Problem 77 - A Complete Resource Book in Chemistry for JEE Main

Question

For the reaction \(2 \mathrm{~A}+\mathrm{B} \longrightarrow 3 \mathrm{C}+\mathrm{D}\) which of the following does not express the reaction rate? (a) \(\frac{d[\mathrm{D}]}{\mathrm{dt}}\) (b) \(-\frac{d[A]}{2 \mathrm{dt}}\) (c) \(\frac{\mathrm{d}[\mathrm{C}]}{3 \mathrm{dt}}\) (d) \(-\frac{\mathrm{d}[\mathrm{B}]}{d t}\)

Step-by-Step Solution

Answer

Option (c) \(\frac{d[C]}{3 \ dt}\) does not express the rate correctly.

Step 1: Understanding the Rate Expression

The rate of a chemical reaction for a given balanced equation can be expressed as the change in concentration of any reactant or product per unit time. For the given reaction \(2 \mathrm{~A} + \mathrm{B} \rightarrow 3 \mathrm{C} + \mathrm{D}\), the rate can be expressed by any of the species involved. The rate expressions based on the stoichiometry of the reaction are -\(\frac{1}{2}\frac{d[A]}{dt}, -\frac{d[B]}{dt}, \frac{1}{3}\frac{d[C]}{dt}, \frac{d[D]}{dt}\).

Step 2: Analyzing Each Option

We must match the given options to the rate expressions derived from stoichiometry: (a) \(\frac{d[D]}{dt}\) is correct, as it corresponds to the formation of \(D\) with a coefficient of 1.(b) \(-\frac{d[A]}{2\ dt}\) is correct because \([A]\) has a coefficient of 2 in the reaction.(c) \(\frac{d[C]}{3\ dt}\) is not correct because the stoichiometry tells us it should be \(\frac{1}{3}\frac{d[C]}{dt}\).(d) \(-\frac{d[B]}{dt}\) is correct, as \([B]\) has a coefficient of 1.

Step 3: Identifying the Incorrect Expression

From the analysis, option (c) \(\frac{d[C]}{3\ dt}\) does not match the expected expression \(\frac{1}{3}\frac{d[C]}{dt}\), indicating this is the incorrect representation for the reaction rate.

Key Concepts

Rate Expression

The rate expression of a chemical reaction is a vital concept that represents how fast a reaction occurs by relating it to the change in concentration of reactants or products over time. For any reaction, the rate can be formulated using the stoichiometric coefficients from the balanced chemical equation. This means that the rate of disappearance of reactants and the rate of formation of products are standardized with respect to their coefficients in the balanced equation.
For example, in the reaction \(2 \mathrm{~A}+\mathrm{B} \rightarrow 3 \mathrm{C}+\mathrm{D}\), the rate of reaction can involve the decrease in concentration of \(\mathrm{A}\), \(\mathrm{B}\), or the increase in concentration of \(\mathrm{C}\) and \(\mathrm{D}\). The correct rate expressions, considering stoichiometric adjustments, are:

• \(-\frac{1}{2}\frac{d[A]}{dt}\): for reactant \(A\) with coefficient 2
• \(-\frac{d[B]}{dt}\): for reactant \(B\) with coefficient 1
• \(\frac{1}{3}\frac{d[C]}{dt}\): for product \(C\) with coefficient 3
• \(\frac{d[D]}{dt}\): for product \(D\) with coefficient 1

Each of these expressions shows the rate of change per unit of time, adjusted for stoichiometry, providing clarity in comparing how fast reactants are consumed or products are formed.

Stoichiometry

Stoichiometry is the field of chemistry that quantifies relationships in chemical reactions based on the coefficients from the balanced equations. These stoichiometric coefficients determine how much of each substance is consumed or produced relative to one another.
In the reaction \(2 \mathrm{~A}+\mathrm{B} \rightarrow 3 \mathrm{C}+\mathrm{D}\), stoichiometry tells us:

• 2 moles of \(\mathrm{A}\) react with 1 mole of \(\mathrm{B}\).
• Produces 3 moles of \(\mathrm{C}\) and 1 mole of \(\mathrm{D}\).

This relationship is crucial for writing correct rate expressions. It ensures that each species is accounted for correctly in terms of its molecule count. For students, it's essential to understand that stoichiometry connects quantities in a chemical equation, enabling the calculation of reactions' extents.

Chemical Reaction

A chemical reaction involves the transformation of reactants into products, changing substances at a molecular level. Understanding this change involves recognizing the rearrangement of atoms and formation of new compounds or molecules.
In our example reaction \(2 \mathrm{~A}+\mathrm{B} \rightarrow 3 \mathrm{C}+\mathrm{D}\), reactants \(\mathrm{A}\) and \(\mathrm{B}\) undergo a process to become products \(\mathrm{C}\) and \(\mathrm{D}\). This transformation can be visualized as breaking bonds in \(\mathrm{A}\) and \(\mathrm{B}\), followed by the formation of new bonds in \(\mathrm{C}\) and \(\mathrm{D}\).
Essential elements of a chemical reaction include:

• Reactants: Initial substances in a reaction.
• Products: New substances formed from reactants.
• Reaction conditions: Often necessary to facilitate transformations, such as temperature or catalysts.

Grasping these basics allows you to conceptualize how substances interact and transform, a foundation for more complex chemistry topics.