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Unsolved Questions for Assignment 11 - Physical Chemistry | CHEM 3520, Assignments of Physical Chemistry

Material Type: Assignment; Class: Physical Chemistry; Subject: CHEM Chemistry; University: Tennessee Tech University; Term: Spring 2004;

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Uploaded on 07/30/2009

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N
ame: Due date: 04/26/04
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.
M(g)(g)IM(g)I(g)I(g) 2+++ k
(g)II(g) 2
k
+I(g)
pf3
pf4
pf5
pf8
pf9
pfa
pfd

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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

I] 0 =[P] 0 = 0

I ]

A ] I P]

) = 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

whose general solution is ( ) (^ ) ∫ ( ) () c where h ( x ) = ∫ p ( x ) dx and c is a

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

A B C P

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

  • 2 ⇒ +

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 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

K

mol 8 ×

  1. 0 × 107 s−^1

− (^6) mol ⋅dm− 3

max

  1. 016 × 10 −^6

. 32 × 10 4.