The vibrational wavenumber of I2 is 214.5 cm-1. Evaluate the vibrational partition function explicitly (without approximation)...
The vibrational wavenumber of I2 is 214.5
cm-1. Evaluate the vibrational partition function
explicitly (without approximation) and plot its value as a function
of temperature. At what temperature is the value within 5% of the
value calculated from the approximate formula, 
?
Homework Answers
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The vibrational wavenumber of I2 is 214.5
cm-1. Evaluate the vibrational partition function
explicitly (without approximation)...
II. (30 pts) The diatomic molecule CO has a vibrational wavenumber of 2170 cm 'and may...
II. (30 pts) The diatomic molecule CO has a vibrational wavenumber of 2170 cm 'and may be treated as a quantized harmonic oscillator. 1. (10 pts) What is the energy of one photon of light which has the same frequency as CO (in J units)? 2. (10 pts) What is the value of the vibrational partition function of CO at 300 K? 3. (10 pts) At what temperature would approximately 5 vibrational quantum states of Co be thermally populated?
The HF/6-31G(d) harmonic vibrational frequency of Cl2 is 600 cm1. Calculate its vibrational partition function based...
The HF/6-31G(d) harmonic vibrational frequency of Cl2 is 600 cm1. Calculate its vibrational partition function based on the harmonic oscillator approximation at 298 K. Report your calculated value to 2 decimal places. Answer:
Write down an expression for calculating the vibrational partition function for a polyatomic mole...
Write down an expression for calculating the vibrational partition function for a polyatomic molecule from the vibrational partition functions of its normal modes. Use the spectroscopic data below to calculate qvib for carbon dioxide and ozone at 300 K. 4 Molecule Carbon dioxide, CO2 13 Ozone, O3 Vi/cm v2/ cm-1 667 701 V3 / cm-1 2349 1042 1103
Write down an expression for calculating the vibrational partition function for a polyatomic molecule from the vibrational partition functions of its normal...
thank you in advanced! Set 1: (50 pts) 1. (20 pts) The diatomic iodine anion (1:')...
thank you in advanced!
Set 1: (50 pts) 1. (20 pts) The diatomic iodine anion (1:') has a vibrational frequency of approximately 110 cm Predict the total heat capacity of I, in the gas phase at 300 K. II. (30 pts) The diatomic molecule Co has a vibrational wavenumber of 2170 cm and may be treated as a quantized harmonic oscillator. 1. (10 pts) What is the energy of one photon of light which has the same frequency as CO...
A. Derive an expression for the rotational partition function in the "high-temperature" limit where qrot can...
A. Derive an expression for the rotational partition function in the "high-temperature" limit where qrot can be approximated as an integral. Remember that the rotational energies as a function of rotational quantum number j are given by: ϵ (j) = B j (j + 1) where B is called the “rotational constant” B = ℏ2 /2µ r 2 , and the degeneracy of each "j" state is D(j) = 2j + 1. B. What is the average rotational energy in...
4. Anharmonic potential (15 points) The adjacent figure shows the experimentally determined potential energy curve of the electronic ground state of"Br2, with a few of the vibrational levels. The...
4. Anharmonic potential (15 points) The adjacent figure shows the experimentally determined potential energy curve of the electronic ground state of"Br2, with a few of the vibrational levels. The vibrational transitions are reasonably well described by a harmonic oscillator model, but much more accurately by including a small anharmonic correction term: En/hcVe(n 1/2) - vexe(n + 1/2)2. From fits to experimental data, the values of the constants are 325.32 cm and exe 1.08 cm .5 10 15 (a) Calculate the...
CALCULUS Consider the function f : R2 → R, defined by ï. Exam 2018 (a) Find the first-order Taylor approximation at the point Xo-(1, -2) and use it to find an approximate value for f(1.1, -2.1 (b) Ca...
CALCULUS Consider the function f : R2 → R, defined by ï. Exam 2018 (a) Find the first-order Taylor approximation at the point Xo-(1, -2) and use it to find an approximate value for f(1.1, -2.1 (b) Calculate the Hessian ã (x-xo)' (H/(%)) (x-xo) at xo (1,-2) (c) Find the second-order Taylor approximation at Xo (1,-2) and use it to find an approximate value for f(1.1, -2.1) Use the calculator to compute the exact value of the function f(1.1,-2.1) 2....
4. (100 points) Two thin coils of radius R = 3 cm are d = 20...
4. (100 points) Two thin coils of radius R = 3 cm are d = 20 cm apart and concentric with a common axis. Both coils contain 10 turns of wire with a conventional current of I = 2 A that runs counter-clockwise as viewed from the right side (see the figure). Q O 2 A 2 A 10 turns 10 turns Side view 20 cm A. What is the magnitude and direction of the magnetic field on the axis,...
Question 5 The rotational energy levels of a diatomic molecule are given by E,= BJ(J+1) with...
Question 5 The rotational energy levels of a diatomic molecule are given by E,= BJ(J+1) with B the rotational constant equal to 8.02 cm Each level is (2) +1)-times degenerate. (wavenumber units) in the present case (a) Calculate the energy (in wavenumber units) and the statistical weight (degeneracy) of the levels with J =0,1,2. Sketch your results on an energy level diagram. (4 marks) (b) The characteristic rotational temperature is defined as where k, is the Boltzmann constant. Calculate the...
(2) Consider the following function: (a) Using a Taylor polynomial of degree three (i.e. up to the term z3, included) and centred at Zo = 1, evaluate V2 correct to the fifth significant digit. (b) Co...
(2) Consider the following function: (a) Using a Taylor polynomial of degree three (i.e. up to the term z3, included) and centred at Zo = 1, evaluate V2 correct to the fifth significant digit. (b) Compare your result using Taylor's formula with the "true" numerical value v2 1.41421, accurate to the fifth significant digit. What is the value of the remainder R4 for the Taylor formula used in (a)? (c) How does the approximation used in (a) improve if we...
II. (30 pts) The diatomic molecule CO has a vibrational wavenumber of 2170 cm 'and may be treated as a quantized harmonic oscillator. 1. (10 pts) What is the energy of one photon of light which has the same frequency as CO (in J units)? 2. (10 pts) What is the value of the vibrational partition function of CO at 300 K? 3. (10 pts) At what temperature would approximately 5 vibrational quantum states of Co be thermally populated?
The HF/6-31G(d) harmonic vibrational frequency of Cl2 is 600 cm1. Calculate its vibrational partition function based on the harmonic oscillator approximation at 298 K. Report your calculated value to 2 decimal places. Answer:
Write down an expression for calculating the vibrational partition function for a polyatomic molecule from the vibrational partition functions of its normal modes. Use the spectroscopic data below to calculate qvib for carbon dioxide and ozone at 300 K. 4 Molecule Carbon dioxide, CO2 13 Ozone, O3 Vi/cm v2/ cm-1 667 701 V3 / cm-1 2349 1042 1103
Write down an expression for calculating the vibrational partition function for a polyatomic molecule from the vibrational partition functions of its normal...
thank you in advanced!
Set 1: (50 pts) 1. (20 pts) The diatomic iodine anion (1:') has a vibrational frequency of approximately 110 cm Predict the total heat capacity of I, in the gas phase at 300 K. II. (30 pts) The diatomic molecule Co has a vibrational wavenumber of 2170 cm and may be treated as a quantized harmonic oscillator. 1. (10 pts) What is the energy of one photon of light which has the same frequency as CO...
4. Anharmonic potential (15 points) The adjacent figure shows the experimentally determined potential energy curve of the electronic ground state of"Br2, with a few of the vibrational levels. The vibrational transitions are reasonably well described by a harmonic oscillator model, but much more accurately by including a small anharmonic correction term: En/hcVe(n 1/2) - vexe(n + 1/2)2. From fits to experimental data, the values of the constants are 325.32 cm and exe 1.08 cm .5 10 15 (a) Calculate the...
CALCULUS Consider the function f : R2 → R, defined by ï. Exam 2018 (a) Find the first-order Taylor approximation at the point Xo-(1, -2) and use it to find an approximate value for f(1.1, -2.1 (b) Calculate the Hessian ã (x-xo)' (H/(%)) (x-xo) at xo (1,-2) (c) Find the second-order Taylor approximation at Xo (1,-2) and use it to find an approximate value for f(1.1, -2.1) Use the calculator to compute the exact value of the function f(1.1,-2.1) 2....
4. (100 points) Two thin coils of radius R = 3 cm are d = 20 cm apart and concentric with a common axis. Both coils contain 10 turns of wire with a conventional current of I = 2 A that runs counter-clockwise as viewed from the right side (see the figure). Q O 2 A 2 A 10 turns 10 turns Side view 20 cm A. What is the magnitude and direction of the magnetic field on the axis,...
Question 5 The rotational energy levels of a diatomic molecule are given by E,= BJ(J+1) with B the rotational constant equal to 8.02 cm Each level is (2) +1)-times degenerate. (wavenumber units) in the present case (a) Calculate the energy (in wavenumber units) and the statistical weight (degeneracy) of the levels with J =0,1,2. Sketch your results on an energy level diagram. (4 marks) (b) The characteristic rotational temperature is defined as where k, is the Boltzmann constant. Calculate the...
(2) Consider the following function: (a) Using a Taylor polynomial of degree three (i.e. up to the term z3, included) and centred at Zo = 1, evaluate V2 correct to the fifth significant digit. (b) Compare your result using Taylor's formula with the "true" numerical value v2 1.41421, accurate to the fifth significant digit. What is the value of the remainder R4 for the Taylor formula used in (a)? (c) How does the approximation used in (a) improve if we...
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