Physical Chemistry
CH213. Physical Chemistry II. Final Exam
Your Name: Your Student Number:
110 Normal Points + 10 Bonus Points If you get 110 points out of 120 points, you will get the full 40% assigned to the midterm exam.
Your scores 1) 2) 3) 4) 5) 6) Total: out of 25 out of 20 out of 20 out of 15 out of 20 out of 20 out of 120
* All the problems are connected. In other words, to solve the problem, you may need the information and/or answers given in other problems. All necessary information is basically given. Also please consult the supplementary material handed out to you.
1) (25 pts) a) (6 pts) The translational energy states in a cubic container are given by the following equation.
Derive the following equation for the molecular translational partition function.
You will need the following integral relation.
0
e
n 2
dn 4
1/ 2
Answers) ( ) ∑ ∑
( )
(
)
∑
∑
∑
(
)
(∫
)
(
) (
√
( ( ) )
)
( a^3 =V
)
(
)
b) (3 pts) If the vibrational energy levels are given as follows, (b-1) where is the zero of vibrational energy? (b-2) What approximation has been made regarding the vibrational motion?
Answers) (b-1) The zero of vibrational energy is at the bottom of the internuclear potential well. (2 pts) (b-2) The vibrational motion is approximated as an harmonic oscillator. (1 pt)
c) (6 pts) Derive the following equation for the molecular vibrational partition function.
You will need the relation applicable when x is less than 1.
xn
0
1 1 x
Answers) ( ) ∑
( )
(
)
∑
(
)
∑
(
)
(
)
d) (2 pts) If the molecular electronic partition function can be approximated as follows, where is the zero of electronic energy?
Answers) The zero of the electronic energy is taken to be the separated atoms at rest in their electronic states (2 pts).
e) (3 pts) If the molecular rotational partition function is given
Your Name: Your Student Number:
110 Normal Points + 10 Bonus Points If you get 110 points out of 120 points, you will get the full 40% assigned to the midterm exam.
Your scores 1) 2) 3) 4) 5) 6) Total: out of 25 out of 20 out of 20 out of 15 out of 20 out of 20 out of 120
* All the problems are connected. In other words, to solve the problem, you may need the information and/or answers given in other problems. All necessary information is basically given. Also please consult the supplementary material handed out to you.
1) (25 pts) a) (6 pts) The translational energy states in a cubic container are given by the following equation.
Derive the following equation for the molecular translational partition function.
You will need the following integral relation.
0
e
n 2
dn 4
1/ 2
Answers) ( ) ∑ ∑
( )
(
)
∑
∑
∑
(
)
(∫
)
(
) (
√
( ( ) )
)
( a^3 =V
)
(
)
b) (3 pts) If the vibrational energy levels are given as follows, (b-1) where is the zero of vibrational energy? (b-2) What approximation has been made regarding the vibrational motion?
Answers) (b-1) The zero of vibrational energy is at the bottom of the internuclear potential well. (2 pts) (b-2) The vibrational motion is approximated as an harmonic oscillator. (1 pt)
c) (6 pts) Derive the following equation for the molecular vibrational partition function.
You will need the relation applicable when x is less than 1.
xn
0
1 1 x
Answers) ( ) ∑
( )
(
)
∑
(
)
∑
(
)
(
)
d) (2 pts) If the molecular electronic partition function can be approximated as follows, where is the zero of electronic energy?
Answers) The zero of the electronic energy is taken to be the separated atoms at rest in their electronic states (2 pts).
e) (3 pts) If the molecular rotational partition function is given