Unit 6 Test Review KEY

1. Use the following experimental data to calculate the rate law for the following reaction. All data were taken at 50.0°C.

A + 2B + 3C → 2Y + Z.

a. Write the rate law for the overall reaction.

= =

b. What is the order with respect to B? Explain. B is first order. When comparing experiments 1 and 2, the concentration of A and C remain constant, while the concentration of B increases 1.5 times. Since the rate also increases by a factor of 1.5, B must be first order.

c. Calculate the rate constant. Include appropriate units.

=

= . .

=

∙=

∙=

=∙

=∙

=∙

d. What is the initial rate of this reaction if each reactant has a concentration of 0.5 M?

= ( . ) ( . )

=∙

Unit 6 Test Review KEY

e. If the rates given in the table are the disappearance rates of B, what is the initial rate of disappearance of C in trial #3? The rate of formation of Y in experiment #6?

− ∆

∆= −

∆∆

− (− ) = − ∆

∆

∆

∆= −

∙

− ∆

∆= +

∆∆

− (− ) = − ∆

∆

∆

∆= +

∙

2. It is known that compounds called chlorofluorocarbons will break up in the presence of ultraviolet radiation, such as found in the upper atmosphere, forming single chlorine atoms.

→ + The Cl atoms then react with ozone, O3, as outlined in the following mechanism.

1: + → + 2: + → +

a. Write the equation for the overall reaction.

+ →

b. Identify any catalysts and intermediates in the reaction mechanism.

Cl is used up in step 1, but then produced again in step 2, so it is a catalyst. ClO is produced in step 1, but then consumed in step 2, so it is an intermediate.

c. If the rate law for the reaction is known to be rate = k[Cl][O3], which step is likely the rate determining step? Justify your response. The rate law for the slowest step in a mechanism will match the rate law of the overall reaction. Since the rate law of step is rate = k [Cl] [O3], this must be the slow step.

3. Consider the following reaction:

+ → +

a. The first step in each of two proposed reaction mechanisms for the above reaction is listed below. If each proposed reaction mechanism consists of only two steps, determine the second step of the mechanism.

Proposed mechanism 1

1: 2 → +

2: + → +

Unit 6 Test Review KEY

Proposed mechanism 2

1: 2 →

2: + → + +

b. Experimental data shows that the rate of the reaction is not affected by a change in the concentration of CO. Which of the two proposed mechanisms is consistent with this data? Justify your response. In mechanism 1, the slow step has a rate law that does not contain [CO], while in the second mechanism, the slow step does include the [CO]. Since experimental data shows that [CO] does not affect the rate of the reaction, it should not be in the rate law. Therefore, mechanism 1 is more consistent with this data.

c. If the initial concentration of NO2 is 0.893 M and it takes 4.70 minutes for the concentration to decrease

to 0.103 M, calculate the value of k. Include appropriate units.

= ,

− =

.−

.= .

= .∙

d. How much time must elapse for the concentration of NO2 to decrease to 0.057 M?

− =

.−

.= .

= .

Unit 6 Test Review KEY

4. Use the following reaction coordinate diagram to answer the questions that follow.

a. Which arrow indicates the activation energy for the first step of the reverse reaction? 5 b. Which arrow indicates the activation energy for the first step of the forward reaction? 1 c. Which arrow indicates the activation energy for the second step of the forward reaction? 2 d. Which arrow indicates the enthalpy change for the overall forward reaction? 6 e. Which arrow indicates the enthalpy change for the overall reverse reaction? 6 f. Which arrow indicates the activation energy for the overall forward reaction? 3 g. Which step would be the rate determining step for the forward reaction? The 2nd step h. Which step would be the rate determining step for the reverse reaction? The 2nd step

5. The organic compound methyl isonitrile (CH3NC) can form an isomer, acetonitrile (CH3CN), as represented in the reaction below.

( ) → ( )

− → − The graph below reflect a single set of reaction rate data plotted in three different ways, where the concentration of the CH3NC is proportional to the partial pressure in torr.

a. Given the information provided above, what are the order of the reaction and the approximate value of the rate law constant k? Since the natural log of pressure vs time is the straightest line, the reaction must be first order. This means that the slope of that line will be the value of the rate constant, k.

− = = −. − .

−=

Unit 6 Test Review KEY

6. Use the reaction given below and the data in the table to answer a – d.

X + 2Y 3Z

Instantaneous Rates Time

(minutes) [X] ∆

∆

∆∆

∆

∆

0 1.032 4.375 ∙

0.25 0.675 - 1.142 ∙

0.5 0.309 2.472 ∙

0.75 0.128 1.539 ∙

1.0 0.073 0.601 ∙

a. Write two statements that compare the rates of the different substances in the reaction. Y disappears twice as fast as X X disappears at half the rate of Y. Z forms at three times the rate that X decomposes. Etc.

b. Calculate the average reaction rate of X during the first 0.25 minutes of the reaction and during the last

0.25 minutes of the reaction. How does the rate of the reaction change over time?

∆∆

=. − .

. −= − .

∙

∆

∆=

. − .. − .

= − .∙

c. Calculate the instantaneous rate of reaction of Y and of Z at 0.25 minutes and fill in those values on the

table above. Show all work.

− ∆

∆= −

∆∆

− (− . ) = −∆

∆

∆

∆= − .

∙

Unit 6 Test Review KEY

− ∆

∆= +

∆∆

− (− . ) = +∆

∆

∆

∆= .

∙

d. Complete the graph below using information in the table.

e. Does this agree with your response in part b about how the rate of reaction changes over time?

Yes, it agrees. In part b we saw that the rate decreased over time, and this is what is observed in the graph as well. 7. Blue food dye can be oxidized by household bleach (containing OCl- ions) according to the reaction below.

+ → A student used a spectrophotometer set at a wavelength of 635 nm to study the absorbance of the food dye over time as this reaction takes place. The bleach was present in large excess, so it’s concentration remained relatively constant the whole time. The following data is gathered.

a. What particle in the reaction is being monitored by the line shown in the graph? How do you know? Since the products and OCl- ion are all colorless, absorbance can only measure the concentration of the blue dye.

Rate

of r

eact

ion

of Z

, ∙

Time, minutes

blue colorless colorless

Unit 6 Test Review KEY

b. At what time was the reaction proceeding at the fastest instantaneous rate?

At time 0, the reaction is proceeding at the fastest rate. The slope of the absorbance vs. time graph is steepest at this point, indicating the fastest rate of change.

c. The absorbance values were measured at a path length of 1 cm and in an aqueous solution with a molar

absorptivity of 1.09/Mcm. Calculate the average rate of disappearance of blue dye from 40 to 60 seconds in mol/Lsec.

=

. = ( . )( )

= .

=

. = ( . )( )

= .

∆

∆=

. − .−

=− .

= − .∙

d. What would the average rate of disappearance of hypochlorite ion, OCl-, be in that same time period?

Since the two reactants both have coefficients of 1 in the balanced chemical reaction, they should react at the same rate. So the OCl- will also react at -0.0046 M/s in the same time period.

e. How would this experiment be performed differently if red dye was used instead of a blue dye?

This experiment was performed using a spectrophotometer taking measurements at 635 nm, which was likely chosen to achieve maximum absorbance of the blue dye particles. If red dye was being used, then a different wavelength would have to be selected. For red solutions, a color other than red, such as blue light, would be more suitable.

8. The initial rate data for the reaction shown below is summarized in the table.

+ →

Experiment [A] [B] ∆

∆ ( )

1 0.5 1.3 2.24x10-3 ∙

2 0.75 1.3 3.36x10-3 ∙

3 0.75 2.09 8.68x10-3 ∙

x 1.5

x 1.5

x 1.61

x 2.58

Unit 6 Test Review KEY

a. Write the rate law for the reaction. When [B] remains constant and [A] increases by a factor of 1.5, the rate also increases by a factor of 1.5. A is therefore 1st order. When [A] remains constant and [B] increases by a factor 1.6, the rate increases by a factor of 2.58. B is therefore 2nd order.

=

b. Calculate the rate constant, k. Include appropriate units. Plug in any experiment from the table and calculate k.

=

. = . .

. = .

= .

∙=

∙=

=∙

=∙

= .∙

Conceptual Questions: 1. What is a reaction rate and how is it measured? How do the rates of decomposition compare to rates of appearance of products? Does stoichiometry play a role? Reaction rate is the speed of the reaction, measured most commonly by tracking how the concentration changes with time. As reactants decompose, their concentrations will decrease, so rate values are negative. As products appear, their concentrations increase, so rate values are positive. Stoichiometry plays an important role. For the reaction A + 2B 3C, the rate of disappearance of B will be twice that of A, and the rate of appearance of C will be triple that of A. 2. The method of initial rates is one way to determine the order of a reaction and the rate law. What is another? Three graphs can be produced: concentration vs. time, ln(concentration) vs. time, and 1/concentration vs. time. If concentration vs. time is a straight line, the reaction is 0th order. If the natural log of the concentration is a straight line, the reaction is 1st order. If the inverse of the concentration vs. time is a straight line, the reaction is second order. Knowing the order of the overall reaction sometimes allows you to write the rate law.

Unit 6 Test Review KEY

3. Compare 0th order, 1st order and 2nd order reactions in terms of how their concentration changes with time, their rate laws, their half-lives and their initial rates. 0th order reactions are the only ones whose reaction rate does not vary with reactant concentration. As time goes on, 1st and 2nd order reactions become slower, while 0th order reactions keep going at the same speed. 0th order reactions have half-lives that decrease with time, while 1st order reaction half-lives remain constant and 2nd order reaction half-lives increase. In general, 2nd order reactions start off going faster than a 1st order reaction would, but the 2nd order reaction will slow down more quickly. 4. Use the collision theory of reaction rates to explain why higher temperatures, higher concentrations, and more surface area result in higher concentrations. At higher temperatures, reactant particles move faster, and collide with each other more, resulting in more reaction producing collisions, and a faster reaction rate. At higher concentrations, there are more reactant molecules so they collide with each other more, resulting in more reaction producing collisions, and a faster reaction rate. 5. How does the speed of a reaction with a lower activation energy compare to the speed of a reaction with higher activation energy? Lower Ea reactions will go faster because more particles will meet or exceed the energy value that is needed for a reaction to take place. 6. What are the different types of catalysts and how does each function differently? Acid-base catalysts, surface catalysts and enzyme catalysts. Most function by allowing the particles to collide in an orientation that is more likely to lead to the proper bond rearrangement and product formation. In all cases however, a catalyst increases the speed of a reaction by lowering the activation energy. 7. How can reaction mechanisms be used to determine the rate law for reactions? What would you have to know about the elementary steps in the mechanism in order to determine the rate law for the overall process? If the slowest step of a reaction mechanism is known, that step will control the rate of the overall reaction. Therefore, the rate law for the slow step, or the rate determining step, will be the same as that of the overall reaction. 8. What is meant by the terms unimolecular, bimolecular and termolecular? Are all of these types of reactions likely to happen? This term refers to how many particles must collide simultaneously for an elementary step of a reaction to occur. Uni- means one reactant simply decomposes, bi- means two reactants must collide, and ter- means that 3 reactant particles must collide. Since it is not likely for 3 particles to collide at the same time, termolecular steps or greater, are not commonly seen. 9. What is the difference between intermediates and catalysts? Intermediates are produced in one elementary step, but then used up in a later step. They do not appear in the net reaction. Catalysts however, are present at the start of the reaction, are changed in some way, and then converted back to their original form. They do not technically appear in the net reaction, but are sometimes written over the reaction arrow to represent their presence.

Unit 6 Test Review KEY

10. What is the difference between an average rate and an instantaneous rate? An average rate is the change in some variable over a range of times, while an instantaneous rate is the change in some variable at any one give instant in time. For reaction rates, the average can be found by ∆[reactant] / ∆t. The instantaneous rate can be found the slope of the tangent line to a curve that is tracking the reactant concentration vs. time. 11. Determine the order of the reaction (0, 1 or 2) based on the given information.

a. For the reaction A B + C, the [A]initial is 0.1 M. After 2 total seconds, the concentration decreases to 0.05 M. After 4 total seconds, the concentration decreases to 0.04 M. The reaction can’t be 0th order because the rate slows down as time goes on. The reaction can’t be first order because it doesn’t have a constant half-life. It must therefore be second order.

b. For the reaction Q R + S, the [R] increases 0.0037 M every minute until there is no more Q. The concentration of R changes by the same amount each minute, regardless of changing concentrations over time. In other words, the rate is constant throughout the reaction. This is only true for 0th order reactions. c. For the reaction X Y + Z, the [X]initial is 1.2 M. After five total minutes, the concentration decreases to 0.60 M. After ten total minutes, the concentration decreases to 0.30 M. The concentration of reactants decreases by half in the same quantity of time, so the half-life is constant. This is only true for 1st order reactions. d. For the reaction L M + N, [N] increases at a constant rate.

This is only true for 0 order reactions. 1st and 2nd order reactions have changing rates over time.

e. For the reaction F G + H, the ∆

∆ is 0.057 at t = 1.5 hours. At t = 4 hours, the ∆

∆ is also 0.057.

The rate is the same at different times, this is only true for 0 order reactions. 1st and 2nd order reactions have changing rates over time.

f. For the reaction W + X U + V, the [X]initial is 0.20 M. After 10 total minutes, the concentration decreases to 0.15 M. After 20 total minutes, the concentration decreases to 0.10 M. The concentration of R changes by the same amount each minute, regardless of changing concentrations over time. In other words, the rate is constant throughout the reaction. This is only true for 0th order reactions.