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Chapter 8: Problem 191

The rate law has the form; Rate \(=\mathrm{k}[\mathrm{A}][\mathrm{B}]^{3 / 2}\), can the reaction be an elementary process? a. yes b. no c. may be yes or no d. can not be predicted

Short Answer

Expert verified
b. no

Step by step solution

01

Understanding Elementary Reactions

Elementary reactions are single-step processes where the rate law is derived directly from the stoichiometry of the reaction itself. This means that the exponents in the rate law correspond to the coefficients of the balanced chemical equation for the reaction.
02

Defining Rate Laws for Elementary Reactions

For an elementary reaction where the rate law is given by Rate = \( k[A]^m[B]^n \), the exponents \( m \) and \( n \) must match the coefficients of species \( A \) and \( B \) in the balanced chemical equation. The exponents must be whole numbers because they physically represent the number of molecules involved in the elementary step.
03

Evaluating Given Rate Law

The given rate law is Rate = \( k[A][B]^{3/2} \). Here, the exponent of \( [B] \) is \( 3/2 \), which is not a whole number. This suggests that the rate law does not match a simple stoichiometry involving whole numbers.
04

Conclusion of Rate Law and Elementary Process

Since the exponent \( 3/2 \) is not a whole number, and because elementary reactions require whole number coefficients derived directly from stoichiometry, the reaction cannot be an elementary process.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Elementary Reactions
Elementary reactions are the simplest type of chemical reactions and represent fundamental steps that occur in a single stage. They occur exactly as they appear in the equation. Each molecule or atom directly participates exactly as described by the stoichiometric coefficients in the reaction.
For an elementary reaction, the rate law can be directly written from the stoichiometry. If a reaction's molecular equation is \( aA + bB \to products \), its rate law is \( ext{Rate} = k[A]^a[B]^b \). Importantly, the exponents, commonly known as the orders of reaction, must be whole numbers. This is because they represent the actual number of each molecule involved in the elementary step.
  • Rate laws derived from elementary reactions depend entirely on the molecularity of the reaction.
  • The orders of reaction provide insights into the number of molecules colliding in this step.
  • Examples include unimolecular reactions, bimolecular reactions, and rare termolecular steps.
Understanding these concepts helps in identifying whether a given reaction could be elementary.
Stoichiometry
Stoichiometry is the calculation of reactants and products in chemical reactions. It's essential for determining the relative quantities required and produced in a given reaction.
In the context of elementary reactions, stoichiometry is directly linked to the rate law. The stoichiometric coefficients from a balanced chemical equation become the exponents in the rate law if the reaction is elementary.
  • For example, in a reaction where 2 moles of A react with 1 mole of B to form products, the rate law for an elementary process would be \( ext{Rate} = k[A]^2[B]^1 \).
  • If the reaction is non-elementary, the rate law can involve fractional exponents or forms that are not directly linked to the balanced equation, indicating a complex mechanism.
  • It reveals how reactant concentrations influence the rate of reaction. This can only be predicted accurately if the reaction mechanism is known to be elementary and stoichiometry directly dictates the rate law.
Understanding stoichiometry is pivotal for analyzing whether a given rate law could be indicative of an elementary reaction.
Reaction Mechanisms
Reaction mechanisms describe the step-by-step process by which reactants are converted into products. They consist of a series of elementary reactions, providing a detailed pathway for the transformation.
Mechanisms help in understanding complex reactions that cannot be explained by a single elementary step. For each step, the rate law can be written based on stoichiometry, but the overall reaction may require combining these steps to deduce the global rate law.
  • Individual steps in a mechanism must sum up to the overall stoichiometric equation.
  • The rate-determining step, typically the slowest in the sequence, controls the overall reaction rate and therefore shapes the rate law.
  • Intermediates may appear in a mechanism but not in the overall balanced equation.
By examining and understanding these mechanisms, chemists can rationalize why certain rate laws, like one involving fractional exponents such as \( [B]^{3/2} \), might suggest complex multi-step processes as opposed to a straightforward elementary reaction.

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Most popular questions from this chapter

The bromination of acetone that occurs in acid solution is represented by this equation. \(\mathrm{CH}_{3} \mathrm{COCH}_{3}(\mathrm{aq})+\mathrm{Br}_{2}\) (aq) \(\rightarrow\) \(\mathrm{CH}_{3} \mathrm{COCH}_{2} \mathrm{Br}(\mathrm{aq})+\mathrm{H}^{+}(\mathrm{aq})+\mathrm{Br}(\mathrm{aq})\) These kinetic data were obtained from given reaction concentrations. Initial concentrations, (M) \(\begin{array}{lll}{\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]} & {\left[\mathrm{Br}_{2}\right]} & {\left[\mathrm{H}^{+}\right]} \\ 0.30 & 0.05 & 0.05 \\ 0.30 & 0.10 & 0.05 \\\ 0.30 & 0.10 & 0.10 \\ 0.40 & 0.05 & 0.20 \\ \text { Initial rate, disappearance of } & \end{array}\) disappearance of \(\mathrm{Br}_{2}, \mathrm{Ms}^{-1}\) \(5.7 \times 10^{-5}\) \(5.7 \times 10^{-5}\) \(1.2 \times 10^{-4}\) \(3.1 \times 10^{-4}\) Based on these data, the rate equation is: a. Rate \(=\mathrm{k}\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]\left[\mathrm{Br}_{2}\right]\left[\mathrm{H}^{+}\right]^{2}\) b. Rate \(=\mathrm{k}\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]\left[\mathrm{Br}_{2}\right]\left[\mathrm{H}^{+}\right]\) c. Rate \(=\mathrm{k}\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]\left[\mathrm{H}^{+}\right]\) d. Rate \(=\mathrm{k}\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]\left[\mathrm{Br}_{2}\right]\)

In the following question two statements Assertion (A) and Reason (R) are given Mark. a. If \(\mathrm{A}\) and \(\mathrm{R}\) both are correct and \(\mathrm{R}\) is the correct explanation of \(\mathrm{A}\); b. If \(A\) and \(R\) both are correct but \(R\) is not the correct explanation of \(\mathrm{A}\); c. \(\mathrm{A}\) is true but \(\mathrm{R}\) is false; d. \(\mathrm{A}\) is false but \(\mathrm{R}\) is true, e. \(\mathrm{A}\) and \(\mathrm{R}\) both are false. (A): A catalyst does not alter the heat of reaction. (R): Catalyst increases the rate of reaction.

The equation tris(1,10-phenanthroline) iron(II) in acid solution takes place according to the equation: \(\mathrm{Fe}(\text { phen })_{3}^{2+}+3 \mathrm{H}_{3} \mathrm{O}^{+}+3 \mathrm{H}_{2} \mathrm{O} \rightarrow\) $$ \mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{2+}+3 \text { (Phen) } \mathrm{H}^{+} $$ If the activation energy (Ea) is \(126 \mathrm{~kJ} / \mathrm{mol}\) and the rate constant at \(30^{\circ} \mathrm{C}\) is \(9.8 \times 10^{-3} \mathrm{~min}^{-1}\), what is the frequency factor (A)? a. \(9.5 \times 10^{18} \mathrm{~min}^{-1}\) b. \(2.5 \times 10^{19} \mathrm{~min}^{-1}\) c. \(55 \times 10^{19} \mathrm{~min}^{-1}\) d. \(5.0 \times 10^{19} \mathrm{~min}^{-1}\)

Which of the following statements are true about reaction mechanisms? (I) A rate law can be written from the molecularity of the slowest elementary step. (II) The final rate law can include intermediates. (III) The rate of the reaction is dependent on the fastest step in the mechanism. (IV) A mechanism can never be proven to be the correct pathway for a reaction. a. I and II b. I and IV c. II and III d. I, II and III

In the following question two statements Assertion (A) and Reason (R) are given Mark. a. If \(\mathrm{A}\) and \(\mathrm{R}\) both are correct and \(\mathrm{R}\) is the correct explanation of \(\mathrm{A}\); b. If \(A\) and \(R\) both are correct but \(R\) is not the correct explanation of \(\mathrm{A}\); c. \(\mathrm{A}\) is true but \(\mathrm{R}\) is false; d. \(\mathrm{A}\) is false but \(\mathrm{R}\) is true, e. \(\mathrm{A}\) and \(\mathrm{R}\) both are false. (A): \(2 \mathrm{FeCl}_{3}+\mathrm{SnCl}_{2} \rightarrow \mathrm{FeCl}_{2}+\mathrm{SnCl}_{4}\) is a \(3^{\text {nd }}\) order reaction ( \(\mathbf{R}\) ): The rate constant for third order reaction has unit \(\mathrm{L}^{2} \mathrm{~mol}^{-2} \mathrm{~s}^{-1}\).
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