Fill in the blanks in the following table for a diatomic molecule: Degree of freedom Quantum...
Fill in the blanks in the following table for a diatomic molecule:
|
Degree of freedom |
Quantum chemical model |
Number of degrees of freedom |
Internal energy contribution according to the equipartition theorem |
|
Translational |
|||
|
Rotational |
|||
|
Vibrational |
Homework Answers
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Fill in the blanks in the following table for a diatomic
molecule:
Degree of freedom
Quantum...
2. Complete this table. Show your work for NH3. Assume there is no vibrational internal energy....
2. Complete this table. Show your work for NH3. Assume there is no vibrational internal energy. Calculate the energy assuming 1 mol of gas and a temperature of 298,15 K. Look up the experimental values in the Handbook of Chemistry and Physics (8 marks. Translational Rotational Vibrational Equipartition Experimental Degrees of Degrees of Degrees of Cp.m Freedom Freedom Freedom (UK-mol (JK-mol He (g) NO (8) NH: (g) Сpn
3. An equation for the average thermal energy per gas molecule (monoatomic or diatomic) is given...
3. An equation for the average thermal energy per gas molecule (monoatomic or diatomic) is given by where f is the number of degrees of freedom accessible to the gas molecules. (a) How many degrees of freedom does a diatomic molecule have at low temperatures, medium temperatures, and high temperatures (consult Figure 20.11). (b) Describe what degrees of freedom are accessible (e.g., "translational but nothing else," "trans- lational + vibrational but nothing else," etc.) to the gas molecules in each...
In the ro-vibrational model for spectra of diatomic molecules, the total rotational and vibrational energy for...
In the ro-vibrational model for spectra of diatomic molecules, the total rotational and vibrational energy for a given state is: Évj = ū(v + 3) + BJC +1) (Equation 1) where v is the vibrational quantum number and J is the rotational quantum number. Complete the following steps to create a model energy level diagram for a hypothetical diatomic molecule with ✓ = 2000 cm-1 and B = 1 cm-1. i) Draw a horizontal line to represent the ground vibrational...
1. Ideal gas with internal degrees of freedom. Consider a free gas of diatomic molecules at...
1. Ideal gas with internal degrees of freedom. Consider a free gas of diatomic molecules at temperature 7. Diatomic molecules have internal rotational excitations. The rotational energy levels of a single molecule are given by J(J+1) 2/2 J = 0,1,23 where J is the angular momentum and I is the moment of inertia. The degeneracy of the level J is 2J +1. Neglect any interaction between the molecules in the gas. The temperature is high enough so that the statistic...
please show the process and answer Consider the model of a diatomic gas lithium (L.) shown...
please show the process and answer
Consider the model of a diatomic gas lithium (L.) shown in Figure 9.3. atom Rigid connector (massless) atom Figure 9.3 (a) Assuming the atoms are point particles separated by a distance of 0.27 nm, find the rotational inertia Ix for rotation about the x axis. kg.ma (b) Now compute the rotational inertia of the molecule about the z axis, assuming almost all of the mass of each atom is in the nucleus, a nearly...
a) what effect does the change in internuclear separation in a diatomic molecule due to its vibration (the binding energ...
a) what effect does the change in internuclear separation in a diatomic molecule due to its vibration (the binding energy curve is asymmetric) have on the rotational energy levels of molecule? b)Explain why the separation between vibrational levels is somewhat smaller in an excited electronic state than in the ground electronic state. Explain the same effect for rotational states. c)show the ratio number of molecules in rotational level r to the number in the r=0 level, in a sample at...
Part A According to the equipartition principle, what is the overall energy in J of one...
Part A According to the equipartition principle, what is the overall energy in J of one mole of water at 1400 K if translational, rotational, and vibrational degrees of freedom are considered? The values of the vibrational constants of water are roughly 1600 cm-and 3700 cm ). kg = 1.381 . 10-23 JK-1 R - 8.314 JK-1 mol-1 Calculate the higher limit for the overall energy in J of one mole of water at 1400 K assuming that all vibrations...
7. For CO2 near room temperature: Cy - molar heat capacity at constant volume = 28.5...
7. For CO2 near room temperature: Cy - molar heat capacity at constant volume = 28.5 J/(mole K) Other useful information gas constant R 8.314 J/(mole K) Boltzmann's constant k - 1.38 x 10-23 J/K a) The internal energy of a sample of N molecules of CO2 near room temperature can be written U = a + bNKT where a and b are constants. What is the value of b? (15 points) b) The Equipartition Theorem allots energy VkT to...
Place the following five diatomic molecules in the first column of the table. For each molecule,...
Place the following five diatomic molecules in the first column of the table. For each molecule, write down its bond order. Li2, H2, C2, O2, N2, Be2 Molecule Bond order Bond length (Å) Dissociation energy (kJ/mol) 0.74 457 1.09 1.21 599 1.21 105 2.72 10.0 942 494 2.67 Number of electrons: H(1), He(2), Li(3), Be(4), C(6), N(7), O(8). Based on the table, draw (on the same plot) the ground state potential energy function of N2, Liz and Be2. Annotate axes....
Fill in the blanks in the following table: Number of Workers Total Output Marginal Product
Fill in the blanks in the following table: Number of Workers Total Output Marginal Product
2. Complete this table. Show your work for NH3. Assume there is no vibrational internal energy. Calculate the energy assuming 1 mol of gas and a temperature of 298,15 K. Look up the experimental values in the Handbook of Chemistry and Physics (8 marks. Translational Rotational Vibrational Equipartition Experimental Degrees of Degrees of Degrees of Cp.m Freedom Freedom Freedom (UK-mol (JK-mol He (g) NO (8) NH: (g) Сpn
3. An equation for the average thermal energy per gas molecule (monoatomic or diatomic) is given by where f is the number of degrees of freedom accessible to the gas molecules. (a) How many degrees of freedom does a diatomic molecule have at low temperatures, medium temperatures, and high temperatures (consult Figure 20.11). (b) Describe what degrees of freedom are accessible (e.g., "translational but nothing else," "trans- lational + vibrational but nothing else," etc.) to the gas molecules in each...
In the ro-vibrational model for spectra of diatomic molecules, the total rotational and vibrational energy for a given state is: Évj = ū(v + 3) + BJC +1) (Equation 1) where v is the vibrational quantum number and J is the rotational quantum number. Complete the following steps to create a model energy level diagram for a hypothetical diatomic molecule with ✓ = 2000 cm-1 and B = 1 cm-1. i) Draw a horizontal line to represent the ground vibrational...
1. Ideal gas with internal degrees of freedom. Consider a free gas of diatomic molecules at temperature 7. Diatomic molecules have internal rotational excitations. The rotational energy levels of a single molecule are given by J(J+1) 2/2 J = 0,1,23 where J is the angular momentum and I is the moment of inertia. The degeneracy of the level J is 2J +1. Neglect any interaction between the molecules in the gas. The temperature is high enough so that the statistic...
please show the process and answer
Consider the model of a diatomic gas lithium (L.) shown in Figure 9.3. atom Rigid connector (massless) atom Figure 9.3 (a) Assuming the atoms are point particles separated by a distance of 0.27 nm, find the rotational inertia Ix for rotation about the x axis. kg.ma (b) Now compute the rotational inertia of the molecule about the z axis, assuming almost all of the mass of each atom is in the nucleus, a nearly...
Part A According to the equipartition principle, what is the overall energy in J of one mole of water at 1400 K if translational, rotational, and vibrational degrees of freedom are considered? The values of the vibrational constants of water are roughly 1600 cm-and 3700 cm ). kg = 1.381 . 10-23 JK-1 R - 8.314 JK-1 mol-1 Calculate the higher limit for the overall energy in J of one mole of water at 1400 K assuming that all vibrations...
7. For CO2 near room temperature: Cy - molar heat capacity at constant volume = 28.5 J/(mole K) Other useful information gas constant R 8.314 J/(mole K) Boltzmann's constant k - 1.38 x 10-23 J/K a) The internal energy of a sample of N molecules of CO2 near room temperature can be written U = a + bNKT where a and b are constants. What is the value of b? (15 points) b) The Equipartition Theorem allots energy VkT to...
Place the following five diatomic molecules in the first column of the table. For each molecule, write down its bond order. Li2, H2, C2, O2, N2, Be2 Molecule Bond order Bond length (Å) Dissociation energy (kJ/mol) 0.74 457 1.09 1.21 599 1.21 105 2.72 10.0 942 494 2.67 Number of electrons: H(1), He(2), Li(3), Be(4), C(6), N(7), O(8). Based on the table, draw (on the same plot) the ground state potential energy function of N2, Liz and Be2. Annotate axes....
Fill in the blanks in the following table: Number of Workers Total Output Marginal Product
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