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Ch.14 - Chemical Kinetics
McMurry - Chemistry 8th Edition
McMurry8th EditionChemistryISBN: 9781292336145Not the one you use?Change textbook
All textbooksMcMurry 8th EditionCh.14 - Chemical KineticsProblem 43c
Chapter 14, Problem 43c

The following pictures represent the progress of the reaction AS B in which A molecules (red spheres) are converted to B molecules (blue spheres).
(c) Suppose that each sphere represents 6.0⨉1021 molecules and that the volume of the container is 1.0 L. What is the rate constant for the reaction in the usual units?

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Determine the initial concentration of A molecules by counting the number of red spheres in the initial picture and multiplying by 6.0\(\times\)10^{21} to find the number of molecules. Divide by Avogadro's number to convert to moles, and then divide by the volume (1.0 L) to find the concentration in mol/L.
Determine the concentration of B molecules at a later time by counting the number of blue spheres in the later picture, multiplying by 6.0\(\times\)10^{21}, converting to moles, and dividing by the volume (1.0 L) to find the concentration in mol/L.
Use the change in concentration of A or B over time to calculate the rate of the reaction. The rate can be expressed as \(-\frac{\Delta [A]}{\Delta t}\) or \(\frac{\Delta [B]}{\Delta t}\), where \([A]\) and \([B]\) are the concentrations of A and B, respectively, and \(\Delta t\) is the time interval.
Assume a reaction order (e.g., first-order or second-order) based on the context or additional information provided. For a first-order reaction, the rate law is \(\text{Rate} = k[A]\), and for a second-order reaction, it is \(\text{Rate} = k[A]^2\).
Solve for the rate constant \(k\) using the rate law equation and the calculated rate and concentration values. Ensure the units of \(k\) are consistent with the assumed reaction order.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Rate of Reaction

The rate of a chemical reaction is a measure of how quickly reactants are converted into products. It is typically expressed in terms of concentration change over time, such as moles per liter per second (mol/L/s). Understanding the rate of reaction is crucial for determining how fast the conversion of A to B occurs in the given scenario.
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Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate law equation that relates the rate of a reaction to the concentration of reactants. It is specific to a particular reaction at a given temperature and has units that depend on the overall order of the reaction. For a first-order reaction, the units are typically s⁻¹, while for a second-order reaction, they are L/(mol·s).
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Concentration and Molarity

Concentration refers to the amount of a substance in a given volume of solution, commonly expressed in molarity (M), which is moles of solute per liter of solution. In this question, knowing that each sphere represents a specific number of molecules allows us to calculate the concentration of A and B in the 1.0 L container, which is essential for determining the rate constant.
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Related Practice
Textbook Question
The relative rates of the reaction A + B S AB in vessels (1)–(3) are 4:4:1. Red spheres represent A molecules, and blue spheres represent B molecules. (1)-(3)

(a) What is the order of the reaction in A and B?
Textbook Question
What is the molecularity of each of the following elementary reactions? (a)

(b)

(c)

Textbook Question

Consider the first-order decomposition of A molecules (red spheres) in three vessels of equal volume. (1)-(3)

(b) What are the relative half-lives of the reactions in vessels (1)–(3)?

Textbook Question
The following pictures represent the progress of a reaction in which two A molecules combine to give a more complex molecule A2, 2 AS A2.

(b) What is the rate law?
Textbook Question
Consider the first-order reaction AS B in which A molecules (red spheres) are converted to B molecules (blue spheres).

(a) Given the 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.
Textbook Question

The following pictures represent the progress of the reaction AS B in which A molecules (red spheres) are converted to B molecules (blue spheres).

(b) Draw a picture that shows the number of A and B molecules present at t = 3 min.