4. N₂ has a molecular weight of 28.0129 Daltons, a bit larger than that of a He atom (4.0017). (a) At a particular temperature, Ztrans = 2.80 x 1026 for He in a specific container. What is the translational partition function for a N₂ molecule in this container at the same temperature? (b) At 100 K, the rotational partition function for N₂ is found to be 17.39. What would you expect it to be at 225 K?
4. N₂ has a molecular weight of 28.0129 Daltons, a bit larger than that of a He atom (4.0017). (a) At a particular temperature, Ztrans = 2.80 x 1026 for He in a specific container. What is the translational partition function for a N₂ molecule in this container at the same temperature? (b) At 100 K, the rotational partition function for N₂ is found to be 17.39. What would you expect it to be at 225 K?
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
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Question
![4. N₂ has a molecular weight of 28.0129 Daltons, a bit larger than that of a He atom (4.0017).
(a) At a particular temperature, Ztrans = 2.80 x 1026 for He in a specific container. What is the
translational partition function for a N₂ molecule in this container at the same
temperature?
(b) At 100 K, the rotational partition function for N₂ is found to be 17.39. What would you
expect it to be at 225 K?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd76a2d57-02e6-4734-ba8a-6fadc8c476a5%2F591a6b51-ac71-4477-98c1-719da1f54fa1%2Fwv35e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. N₂ has a molecular weight of 28.0129 Daltons, a bit larger than that of a He atom (4.0017).
(a) At a particular temperature, Ztrans = 2.80 x 1026 for He in a specific container. What is the
translational partition function for a N₂ molecule in this container at the same
temperature?
(b) At 100 K, the rotational partition function for N₂ is found to be 17.39. What would you
expect it to be at 225 K?
![Label
A
B
с
D
E
F
G
H
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Equation
Etotal= Eetec + Evib + Erot + Etrans
E₂ = hw (v + ²)
Zvib =
Evib =
h²
Erot= 27 J+1)=Bjj+1)
Etrans (nx. ny. ₂) =
3N-6
[₁ hw; (v₁ + ²)
3N-6
(-1
w(n)=
-
E-ENG
E=
N = n₁
Ztrans
P₁ = gjeti/kg
z
τα
z=₁9₁e-B, or z=₁e-/kg
h² (n.2
B=
8m L
-
Z=
1 az
z ap
Zrot
Zrot =
1
kgT
(9₁)",
n₂!
Zvib =
■
N!
+
A₁ e₁/kt
gjet/kat
Σge-B
(2mmk, T., 3/2
h²
B
erot= ks
z = Zelec Zvib Zrot Ztrans
kgT
Ba
erib=
a In Z
aß
√R T3
, Ꮎ Ꮎ Ꮎ
e-Bho/2
1-e-Bhu
ho
kB
2
V
+
3N-6
e-Bhoj/z
=
-ПIG
-e-Bhay
-Oyib./2T
-e-vib/T
Zvibi
P(b) = (1-e-b/T)e-/T](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd76a2d57-02e6-4734-ba8a-6fadc8c476a5%2F591a6b51-ac71-4477-98c1-719da1f54fa1%2Fjzow5or_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Label
A
B
с
D
E
F
G
H
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Equation
Etotal= Eetec + Evib + Erot + Etrans
E₂ = hw (v + ²)
Zvib =
Evib =
h²
Erot= 27 J+1)=Bjj+1)
Etrans (nx. ny. ₂) =
3N-6
[₁ hw; (v₁ + ²)
3N-6
(-1
w(n)=
-
E-ENG
E=
N = n₁
Ztrans
P₁ = gjeti/kg
z
τα
z=₁9₁e-B, or z=₁e-/kg
h² (n.2
B=
8m L
-
Z=
1 az
z ap
Zrot
Zrot =
1
kgT
(9₁)",
n₂!
Zvib =
■
N!
+
A₁ e₁/kt
gjet/kat
Σge-B
(2mmk, T., 3/2
h²
B
erot= ks
z = Zelec Zvib Zrot Ztrans
kgT
Ba
erib=
a In Z
aß
√R T3
, Ꮎ Ꮎ Ꮎ
e-Bho/2
1-e-Bhu
ho
kB
2
V
+
3N-6
e-Bhoj/z
=
-ПIG
-e-Bhay
-Oyib./2T
-e-vib/T
Zvibi
P(b) = (1-e-b/T)e-/T
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