1. A(g) + B(g) → C(g)
The reaction above is second order with respect to A and zero order with respect to B. Reactants A and B are present in a closed container. Predict how each of the following changes to the reaction system will affect the rate and rate constant, and explain why.
(a) More gas A is added to the container.
(b) More gas B is added to the container.
(c) The temperature is increased.
(d) An inert gas D is added to the container.
(e) The volume of the container is decreased.
Correct Answer:
(a)
The rate of the reaction will increase because the rate depends on the concentration of A as given in the rate law: Rate = k[A]2.
The rate constant is independent of the concentration of the reactants and will not change.
(b)
The rate of the reaction will not change. If the reaction is zero order with respect to B, then the rate is independent of the concentration of B.
The rate constant is independent of the concentration of the reactants and will not change.
(c)
The rate of the reaction will increase with increasing temperature because the rate constant increases with increasing temperature.
The rate constant increases with increasing temperature because at a higher temperature more gas molecules will collide with enough energy to overcome the activation energy for the reaction.
(d)
Neither the rate nor the rate constant will be affected by the addition of an inert gas.
(e)
The rate of the reaction will increase because decreasing the volume of the container will increase the concentration of A: Rate = k[A]2.
The rate constant is independent of the concentration of the reactants and will not change.
2. Use your knowledge of kinetics to answer the following questions. Justify your answers.
(a)
The two lines in the diagram above show different reaction pathways for the same reaction. Which of the two lines shows the reaction when a catalyst has been added?
(b)
Which of the two lines in the energy distribution diagram shows the conditions at a higher temperature?
(c)
Which of the two lines in the diagram above shows the relationship of ln[A] to time for a first-order reaction with the following rate law?
Rate = k[A]
(d)
Which of the two graphs above shows the changes in concentration over time for the following reaction?
A → B
Correct Answer:
(a)
Line 2 is the catalyzed reaction. Adding a catalyst lowers the activation energy of the reaction, making it easier for the reaction to occur.
(b)
Line 2 shows the higher temperature distribution. At a higher temperature, more of the molecules will be at higher energies, causing the distribution to flatten out and shift to the right.
(c)
Line 1 is correct. The ln[reactant] for a first-order reaction changes in a linear fashion over time, as shown in the following equation.
ln[A]t = -kt + ln[A]0
y = mx + b
Notice the similarity to the slope-intercept form for a linear equation.
(d)
Graph 1 is correct, showing a decrease in the concentration of A as it is consumed in the reaction and a corresponding increase in the concentration of B as it is produced.
3. Hydrazine (N2H4) can be produced commercially via the Raschig process. The following is a proposed mechanism:
Step 1: NH3(aq) + OCl-(aq) → NH2Cl(aq) + OH-
Step 2: NH2Cl(aq) + NH3(aq) → N2H5+(aq) + Cl-
Step 3: N2H5+(aq) + OH- → N2H4(aq) + H2O(l)
(a) (i) What is the equation for the overall reaction?
(ii) Identify any catalysts or intermediates from the reaction mechanism.
(b) The rate law for the reaction is determined to be rate = k[NH3][OCl-]
(i) Which elementary step is the slowest one? Justify your answer.
(ii) If the reaction is measured over the course of several minutes, what would the units of the rate constant be?
Correct Answer:
Hydrazine (N2H4) can be produced commercially via the Raschig process. The following is a proposed mechanism:
Step 1: NH3(aq) + OCl-(aq) → NH2Cl(aq) + OH-
Step 2: NH2Cl(aq) + NH3(aq) → N2H5+(aq) + Cl-
Step 3: N2H5+(aq) + OH- → N2H4(aq) + H2O(l)
(a)
(i) What is the equation for the overall reaction?
To determine the net equation, all three equations must be added together, and species that appear on both sides of the arrow can be eliminated.
(ii) Identify any catalysts or intermediates from the reaction mechanism.
There are no catalysts present, but NH2Cl, N2H5+, and OH- are all intermediates in the process.
(b)
The rate law for the reaction is determined to be rate = k[NH3][OCl-].
(i) Which elementary step is the slowest one? Justify your answer.
The overall rate law will match the rate law of the slowest step. The rate law of an elementary step can be determined by the reactants present, and in this case, the rate law for Step 1 matches the overall rate law. Therefore, Step 1 is the slowest step.
(ii) If the reaction is measured over the course of several minutes, what would the units of the rate constant be?
Using unit analysis:
rate = k[NH3][OCl-]
M/min = k(M)(M)
k = M-1min-1
4. The reaction between crystal violet (a complex organic molecule represented by CV+) and sodium hydroxide is as follows:
As the crystal violet is the only colored species in the reaction, a spectrophotometer calibrated to a specific wavelength can be used to determine its concentration over time. The following data was gathered:
[CV+] (M) | Time (s) |
5.5 × 10-5 | |
3.8 × 10-5 | 60 |
2.6 × 10-5 | 120 |
1.8 × 10-5 | 180 |
(a) (i) What is the rate of disappearance for crystal violet from t = 60 s to t = 120 s?
(ii) If the solution is placed in the spectrophotometer 30 s after mixing instead of immediately after mixing, how would that affect the calculated rate of disappearance for crystal violet in part (i)?
(b) Given the path length of the cuvette is 1.00 cm and the molar absorptivity of the solution is 26,000 cm-1M-1 at the wavelength of the spectrophotometer, what would the absorbance reading on the spectrophotometer be at t = 60 s?
(c) This reaction is known to be first order with respect to crystal violet. On the provided axes, graph a function of [CV+] vs. time that will provide you with a straight line graph.
The following data was also gathered over the course of three experiments:
(d) Write the rate law for this reaction.
(e) What is the rate constant, k, for this reaction? Include units in your answer.
(f) Determine the initial rate of formation of CVOH for experiment 3.
Correct Answer:
(a)
(i) 
(ii) The solution starts reacting (and thus, fading) immediately after it is mixed. If the student waited 30 seconds before putting the cuvette in, the calculated rate of disappearance would thus decrease.
(b)
A = abc
A = (26,000 cm-1M-1)(1.00 cm)(3.8 × 10-5 M)
A = 0.98
(c)
A reaction that is first order with respect to [CV+] will create a straight line in a graph of ln [CV+] vs. time.
(d)
Between trials 1 and 2, the value of the [CV+] remained constant, while the [OH-] doubled. At the same time, the rate of reaction also doubled, meaning there is a direct relationship between [OH-] and the rate, so the reaction is first order with respect to [OH-]. The rate with respect to [CV+] has already been established as first order, so:
rate = k[CV+][OH-]
(e)
Either of the trials can be used for this. Taking trial 2:
7.20 × 10-7 M/s = k(5.5 × 10-5 M)(0.24 M)
k = 0.055 M-1s-1
(f)
Rate = k[CV+][OH-]
Rate = (0.055 M-1s-1)(4.1 × 10-5 M)(0.18 M)
Rate = 4.1 × 10-7s-1
