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Homework 8B: More Chemical Kinetics

There are select solutions to these problems here.

Q8B.1

In the reaction

\[\ce{3A + 2B \rightarrow C + D}\]

the reactant \(\ce{A}\) is disappear at the rate of \(-8.2 \times 10^{-4} \; M/s\).

  1. What is the rate of reaction at this point?
  2. What is the rate of disappearance of \(\ce{B}\)?
  3. What is the rate of formation of \(\ce{D}\)?

Q8B.3

In the reaction \(\ce{B \rightarrow products}\), \(\ce{[B]}\) is found to be 0.567M at \(\mathrm{t=31.6\,s}\) and 0.356M at \(\mathrm{t=50.3\,s}\). During this time interval, what is the average rate of the reaction?

Q8B.11

The initial rate of the reaction

\[\ce{2A + B \rightarrow 3C + D}\]

can be determined by the following table. Using the given information to:

  1. Find the order of reaction with respect to \(\ce{A}\) and to \(\ce{B}\).
  2. Solve the overall reaction order.
  3. Solve for the rate constant, \(\ce{k}\)
   \(\ce{[A]}\) M  \(\ce{[B]}\) M Initial rate M/s
Experiment 1 0.150 0.123 \(3.52 \times 10^{-3}\)
Experiment 2 0.150 0.246 \(1.408 \times 10^{-2}\)
Experiment 3 0.300 0.123 \( 7.04 \times 10^{-3}\)

Q8B.13

These rate were obtained in three experiments with the reaction

\[\ce{2CO(g) + F2(g) \rightarrow 2COF2(g)}\]

Experiment Initial \(\ce{CO}\) Initial \(\ce{F2}\) Initial Rate of Reaction
1. 0.0155M 0.0265 \(2.27 \times 10^{-5}\)
2. 0.0155M 0.053 \(4.55 \times 10^{-5}\)
3. 0.0310M 0.0265 \(9.08 \times 10^{-5}\)

What is the rate law?

Q4.7N

The following data were obtained for the reaction of methane with oxygen:

\(\ce{CH4(g)  +  2 O2(g)   \rightarrow   CO2(g)  +  2 H2O(l)}\)

time(min)

\(\ce{[CH4]}\) (mol/L)

\(\ce{[CO2]}\) (mol/L)

0

0.050

0

10

0.030

0.020

20

0.020

?

30

0.015

?

  1. How many moles of \(\ce{CO2}\) are produced for each mole of \(\ce{CH4}\) that is used up?
  2. What concentration of \(\ce{CH4}\) is used up after 10 minutes?
  3. What is the concentration of carbon dioxide produced after 20 minutes?
  4. Write an equation for reaction rate in terms of \(\mathrm{\Delta [CO_2]}\) over a time interval.
  5. What is the reaction rate for the formation of carbon dioxide between 10 and 20 minutes?
  6. What is the average reaction rate between 0 and 30 minutes?
  7. Write an expression for reaction rate relating \(\mathrm{\Delta [O_2]}\) to \(\mathrm{\Delta [CO_2]}\).
  8. At what rate is \(\ce{O2}\) used up between 10 and 20 minutes?

Q4.8N

The rate of the reaction,

\[\ce{HgCl2(aq)  +  \frac{1}{2} C2O4^2- (aq)  \rightarrow   Cl- (aq)  +  CO2(g)  +  \frac{1}{2} Hg2Cl2(s)}\]

is followed by measuring the number of moles of \(Hg_2Cl_2\) that precipitate per liter per second. The following data are obtained:

\(\ce{[HgCl2]}\)

\(\ce{[C2O4^{2-}]}\)

Initial Rate (mol/L·s)

0.10

0.10

1.3 × 10-7

0.10

0.20

5.2 × 10-7

0.20

0.20

1.0 × 10-6

0.20

0.10

2.6 × 10-7

  1. What is the order of the reaction with respect to \(\ce{HgCl2}\), with respect to \(\ce{C2O4^2-}\), and total?
  2. Write the rate equation for the reaction.
  3. Calculate \(\ce{k}\) for the reaction.
  4. When the concentrations of both mercury(II) chloride and oxalate ion are 0.30 M, what is the rate of the reaction?

Q8B.17

The first order reaction \(\ce{A \rightarrow products}\) has \(\mathrm{t_{1/2} = 180\, s}\):

  1. What percent of a sample of \(\ce{A}\) remains unreacted 720 s after a reaction has been started?
  2. What is the rate of reaction when \(\mathrm{[A] = 0.25\, M}\)?

Q8B.19

The reaction \(\mathrm{A \rightarrow products}\) is first order in \(\ce{A}\).

  1. If 12.24 g \(\ce{A}\) is allowed to decompose for 24 minutes, the mass of \(\ce{A}\) remaining undecomposed is found to be 1.53 g. What is the half life, \(\mathrm{t_{1/2}}\), of this reaction?
  2. Starting with 12.24g \(\ce{A}\), what is the mass of \(\ce{A}\) remaining undecomposed after 1.00 hours?

Q8B.21

A first order reaction of \(\mathrm{B \rightarrow products}\) has 80% of the initial amount of reactant decompose in 215 minutes. What is the half-life of this reaction?

Q8B.2

A first order decomposition reaction \(\ce{A \rightarrow B + C}\) has a half-life of 125 mins. How long does it take for a sample of \(\ce{A}\) to be 60% decomposed?

Q8B.27

Identify the reaction order for each reaction below (giving the concentration of only one reactant).

Time (s) 0 25 50 75 100 125 150
Reaction 1: \([A_1]\) (m) 1 0.8 0.6 0.4 0.2 0 0
Reaction 2: \([A_2]\) (m) 1 0.7 0.65 0.585 0.448 0.342 0.262
Reaction 3: \([A_3]\) (m) 1 0.656 0.488 0.388 0.323 0.276 0.241

Q8B.29

What is the approximate half-life for each of the following three reactions?  

\(A_1 \rightarrow B_1\) \(A_2 \rightarrow B_2\) \(A_3 \rightarrow B_3\)
Time, s \(\ce{[A]}\), M Time, s \(\ce{[A]}\),M Time, s \(\ce{[A]}\), M
0 1.00 0 1.00 0 1.00
25 0.80 25 0.77 25 0.82
50 0.64 50 0.52 50 0.70
75 0.52 75 0.27 75 0.60
100 0.40 100 0.00 100 0.51
150 0.24     150 0.42
200 0.15      200 0.35
250 0.07     250 0.29

Q8B.33

The reaction \(\ce{A + B \rightarrow C + D}\) is in second order in \(\ce{A}\) and first order in \(\ce{B}\). The value of \(\ce{k}\) is 0.0205 M-2 min-1. What is the rate of this reaction when \(\ce{[A]}\) is 0.005M and \(\ce{[B]}\) is 3.02M.

Q8B.35

The reaction

\[\ce{H2O2(aq) \rightarrow H2O(l) + \dfrac{1}{2}O2(g)}\]

yields the following data when decomposed at 600 K was obtained. 

Time(s) \(\ce{[H_2O_2]}\) (M)
0 2.00
100 1.80
200 1.62
300 1.48
400 1.36
500 1.26


What are the average rate of reaction over the first 500 seconds and reaction order?

Q8B.37

For the following reaction \(\mathrm{A\rightarrow B}\) the following information was obtained. 

Time(s) \(\mathrm{[A]}\) (M)
0 0.715
20 0.615
52 0.455
81  0.310
126 0.085

Find the order and half life of this reaction

Q8B.43

Since zero-order and second-order reactions both depend on the initial concentration and the rate constant, why does the half-life for one get longer as the initial concentration increases while the other decreases? (Make sure to label which reaction is which.)

Q8B.45

Explain

  1. Why a reactions rate is only a fraction of the calculated collision frequency.
  2. The effects of a raise in temperature on collision frequency and the reaction’s rate.
  3. The catalysts effect on reaction rate and how temperature is independent of this.

Q8B.47

For the reversible reaction \(\mathrm{A + B \rightleftharpoons A + B}\) the enthalpy change of the forward reaction is +34kJ/mol. The activation energy of the forward reaction is 66 kJ/mol.

  1. What is the activation energy of the reverse reaction?
  2. Sketch the reaction profile of this reaction with the x-axis as the reaction progress and the y-axis as the potential energy.

Q8B.49

Determine the following from the reaction profile for the reaction \(\ce{A}\) to \(\ce{E}\) given

Chem49.png

  1. How many intermediates are there?
  2. How many transition states are there?
  3. Is the first step exothermic or endothermic?
  4. Is the overall reaction exothermic or endothermic?
  5. Which is the fastest step?
  6. Which is the slowest step?

Q8B.51

Given for following data for the reaction \(\ce{A + B \rightarrow C}\) at different temperatures. Find the activation energy for the reaction. 450k, \(\mathrm{k=4.5\times10^{-4}\, M^{-1}s^{-1}}\); 625k, \(\mathrm{k=1.9\times10^{-2}\, M^{-1}s^{-1}}\).

Q8B.61

Compare and contrast the catalytic activity of rhodium and of an enzyme.

Q8B.63

What reaction conditions are necessary to account for a linear relationship between enzyme concentration and reaction rate?

Q8B.67

Hypothetically, the reaction \(\ce{H2 + 2ICl \rightarrow I2 + 2HCl}\) is first order in \(\ce{[H2]}\) and second order in \(\ce{[ICl]}\). Based on the first fast step given below and the fact that the second step is the slow step, propose a second-step mechanism, and show that it conforms to the experimentally determined reaction order. Assume that \(\ce{[I2]}\) does not affect the reaction rate.

\(\ce{H2 + 2ICl \rightarrow I2 + 2HCl}\)

\(\textrm{Fast: }\ce{2ICl \rightarrow I2 + 2Cl}\)
\(\textrm{Slow: ???}\)

Q8B.78

The units of \(\ce{k}\) depend on the overall reaction order. Derive a general expression for the units of \(\ce{k}\) using the units of the order of the reaction (o) units of concentration (M) and time (s)

Q8B.87

The following is a two-step reaction for the reaction of Nitric oxide and Oxygen.

  1. \(\mathrm{NO+ NO \xleftarrow{k_{-1}} \xrightarrow{\:\,k_1\:\,} N_2O_2}\)
  2. \(\mathrm{N_2O_2 +O_2 \xrightarrow{k_2} 2NO_2 }\)

The rate constants have been determined to be \(\mathrm{k_1=3.4\times10^2}\); \(\mathrm{k_{-1} = 2.8\times10^2}\); \(\mathrm{k_2= 3.48\times10^2}\)

Determine \(\ce{k}\) and the rate law.