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Material Type: Assignment; Class: Physical Chemistry; Subject: CHEM Chemistry; University: Tennessee Tech University; Term: Spring 2004;
Typology: Assignments
1 / 13
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Name: Due date: 04/26/
1. Determine the rate law for the reaction where M is any
molecule present in the reaction container. What is the units of k and the molecularity of this
reaction? Is the above reaction identical to? What is the units of k and the
molecularity of this second reaction? Compare the two results.
I(g) + I(g)+M(g)⇒I 2 (g)+ M(g)
k
I(g) I 2 (g)
k I(g)+ ⇒
2. Consider the reaction mechanism A I Pwhere [
k 1 k 2 ⇒ ⇒ A] = [A] 0 and [ at time t. Determine the expression for [ , [ ], and [. (Note: Determining the expression
for [ requires solving
) = q ( x ) x eh^ x dx +
( ) p ( x ) y ( x dx
dy x +
y xeh^ x = q
that is a linear, first-order differential equation
constant.)
4. Consider the mechanism for the decomposition of ozone presented below. Explain why either (a) and or (b) and v must be true for the steady-
state approximation to apply. The rate law for the decomposition reaction is found to be
v (^) − 1 >> v 2 v (^) − 1 >> v 1 v 2 (^) >> v − 1 2 >> v 1
[ O 3 ] M ] dt
d (^) = [ O ][ k (^) obs 3. Is this rate law consistent with the conditions (a) or (b) or both?
M(g) O 3 (g) O 2 (g) O(g) M(g) 1
1
⇐
k −
k
O(g) O 3 (g) 2 O 2 (g )
k 2
5. Consider the reaction mechanism below. Write the expression for , the rate of
product formation. Assume equilibrium is established in the first reaction before any appreciable amount of product is formed (this assumption is called the fast-equilibrium approximation ), and
thereby show that
d [P]/ dt
[P ] k 2 Kc [A][B ] dt
d (^) = where is the equilibrium constant for step (1) of the
reaction mechanism.
K c
2
1
(^1) k
k
k ⇒ ⇐
−
7. The rate law for the reaction between CO(g) and to form phosgene :
is
Cl 2 (g) (Cl 2 CO) Cl 2 (g)+ CO(g) k^ obs →Cl 2 CO(g ) d [^ Cl^2 CO] k obs[Cl 2 ]^3 /^2 [CO] dt =. Show that the
following mechanism is consistent with this rate law
Cl (g) M(g) 2Cl(g) M(g) (fast equilibrium)
1
1
−
k
k
) (fast equilibrium)
Cl(g) CO(g) M(g) ClCO(g) M( g
2
2
−
k
k
ClCO( g) Cl (g) Cl 2 CO(g) Cl(g (slow)
3
k
where M is any gas molecule present in the reaction container. Express in terms of the rate
constants for the individual steps of the reaction mechanism.
k obs
8. An alternative mechanism for the reaction Cl 2 (g) + CO(g) → k obs Cl 2 CO(g)is
Cl (g) M(g) 2Cl M(g ) (fast equilibrium)
1
1
−
k
k
Cl(g) Cl (g) Cl 3 (g ) (fast equilibrium)
2
2
2
k
k −
Cl (g) CO(g) Cl 2 CO(g) Cl(g) (slow)
3 3 + ⇒ +
k
where M is any molecule present in the reaction chamber. Show that this mechanism also gives
the observed rate law, [Cl^2 CO] k obs[Cl 2 ]^3 /^2 [CO] dt
d (^) =. Propose one way of determining whether
this mechanism or the one given in Problem 7 is correct?
10. The unimolecular reaction CH can also be carried out in the presence of a helium buffer gas. The collision of a CH molecule with either another molecule or a helium atom can energize the molecule, thereby leading to reaction. If the energizing reactions involving a molecule and a He atom occur with different rates,
the reaction mechanism would be given by
3 NC(g)^ ⇒CH 3 CN(g) 3 NC
CH 3 NC
CH NC(g) CH NC(g) CH 3 NC*(g) CH 3 NC(g)
1
1
−
k
k
CH NC(g) He(g) CH 3 NC*(g) He(g)
2
2
−
k
k
CH NC(g) CH 3 CN *^3 3
k ⇒
Apply the steady-state approximation to the intermediate species, CH 3 NC*(g), to show that
1 3 2 3
3 3 1 3 2 2 3 [CH NC] [He]
[CH CN] [CH NC] [CH NC][He] k k k
k k k dt
d
− −
Show that this equation becomes [CH^3 CN]^ k obs[CH 3 NC] dt
d (^) = when [ He] = 0.
11. A proposed mechanism for the thermal decomposition of acetaldehyde CH 3 CHO(g) → k obs^ CH 4 (g)+CO(g)include the following elementary steps:
CH CHO(g) CH 3 (g) CHO(g) (1)
1 3 ⇒ +
k
CH (g) CH CHO(g) CH 4 (g) CH 3 CO(g) (2)
2 3 + 3 ⇒ +
k
CH CO(g) CH 3 (g) CO(g) (3)
3 3 ⇒ +
k
2CH (g) C 2 H 6 (g) (4)
4 3
k ⇒
The overall reaction is a chain reaction. Identify the initiation, propagation, inhibition, and termination step(s). Determine the rate laws for , , and. Assume the steady-state approximation for the intermediate species, and , to determine the expression of the rate law for methane formation as a function of [.
CH 4 (g) CH 3 (g) CH 3 (g)
CH 3 CO(g) CH 3 CO(g) CH 3 CHO]
13. The protein catalase catalyzes the reaction and has a
single active site. It has a Michaelis constant of and a turnover
number of. Calculate v for this enzyme and the initial rate of this reaction if
the total enzyme concentration is and the initial substrate concentration is 4. In the presence of of a competitive inhibitor the initial rate decreases by a factor of 3.6. Calculate , the equilibrium constant for the binding
reaction between the enzyme and the inhibitor.
2 H 2 O 2 (aq)→ 2 H 2 O(l)+O 2 (g ) m =^25 ×^10 −^3 mol⋅dm−^3
⋅dm−^3 10 −^6 mol⋅dm−^3 K I
mol 8 ×
− (^6) mol ⋅dm− 3
max
. 32 × 10 4.
