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Elementary Inorganic Chemistry Problem Set 1 for Morehouse College's Chemistry 112 - Prof., Assignments of Inorganic Chemistry

A problem set for morehouse college's chemistry 112 elementary inorganic chemistry course. The problem set includes various chemistry-related questions, some of which involve determining reaction orders, calculating rate constants, and using the arrhenius equation. Students are required to answer all questions neatly and submit them by a certain date.

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Pre 2010

Uploaded on 08/04/2009

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Chemistry 112 – Elementary Inorganic Chemistry
Morehouse College – Problem Set #1
DUE: Monday, February 2, 2009 in class
Answer all questions in the space provided, neatly written. Thanks.--BML
1. (1 pt. each) For each of the following questions, circle the BEST answer (no
explanation is required for full credit).
a. Consider the following reaction: 2NO
(g)
+ 2H
2(g)
N
2(g)
+ 2H
2
O
(g)
The experimentally determined rate law for the above process is
rate = k[NO]
2
[H
2
]. What is the reaction order for this process with respect to
hydrogen gas (H
2(g)
)?
0 1 2 3 none of these
b. Consider the following reaction: A
(g)
B
(g)
In consideration of the energy of activation (E
a
) for this process, which of the
following are true?
A catalyst will E
a
α
T(K) E
a
α
[A] A catalyst will none of these
increase E
a
decrease E
a
c. Consider the following chemical reaction: 2A + 2B 2C + 2D + E
If the reaction above is found to be first order in A and first order in B, what is the
rate law for this reaction?
k[A][B] k[A]
2
[B]
2
k[2A][2B] k[2A]
2
[2B]
2
none of these
d. Radioactive decay of
212
Bi is observed to be a first-order process with a rate
constant (k) of 7.21 x 10
-3
hr
-1
. It is noted that a 2.82 g sample of
212
Bi decays
over 8 days to leave only 705 mg behind. What is the half-life (t
½
) for this
process?
12.0 days 8.00 days 4.00 days 2.00 days none of these
e. A certain reaction is first order in reactant “C” and has a rate constant (k) of
1.2 x 10
-2
s
-1
. If [C]
0
= 2.9
M
, what is the [C] after 3.33 min?
0.18
M
0.55
M
1.0
M
6.0 x 10
-3
M
none of these
pf2

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Chemistry 112 – Elementary Inorganic Chemistry

Morehouse College – Problem Set

DUE: Monday, February 2, 2009 in class

Answer all questions in the space provided, neatly written. Thanks.--BML

  1. (1 pt. each) For each of the following questions, circle the BEST answer (no explanation is required for full credit).

a. Consider the following reaction: 2NO(g) + 2H2(g) N2(g) + 2H 2 O(g) The experimentally determined rate law for the above process is rate = k[NO]^2 [H 2 ]. What is the reaction order for this process with respect to hydrogen gas (H2(g))?

0 1 2 3 none of these

b. Consider the following reaction: A(g) B(g) In consideration of the energy of activation ( Ea ) for this process, which of the following are true?

A catalyst will Ea α T(K) Ea α [A] A catalyst will none of these increase Ea decrease Ea

c. Consider the following chemical reaction: 2A + 2B 2C + 2D + E

If the reaction above is found to be first order in A and first order in B, what is the rate law for this reaction?

k[A][B] k[A]^2 [B]^2 k[2A][2B] k[2A]^2 [2B]^2 none of these

d. Radioactive decay of 212 Bi is observed to be a first-order process with a rate constant ( k ) of 7.21 x 10-3^ hr-1. It is noted that a 2.82 g sample of 212 Bi decays over 8 days to leave only 705 mg behind. What is the half-life ( ) for this process?

12.0 days 8.00 days 4.00 days 2.00 days none of these

e. A certain reaction is first order in reactant “C” and has a rate constant ( k ) of 1.2 x 10-2^ s-1. If [C] 0 = 2.9 M, what is the [C] after 3.33 min?

0.18 M 0.55 M 1.0 M 6.0 x 10-3^ M none of these

  1. (5 pts) Dinitrogen tetroxide, N 2 O 4 , decomposes spontaneously at room temperature in the gas phase to give nitrogen dioxide. The rate law governing the disappearance of dinitrogen tetroxide obeys first-order kinetics. At 30 °C, the rate constant k is measured to be 5.1 x 10^6 s-1^ and the activation energy for the reaction is 54.0 kJ mol-1. Using this information to guide you, calculate the time it takes, in seconds, for the partial pressure of nitrogen dioxide in a sealed vessel to decrease from 0.10 atm to 0.010 atm at both 30 °C and 300 °C. Report your answer in the space provided with the correct number of significant figures. Show your work. A correct response without any justification (work) will receive no credit.

Since the decomposition reaction described above is 1st^ order, we know that…

[N 2 O 4 ]t = [N 2 O 4 ] 0 x e-kt^ …where k = 5.1 x 10^6 s-

From the ideal gas law, we also know that the pressure of a gas is proportional to it’s concentration. That is...

[ ] [ ]

  • kt NO NO( 0)

NO NO 2 4 2 4

P P x e

Subsitutionofthisresultintotheintegratedratelaw/equationfromaboveyields...

RT

P

RT NO xRTorinsimplerterms,NO V

n V

nRT P

24 24

2 4 24

t

Since the initial and final pressures of N 2 O 4 are given, we can solve this equation for t.

4.5x 10 sor 451 ns 5.1x 10 s

0.10atm

0.010atm ln(

k

P

P

ln( time (t) NO( 0) 6 - 1 7

NO 24

24

= − t =^ =− =^ −

At 300 °C (573 K), the reaction rate constant is ex pected to be different. Using the Arrhenius equation, we will first solve for A at 30 °C (303 K ).

16 1 10

6 1

(8.314Jmol K)(303K)

  • 54000 Jmol

6 1

RT

  • E (^) 4.9x 10 1.0x^10 s

k 5.1x 10 s 5.1x 10 s A

  • 1 - 1 a -^1

− −

− − = = = = e e

If we assume that the Arrhenius factor (A) is constant at both temperatures (Question: Why can we do this?), we can use the Arrhenius equation to determine the new rate constant…

k A 1.0x 10 s x (8.314JmolK )(573K) 1.2x 1011 s^1 (at 300 o C)

54000 RT^161

E (^) a - 1 1 −

− −

− = = =

e e

Lastly, we substitute this “new” rate constant into our expression from above for time…

1.9x 10 sor 19 ps 1.2x 10 s

0.10atm

0.010atm ln(

k

P

P

ln( time (t) NO( 0) 11 - 1 11

NO 24

24

= − t =^ =− =^ −