reaction speed can help predict and control chemical processes.

Light Intensity

Light intensity refers to the amount of light energy hitting a certain area. In photochemical reactions, such as the one given \(\mathrm{AB} + \mathrm{hv} \rightarrow \mathrm{AB} \bullet, \)this parameter is key because it provides the energy required to initiate and sustain the reaction.

• The reaction rate is often proportional to light intensity because more energy results in more reactants transitioning to products.
• As intensity increases, more photons are available to interact with molecules, driving the chemical change.
• In some reactions, too much light can lead to side effects, like degradation of products, so balance is crucial.

Therefore, effectively controlling light intensity can optimize the efficiency and outcome of photochemical processes.

Concentration

Concentration, in the context of chemistry, refers to how much of a substance is present in a mixture or solution. In the discussed photochemical reaction \(\mathrm{AB} + \mathrm{hv} \longrightarrow \mathrm{AB} \bullet, \)the concentration \( \mathrm{C} \) of reactant \( \mathrm{AB} \) affects reaction rate significantly.

• A higher concentration of \( \mathrm{AB} \) means more molecules are available to absorb light and form \( \mathrm{AB} \bullet \).
• This increase in reactant molecules can lead to a faster reaction.
• Since the rate of the reaction depends on this initial concentration, it is directly proportional to the product formation.

Contractions or a lack thereof can alter reaction dynamics and understanding these changes is vital for controlling chemical systems.