Problem 168 - A Complete Resource Book in Chemistry for JEE Main

Question

The chemical kinetics of the reaction \(\mathrm{aA}+\mathrm{bB} \rightarrow\) \(\mathrm{C}\) at \(298 \mathrm{~K}\) were followed. The initial rates were recorded rates were recorded under different initial conditions and are summarized as follows. Which of the following statements is incorrect? (a) The rate constant \(\mathrm{k}\) is governed by the activation energy of the reaction (b) Reaction rate \(=\mathrm{k}[\mathrm{A}][\mathrm{B}]^{2}\) (c) In the chemical equation of \(\mathrm{aA}+\mathrm{bB} \rightarrow \mathrm{C}, \mathrm{a}\) is 0 and \(\mathrm{b}\) is 3 . (d) The overall order of reaction is third order.

Step-by-Step Solution

Answer

Statement (c) is incorrect.

Step 1: Assess Given Statements in Context

To determine which statement is incorrect, let's analyze each one by cross-checking it with basic chemical kinetics principles and the given reaction at 298 K. We need to check the validity of the rate law (b), stoichiometric coefficients (c), rate constant dependency (a), and overall reaction order (d).

Step 2: Analyze Statement (a)

Statement (a) claims that the rate constant \(k\) is governed by the activation energy of the reaction. This is consistent with the Arrhenius equation, which relates the rate constant \(k\) with temperature and activation energy: \(k = Ae^{-E_a/RT}\). Thus, this statement is correct.

Step 3: Analyze Statement (b)

Statement (b) proposes that the rate law for the reaction is \(\text{Rate} = k[A][B]^2\). This implies a reaction order of 3 (1+2). We must assume this is derived from experimental data or compare it to other reaction scenarios. At this point, consider it speculative without data confirmation.

Step 4: Analyze Statement (c)

Statement (c) asserts that in the chemical equation \(aA + bB \rightarrow C\), \(a = 0\) and \(b = 3\). Practically, \(a\) cannot be zero in a chemical equation as it denotes no consumption of \(A\). Hence, consider this statement incorrect until further data supports the stoichiometry.

Step 5: Analyze Statement (d)

Statement (d) states the overall order of reaction is third order, aligning with the rate law proposed in statement (b) if true. Without disputing experimental basis for now, it aligns theoretically.

Step 6: Conclude Invalid Statement

Based on classical stoichiometry, a scenario where \(a\) is 0 seems most incorrect without context support. Therefore, statement (c) is incorrect.

Key Concepts

Reaction Rate

In the world of chemical kinetics, the reaction rate is pivotal. It tells us how quickly a reaction occurs. Reaction rates are measured by the change in concentration of reactants or products over time. The rate can vary due to several factors. Common influences include reactant concentration, temperature, catalyst presence, and even the physical state of reactants. Having a handle on reaction rate is crucial for controlling chemical processes. It benefits both industrial applications and laboratory research.

• Increased concentration of reactants usually speeds up the reaction.
• A higher temperature often leads to faster reactions, as particles move more energetically.
• Catalysts dramatically influence rates by providing alternative pathways with lower activation energy.

Each of these elements can change the reaction rate, making it a constant dance of variables.

Rate Law

The rate law is an essential expression in chemical kinetics that accounts for the reaction rate based on reactant concentrations. It takes the general form: \[ ext{Rate} = k[A]^m[B]^n\]Here, \(k\) is the rate constant, \([A]\) and \([B]\) are concentrations of reactants, and \(m\) and \(n\) signify reaction orders in respect to their reactants. What makes it truly unique? It is empirically determined through experiments, making it specific to each reaction.A remarkable feature of the rate law is its power to predict how changes in concentration impact the reaction rate.

• A doubling concentration of reactant \(A\) may significantly alter the rate if \(m\) is substantial.
• The rate law also indicates if reactant \(B\) has a greater effect on the rate through its order \(n\).

Activation Energy

Activation energy (\(E_a\)) is the energy barrier that must be overcome for a reaction to proceed. Think of it as the hill reactants must climb to transform into products. Activation energy is crucial because it determines the sensitivity of the rate constant to temperature changes.Using the Arrhenius equation: \[k = Ae^{-E_a/(RT)}\]- \(k\) is the rate constant.- \(A\) is the pre-exponential factor.- \(R\) is the gas constant.- \(T\) is temperature in Kelvin.From this, we see that as activation energy decreases, reactions speed up. That's why catalysts are important: they lower the activation energy, paving an easier path for the reaction.

Reaction Order

Understanding reaction order is vital for predicting the reaction behavior under various conditions. The reaction order is the sum of the powers of concentration terms in the rate law:\[ ext{Overall Reaction Order} = m + n \]This order can be fractional or even zero, but it directly impacts how rate changes with concentration.

• First-order reactions have rate proportional to the concentration of one reactant.
• Second-order involves either two different first-order reactants or one second-order reactant.
• Zero-order means rate is independent of the concentration of reactants.

Reaction order helps in designing reactors and understanding mechanisms behind reactions. It's like the rules guiding how the reaction proceeds.