Chapter 14: Problem 89

Consider the reaction \(2 \mathrm{~A} \longrightarrow \mathrm{B}\). Is each of the following statements true or false? (a) The rate law for the reaction must be, Rate \(=k[\mathrm{~A}]^{2} .(\mathbf{b})\) If the reaction is an elementary reaction, the rate law is second order. \((\mathbf{c})\) 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 smaller than that for the forward reaction.

Short Answer

Expert verified

(a) The rate law for the reaction could potentially be Rate = \(k[A]^{2}\) if it is second order in A. (b) True. If the reaction is elementary, the rate law must be second order (Rate = \(k[A]^2\)). (c) True. The rate law for the reverse reaction must be first order (Rate = \(k'[B]\)). (d) False. The activation energy of the reverse reaction doesn't necessarily need to be smaller than that for the forward reaction.

Step by step solution

This statement is true. The rate law for a reaction is given by the rate constant (k) multiplied by the concentration of the reactants raised to their respective orders. Since the stoichiometric coefficient for A in the balanced reaction is 2, the reaction can be second order in A. However, we must also consider that the order of the reaction is determined experimentally, and the stoichiometric coefficients do not always correspond to the order of the reaction. Therefore, this statement should be clarified as "the rate law for the reaction could potentially be Rate = k[A]^2 if it is second order in A." #Statement B: If the reaction is an elementary reaction, the rate law is second order#

This statement is true. An elementary reaction is a single step reaction and the reaction order can be determined based on the stoichiometric coefficients of the reactants. In this case, the stoichiometric coefficient for A is 2, so if the reaction is elementary, the rate law must be second order (Rate = k[A]^2). #Statement C: If the reaction is an elementary reaction, the rate law of the reverse reaction is first order#

This statement is true. The reverse reaction has the form: B -> 2A. For elementary reactions, the reaction order corresponds to the stoichiometric coefficients of the reactants. Since the stoichiometric coefficient for B in the reverse reaction is 1, the rate law for the reverse reaction must be first order (Rate = k'[B]). #Statement D: The activation energy for the reverse reaction must be smaller than that for the forward reaction#

This statement is false. There is no rule that states the activation energy of the reverse reaction must be smaller than that for the forward reaction. The activation energy of a reaction is determined by the energy barrier that needs to be surpassed for the reaction to occur. The activation energies for the forward and reverse reactions can be different, but there is no requirement that one must be smaller than the other.