Homework 8B: More Chemical Kinetics
- Page ID
- 2829
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 \(-8.2 \times 10^{-4} \; M/s\).
- What is the rate of reaction at this point?
- What is the rate of disappearance of \(\ce{B}\)?
- 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:
- Find the order of reaction with respect to \(\ce{A}\) and to \(\ce{B}\).
- Solve the overall reaction order.
- 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 |
? |
- How many moles of \(\ce{CO2}\) are produced for each mole of \(\ce{CH4}\) that is used up?
- What concentration of \(\ce{CH4}\) is used up after 10 minutes?
- What is the concentration of carbon dioxide produced after 20 minutes?
- Write an equation for reaction rate in terms of \(\mathrm{\Delta [CO_2]}\) over a time interval.
- What is the reaction rate for the formation of carbon dioxide between 10 and 20 minutes?
- What is the average reaction rate between 0 and 30 minutes?
- Write an expression for reaction rate relating \(\mathrm{\Delta [O_2]}\) to \(\mathrm{\Delta [CO_2]}\).
- 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 |
- What is the order of the reaction with respect to \(\ce{HgCl2}\), with respect to \(\ce{C2O4^2-}\), and total?
- Write the rate equation for the reaction.
- Calculate \(\ce{k}\) for the reaction.
- 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 \(\mathrm{t_{1/2} = 180\, s}\):
- What percent of a sample of \(\ce{A}\) remains unreacted 720 s after a reaction has been started?
- What is the rate of reaction when \(\mathrm{[A] = 0.25\, M}\)?
Q8B.19
The reaction \(\mathrm{A \rightarrow products}\) is first order in \(\ce{A}\).
- 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?
- 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
- Why a reactions rate is only a fraction of the calculated collision frequency.
- The effects of a raise in temperature on collision frequency and the reaction’s rate.
- 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.
- What is the activation energy of the reverse reaction?
- 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
- How many intermediates are there?
- How many transition states are there?
- Is the first step exothermic or endothermic?
- Is the overall reaction exothermic or endothermic?
- Which is the fastest step?
- 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.
- \(\mathrm{NO+ NO \xleftarrow{k_{-1}} \xrightarrow{\:\,k_1\:\,} N_2O_2}\)
- \(\mathrm{N_2O_2 +O_2 \xrightarrow{k_2} 2NO_2 }\)
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.