EECE 503 Spring 2010
Homework No. 2
1.A reaction has the following stoichiometry:
A + 2B = 2P
Suppose that initially in a batch system there are 0.28 mol of A, 0.39 mol of B, and 0.13 mol of P.
a)After a certain time 0.18 mol of A remains. What is the extent of reaction and what are the amounts of B and P at that time?
b)What is the extent of reaction if the process goes to completion?
2.Reaction stoichiometry is:
2A + B = 3P
If the initial rate of consumption of A is 3.36 x 10-4 (mol/Ls), what is the rate of
consumption of B? What is the rate of formation of P and what is the rate of reaction ( intrinsic rate)?
3.The stoichiometric equation for the oxidation of bromide ions by hydrogen peroxide in acid solution is
2Br- + H2O2 + 2H+ = Br2 + 2H2O
The intrinsic rate of reaction is:
r = k [H2O2][H+][Br-]
a)If the concentration of H2O2 is increased by a factor of 3, by what factor is the rate of consumption of Br- ions increased?
b)If, under certain conditions, the rate of consumption of Br- ions is
7.2 x 10-3 mol dm-3 s-1, what is the rate of consumption of hydrogen peroxide? What is the rate of formation of bromine? What is the rate of reaction?
c)If by the addition of water to the reaction mixture the total volume were doubled, what would be the effect on the rate of change of the concentration of Br-? What would be the effect on the rate of reaction?
4.A reaction obeys the stoichiometric equation
A + 2B = 2P
The rate of formation of P at various concentration levels of A and B is listed in the table below:
[A] (mol/L)[B] (mol/L)r (mol/Ls)
______
3.5 x 10-22.3 x 10-25.0 x 10-7
7.0 x 10-24.6 x 10-22.0 x 10-6
7.0 x 10-29.2 x 10-24.0 x 10-6
If the rate of formation of P can be represented by
What values do have and what are they, and what is the value of rate constant kP?
What is the numerical value of the rate constant k for the intrinsic rate.
5.A substance decomposes according to first-order kinetics, the rate constants at various temperature being as follows:
Temperature/˚C Rate constant, k/s-1
15.0 4.18 x 10-6
20.0 7.62 x 10-6
25.0 1.37 x 10-5
30.0 2.41 x 10-5
37.0 5.15 x 10-5
Calculate the activation energy. Also at 25.0˚C, calculate , and the
pre-exponential factor.
6.Based on the Lindemann-Christansen model of unimolecular reactions calculate the ratio k2/k-1 knowing that at reactant concentration of 10-4 (L/mol) k1 has reached 80% of its limiting value .
7. The primary reaction occurring in the homogeneous decomposition of nitrous oxide is found to be:
with rate
Devise a mechanism to explain this observed rate.
Experiments reveal that in the above rate form
What is the order of the reaction? What is the activation energy for this reaction?
Can you simplify the rate form knowing that the temperatures of interest are between 30 and 200 0C and pressure is about 1 atmosphere.
8. The formation and decomposition of phosgene has the following stoichiometry:
Forward reaction:
Reverse reaction:
a)Are these rate expressions thermodynamically consistent?
b)Determine which of the following mechanisms is consistent with these experimentally found rates. How are the rate constants of the elementary reactions in the proposed mechanism (see the two proposed mechanisms below) related to kf and kb?
MECHANISM I: fast, at equilibrium
fast, at equilibrium
slow and rate controlling
MECHANISM II:fast, at equilibrium
fast, at equilibrium
slow and rate controlling
9. Consider the following reaction systems:
Assume M is present in great excess, so that [M ] constant. The concentration of B and C are zero at t = 0 while initial concentration of A, is given.
a)Derive analytical expressions for the exact dynamic behavior of this batch system over time. Show mathematically under what conditions the pseudo-steady approximation (PSSA) can be made for [B ].
b)Use the PSSA to derive a simpler set of equations for the concentrations of A, B, and C.
c)Draw a graph (on log-log paper) that compares the exact behavior of the system to calculations based on the PSSA for the following three sets of conditions. Discuss your results.
Set 1 / Set 2 / Set 3[M ] = 105
[A ]0 = 102
k 1 = 10-5
k 2 = 10-6 / [M ] = 105
[A ]0 = 102
k 1 = 10-3
k 2 = 10-6 / [M ] = 105
[A]0 = 102
k 1 = 10-1
k 2 = 10-6
Note that the above quantities are presented in consistent units. Concentrations [M], [A]0 are in (mmol/m3), k1 is in (1/s), and k2 in (m3/mmol s).