Question

Consider the reaction \(\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{C}+\mathrm{D} .\) Is each of the following statements true or false? (a) The rate law for the reaction must be Rate \(=k[\mathrm{A}][\mathrm{B}] .\) (b) If the reaction is an elementary reaction, the rate law is second order. (c) If the reaction is an elementary reaction, the rate law of the reverse reaction is first order. (d) The activation energy for the reverse reaction must be greater than that for the forward reaction.

Short answer

The short version of the answer is: (a) False (b) True (c) False (d) False

Step-by-step solution

(a) Checking the rate law for the reaction

: The statement says the rate law must be \(Rate = k[A][B]\). This is not necessarily true. The rate law of the reaction would depend on the reaction mechanism and would be determined experimentally. So, the provided statement is false.

(b) Checking if the rate law is second order for an elementary reaction

: If the given reaction is an elementary reaction, then the rate law would depend on the concentrations of the reacting species with an exponent equal to their stoichiometric coefficients. In this case, the rate law would be \(Rate = k[A][B]\). This is indeed a second-order reaction. So, the provided statement is true.

(c) Checking if the rate law of the reverse reaction is first order for an elementary reaction

: The reverse reaction would be \(C + D \longrightarrow A + B\). If the given reaction is an elementary reaction, then the rate law of the reverse reaction would also depend on the concentrations of the reacting species in the reverse reaction, with an exponent equal to their stoichiometric coefficients. In this case, the rate law for the reverse reaction would be \(Rate = k'[C][D]\). This is also a second-order reaction, not first order. So, the provided statement is false.

(d) Checking if the activation energy for the reverse reaction must be greater than that for the forward reaction

: The activation energy for the reverse reaction (\(E_{a,reverse}\)) doesn't necessarily have to always be greater than that for the forward reaction (\(E_{a,forward}\)). The relation between the activation energies would depend on the reaction and cannot be generalized. So, the provided statement is false. In summary: (a) False (b) True (c) False (d) False

Key concepts

Rate Law

Rate law is a fundamental concept in reaction kinetics. It explains how the rate of a chemical reaction depends on the concentration of the reactants. The rate law is generally expressed in the form: \[ \text{Rate} = k[A]^m[B]^n \]where:- \( k \) is the rate constant,- \([A]\) and \([B]\) are the concentrations of the reactants,- \( m \) and \( n \) are the orders of the reaction with respect to each reactant.

It is important to note that the orders \( m \) and \( n \) are not simply the stoichiometric coefficients from the balanced equation; they must be determined experimentally. This means that, for complex reactions, rate laws can vary significantly from expected values based on stoichiometry.

For the given reaction \(\mathrm{A} + \mathrm{B} \rightarrow \mathrm{C} + \mathrm{D} \), the rate law \( \text{Rate} = k[A][B] \) might imply a second-order reaction only if the reaction occurs in a single step as an elementary process with respective stoichiometric coefficients one each for A and B.

Elementary Reaction

An elementary reaction is a single-step process within a reaction mechanism where reactants are converted directly into products. The distinct feature of elementary reactions is that their rate laws can be directly written from their stoichiometric equations.

For example, if you have an elementary reaction \(\mathrm{A} + \mathrm{B} \rightarrow \mathrm{C} + \mathrm{D}\), the rate law is simply:\[ \text{Rate} = k[A][B] \]This means that the reaction is second-order, as each reactant contributes a power of one to the rate equation, based directly on their stoichiometry.

However, if the reaction is not elementary, the rate law cannot be straightforwardly derived from stoichiometry, and experimental methods must be employed to determine it. Elementary reactions often serve as the building blocks composing more complex reaction mechanisms.

Activation Energy

Activation energy (\(E_a\)) is the minimum energy required to initiate a chemical reaction. It is a crucial factor in understanding how fast a reaction will occur. The higher the activation energy, the slower the reaction, as more energy is required to reach the transition state.

Activation energy can differ between the forward and reverse reactions. For instance, in the given reversible reaction:\[ \mathrm{A} + \mathrm{B} \rightleftharpoons \mathrm{C} + \mathrm{D} \]the activation energy for the reverse reaction may or may not be greater than the activation energy for the forward reaction, as it depends on the specific reaction path and energy barriers involved.

In practical terms, catalysts are often used to lower the activation energy required for a reaction, which speeds up both the forward and reverse reactions, without changing the equilibrium position. Understanding activation energy is essential for controlling reaction rates in both industrial and laboratory settings.