What is the partition function of a canonical ensemble of N indistinguishable particles that occupy energy levels, ɛ with degeneracy g, į being integers j=0,1,2.m
Q: Calculate the rotational partition function for a non-linear molecule whose σ=5 at 25°C. Given A =…
A: Where Kb is Boltzmann constant, which equals to 0.695 cm-1 T = Temperature in Kelvin (K)
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A: The rotational partition function expression is shown below,
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Q: Evaluate the translational partition function of (a) N2, (b) gaseous CS2 in a flask of volume 10.0…
A: The mass of N2 in kg is calculated as shown below.
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A: The vibration partition function can be expressed as follows:
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Q: The following have to do with rotational partition functions. a) What are the symmetry numbers o for…
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A: Jajan
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A: The vibrational partition function of HCN at 900 K given the wavenumbers, 3311 cm-1, 712 cm-1, 2097…
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Q: What is the numerical value of the molecular partition function of a heteronuclear diatomic molecule…
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Q: What is overall molecular partition function Q, and how it is constructed using the partition…
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Q: The ratio between the translational partition function of H2 to that of unknown gas X2 at 400 K is…
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Q: (b) Write an expression of the vibrational partition function. Obtain the relation of the…
A: The answers are given below:
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- Imagine gaseous Kr at 298K confined to move in a two-dimensional plane of area 4.00 cm2. What is the value of the translational partition function?The ground configuration of oxygen gives rise to the three levels 3P2, 3P1, and 3P0 at 0, 158.5. and 226.5 cm-1, respectively. (a) Before doing any calculation, state the value of the partition function at T = 0. (b) Write an expression for the partition function at temperature T. Remember that a level with quantum number J has 2J + 1 states. Confirm that its value at T = 0 is what you anticipated. (c) Calculate the value of the partition function at 298 K. (d) Derive an expression for the electronic contribution to the molar heat capacity of an oxygen atom and plot it as a function of temperature. (e) Eva luate the expression at 25 °C.N2O and CO2 have similar rotational constants (12.6 and 11.7 GHz, respect ively) but strikingly different rotational partition functions. Why?
- Evaluate the rotational partition function of pyridine, C5H5N, at 25 °C given that ᷉ A = 0.2014 cm−1, ᷉ B = 0.1936 cm−1, ᷉ C = 0.0987 cm−1. Take the symmetry number into account.Calculate the rotational partition function for a non-linear molecule whose σ=5 at 25°C. Given A = 4.828 cm-1 , B = 1.015 cm-1 and C = 0.824 cm-1.Evaluate the translational partition function of (a) N2, (b) gaseous CS2 in a flask of volume 10.0 cm3. Why is one so much larger than the other?
- Calculating Partition Functions. Consider the acetylene molecule, which is linear and has the chemical structure H−C≡C−H. Calculate or determine the following: a. Symmetry number (?) and degrees of freedom b. Moment of inertia (I) and rotational temperature (Θr) c. Vibrational temperatures (Θv,i) d. Translational (qt), rotational (qr), vibrational (qv), and electronic (qe) partition functions at 298 K. e. Total partition function, (q/V). Helpful information: mass of H atom = 1.007947 amu mass of C atom = 12.01078 amu C≡C bond length = 1.203 Å C−H bond length = 1.060 Å vibrational frequencies = 1975, 3370, 3277, 729 (2), 600 (2) cm-1 (numbers in parenthesis indicate the degeneracy of that mode) ground state electronic degeneracy = 1Consider a system having four energy levels. Assuming the levels have energy values of(0, 1, 4, 9, and 16) x 10-24 J, and the degeneracies of the levels are 1, 2, 3, 4 and 5 (startingfrom ground state to highest excited state respectively), calculate the value of partitionfunction at 298 K?The diatomic molecule N2 has a rotational constant B(~) = 2.0 cm-1 and a vibrational constant v(~) = 2400 cm-1. The symmetry number for the molecule is 2. Sorry that I cannot write the symbols properly here for the wavenumber versions of the spectroscopic constants. (a) Suppose that a high-temperature limit for a partition function gives the value q = 0.34. Comment on the value and whether the high-temperature limit is valid.
- Calculate (i) the thermal wavelength, (ii) the translational partition function of a Ne atom in a cubic box of side 1.00 cm at 300 K and 3000 K.Calculate the translational partition function at (a) 300 K and (b) 600 K of a molecule of molar mass 100 g mol-1 in a container of volume 4.20 cm3.qtr at 300 K qtr at 600 K Note: this is a measure of the vast number of accessible microstates of translation available to a molecule under these conditions.For one mole of Br2 (molar mass 159.82 g/mol, vibrational frequency 325 cm-1,rotational constant 0.082 cm-1, nondegenerate ground electronic state) gas at 400 Kand 1 bar, calculate the molecular rotational partition function.A) 1,695B) 3,390C) 4,560D) 5,735E) 6,256 Please type answer note write by hend