Question

part 2: continued

1. use the concentrations values and rates determined for each time to find the order of reaction with respect to di - t - butyl peroxide.
2. what units will the rate constant k have for this reaction? what is the magnitude of k?
3. write the complete (differential) rate law for this reaction. include all information you have available.
4. what is the corresponding integrated rate law for this reaction?
5. how much time would it take before the concentration of di - t - butyl peroxide reaches 0.10 μmol/l?

checkpoint 1
part 3: defining a reaction mechanism
the synthesis of ammonia (nh3) from nitrogen gas (n2) is one of the most important industrial processes worldwide.
the reaction coordinate diagram shown on the right for the uncatalyzed and catalyzed processes.

1. for the uncatalyzed reaction:

a. how many elementary steps does the reaction have?
b. which step is the rate - determining step?
c. how many transition states are there in this mechanism? how many intermediates?
d. what step has the largest rate constant k?
e. is the overall reaction endothermic or exothermic?

1. for the catalyzed reaction:

a. did the catalyst affect the overall energy change of the reaction? (should we expect it to?)
b. does the addition of a catalyst affect the final yield of the reaction?
c. explain using kinetic - molecular theory and collision theory how the addition of a catalyst will affect the rate of the reaction.

Explanation:

Step1: Analyze part 2 questions

For question 3, we use rate - concentration data to find reaction order. For question 4, we use the general rate law to find units of rate constant. For question 5, we write the differential rate law based on reaction order. For question 6, we derive the integrated rate law from the differential rate law. For question 7, we use the integrated rate law to solve for time.

Step2: Analyze part 3 questions (uncatalyzed reaction)

For 1a, we count the number of peaks in the reaction - coordinate diagram to find the number of elementary steps. For 1b, the rate - determining step is the step with the highest activation energy. For 1c, transition states are at the peaks and intermediates are at the valleys. For 1d, the step with the lowest activation energy has the largest rate constant. For 1e, we compare the energy of reactants and products to determine if the reaction is endothermic or exothermic.

Step3: Analyze part 3 questions (catalyzed reaction)

For 2a, a catalyst does not affect the overall energy change of a reaction. For 2b, a catalyst does not affect the final yield of a reaction. For 2c, we explain based on kinetic - molecular and collision theories that a catalyst lowers the activation energy, increasing the frequency of effective collisions and thus the reaction rate.

Answer:

Detailed answers for each sub - question would require the actual concentration values and rates (for part 2) and a more in - depth analysis of the reaction - coordinate diagram. But in general:
For part 2:

1. Reaction order is found by comparing rate changes with concentration changes.
2. Units of \(k\) depend on reaction order (\(M^{1 - n}s^{-1}\) for an \(n\)th - order reaction).
3. Differential rate law: \(rate = k[A]^n\) (where \([A]\) is the concentration of di - t - butyl peroxide and \(n\) is the reaction order).
4. Integrated rate law depends on \(n\) (e.g., for first - order: \(\ln\frac{[A]_0}{[A]_t}=kt\)).
5. \(t=\frac{1}{k}\ln\frac{[A]_0}{[A]_t}\) (for first - order, adjust according to actual reaction order).

For part 3 (uncatalyzed reaction):
1a. Number of elementary steps = number of peaks in the diagram.
1b. Rate - determining step is the step with the highest activation energy.
1c. Number of transition states = number of peaks, number of intermediates = number of valleys.
1d. Step with the lowest activation energy has the largest \(k\).
1e. If products have higher energy than reactants, endothermic; if lower, exothermic.
For part 3 (catalyzed reaction):
2a. No, a catalyst does not affect the overall energy change.
2b. No, a catalyst does not affect the final yield.
2c. A catalyst lowers the activation energy, increasing the frequency of effective collisions and thus the reaction rate according to kinetic - molecular and collision theories.