# The following reaction is first order in A (red spheres) and first order in B (blue spheres): A + B Products Rate = k[A][B]

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The following reaction is first order in A (red spheres) and first order in B (blue spheres):
A + B Products Rate = k[A][B]      12.22 (a) What are the relative rates of this reaction in vessels (1)–(4)? Each vessel has the same volume. (b) What are the relative values of the rate constant k for cases (1)–(4)?

Consider the first-order decomposition of A molecules (red spheres) in three vessels of equal volume. 12.23 (a) What are the relative rates of decomposition in vessels (1)–(3)? (b) What are the relative half-lives of the reactions in vessels (1)–(3)? (c) How will the rates and half-lives be affected if the volume of each vessel is decreased by a factor of 2?

Consider the first-order reaction A B in which A molecules (red spheres) are converted to B molecules (blue spheres). 12.24 (a) Given the following pictures at t = 0 min and t = 1 min, draw pictures that show the number of A and B molecules present at t = 2 min and t = 3 min. (b) What is the half-life of the reaction?

12.25 The following pictures represent the progress of the reaction A B in which A molecules (red spheres) are converted to B molecules (blue spheres). (a) What is the order of the reaction? (b) Draw a picture that shows the number of A and B molecules present at t = 3 min. (c) Suppose that each sphere represents 6.0  molecules and that the volume of the container is 1.0 L. What is the rate constant for the reaction in the usual units?

12.26 The following pictures represent the progress of a reaction in which two A molecules combine to give a more complex molecule A2, 2A A2. (a) Is the reaction first order or second order in A? (b) What is the rate law? (c) Draw an appropriate picture in the last box, and specify the time.

12.27 What is the molecularity of each of the following elementary reactions?

12.28 Consider a reaction that occurs by the following mechanism: A + BC AC + B AC + D A + CD The potential energy profile for this reaction is shown to the right: (a) What is the equation for the overall reaction? Write structural formulas for all species present at reaction stages 1–5. Identify each species as a reactant, product, catalyst, intermediate, or transition state. Which of the two steps in the mechanism is the rate-determining step? Write the ratelaw for the overall reaction. Is the reaction endothermic or exothermic? Add labels to the diagram that show the values of the energy of reaction ∆E and the activation energy Ea for the overall reaction. (b) (c) (d)

Draw a plausible transition state for the bimolecular reaction of nitric oxide with ozone. Use dashed lines to indicate the atoms that are weakly linked together in the transition state. 12.29

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