Rotational Partition Function for Homonuclear Diatomic Molecules Solution

STEP 0: Pre-Calculation Summary
Formula Used
Rotational Partition Function = Temperature/Symmetry Number*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2)
qrot = T/σ*((8*pi^2*I*[BoltZ])/[hP]^2)
This formula uses 3 Constants, 4 Variables
Constants Used
[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23
[hP] - Planck constant Value Taken As 6.626070040E-34
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Rotational Partition Function - Rotational Partition Function is the rotational contribution to the total partition function.
Temperature - (Measured in Kelvin) - Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius or Kelvin.
Symmetry Number - Symmetry Number or symmetry order of an object is the number of different but indistinguishable arrangements of the object, that is, it is the order of its symmetry group.
Moment of Inertia - (Measured in Kilogram Square Meter) - Moment of Inertia is the quantitative measure of the rotational inertia of a body or the opposition that the body exhibits to having its speed of rotation about an axis altered by torque.
STEP 1: Convert Input(s) to Base Unit
Temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
Symmetry Number: 2 --> No Conversion Required
Moment of Inertia: 1.95E-46 Kilogram Square Meter --> 1.95E-46 Kilogram Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
qrot = T/σ*((8*pi^2*I*[BoltZ])/[hP]^2) --> 300/2*((8*pi^2*1.95E-46*[BoltZ])/[hP]^2)
Evaluating ... ...
qrot = 72.6250910784032
STEP 3: Convert Result to Output's Unit
72.6250910784032 --> No Conversion Required
FINAL ANSWER
72.6250910784032 72.62509 <-- Rotational Partition Function
(Calculation completed in 00.004 seconds)

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15 Statistical Thermodynamics Calculators

Determination of Helmholtz Free Energy using Sackur-Tetrode Equation
​ Go Helmholtz Free Energy = -Universal Gas Constant*Temperature*(ln(([BoltZ]*Temperature)/Pressure*((2*pi*Mass*[BoltZ]*Temperature)/[hP]^2)^(3/2))+1)
Determination of Gibbs Free Energy using Sackur-Tetrode Equation
​ Go Gibbs Free Energy = -Universal Gas Constant*Temperature*ln(([BoltZ]*Temperature)/Pressure*((2*pi*Mass*[BoltZ]*Temperature)/[hP]^2)^(3/2))
Determination of Entropy using Sackur-Tetrode Equation
​ Go Standard Entropy = Universal Gas Constant*(-1.154+(3/2)*ln(Relative Atomic Mass)+(5/2)*ln(Temperature)-ln(Pressure/Standard Pressure))
Determination of Gibbs Free energy using Molecular PF for Distinguishable Particles
​ Go Gibbs Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*ln(Molecular Partition Function)+Pressure*Volume
Determination of Helmholtz Free Energy using Molecular PF for Indistinguishable Particles
​ Go Helmholtz Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*(ln(Molecular Partition Function/Number of Atoms or Molecules)+1)
Determination of Gibbs Free energy using Molecular PF for Indistinguishable Particles
​ Go Gibbs Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*ln(Molecular Partition Function/Number of Atoms or Molecules)
Total Number of Microstates in All Distributions
​ Go Total Number of Microstates = ((Total Number of Particles+Number of Quanta of Energy-1)!)/((Total Number of Particles-1)!*(Number of Quanta of Energy!))
Vibrational Partition Function for Diatomic Ideal Gas
​ Go Vibrational Partition Function = 1/(1-exp(-([hP]*Classical Frequency of Oscillation)/([BoltZ]*Temperature)))
Determination of Helmholtz Free Energy using Molecular PF for Distinguishable Particles
​ Go Helmholtz Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*ln(Molecular Partition Function)
Translational Partition Function
​ Go Translational Partition Function = Volume*((2*pi*Mass*[BoltZ]*Temperature)/([hP]^2))^(3/2)
Rotational Partition Function for Homonuclear Diatomic Molecules
​ Go Rotational Partition Function = Temperature/Symmetry Number*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2)
Rotational Partition Function for Heteronuclear Diatomic Molecule
​ Go Rotational Partition Function = Temperature*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2)
Mathematical Probability of Occurrence of Distribution
​ Go Probability of Occurrence = Number of Microstates in a Distribution/Total Number of Microstates
Boltzmann-Planck Equation
​ Go Entropy = [BoltZ]*ln(Number of Microstates in a Distribution)
Translational Partition Function using Thermal de Broglie Wavelength
​ Go Translational Partition Function = Volume/(Thermal de Broglie Wavelength)^3

Rotational Partition Function for Homonuclear Diatomic Molecules Formula

Rotational Partition Function = Temperature/Symmetry Number*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2)
qrot = T/σ*((8*pi^2*I*[BoltZ])/[hP]^2)

What is Statistical Thermodynamics?

Statistical thermodynamics is a theory that uses molecular properties to predict the behavior of macroscopic quantities of compounds. While the origins of statistical thermodynamics predate the development of quantum mechanics, the modern development of statistical thermodynamics assumes that the quantized energy levels associated with a particular system are known. From these energy-level data, a temperature-dependent quantity called the partition function can be calculated. From the partition function, all of the thermodynamic properties of the system can be calculated. Statistical thermodynamics has also been applied to the general problem of predicting reaction rates. This application is called transition state theory or the theory of absolute reaction rates.

How to Calculate Rotational Partition Function for Homonuclear Diatomic Molecules?

Rotational Partition Function for Homonuclear Diatomic Molecules calculator uses Rotational Partition Function = Temperature/Symmetry Number*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2) to calculate the Rotational Partition Function, The Rotational Partition Function for Homonuclear Diatomic Molecules formula is defined as the contribution to the molecular partition function due to rotational motion for diatomic molecule. Rotational Partition Function is denoted by qrot symbol.

How to calculate Rotational Partition Function for Homonuclear Diatomic Molecules using this online calculator? To use this online calculator for Rotational Partition Function for Homonuclear Diatomic Molecules, enter Temperature (T), Symmetry Number (σ) & Moment of Inertia (I) and hit the calculate button. Here is how the Rotational Partition Function for Homonuclear Diatomic Molecules calculation can be explained with given input values -> 72.62509 = 300/2*((8*pi^2*1.95E-46*[BoltZ])/[hP]^2).

FAQ

What is Rotational Partition Function for Homonuclear Diatomic Molecules?
The Rotational Partition Function for Homonuclear Diatomic Molecules formula is defined as the contribution to the molecular partition function due to rotational motion for diatomic molecule and is represented as qrot = T/σ*((8*pi^2*I*[BoltZ])/[hP]^2) or Rotational Partition Function = Temperature/Symmetry Number*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2). Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius or Kelvin, Symmetry Number or symmetry order of an object is the number of different but indistinguishable arrangements of the object, that is, it is the order of its symmetry group & Moment of Inertia is the quantitative measure of the rotational inertia of a body or the opposition that the body exhibits to having its speed of rotation about an axis altered by torque.
How to calculate Rotational Partition Function for Homonuclear Diatomic Molecules?
The Rotational Partition Function for Homonuclear Diatomic Molecules formula is defined as the contribution to the molecular partition function due to rotational motion for diatomic molecule is calculated using Rotational Partition Function = Temperature/Symmetry Number*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2). To calculate Rotational Partition Function for Homonuclear Diatomic Molecules, you need Temperature (T), Symmetry Number (σ) & Moment of Inertia (I). With our tool, you need to enter the respective value for Temperature, Symmetry Number & Moment of Inertia and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Rotational Partition Function?
In this formula, Rotational Partition Function uses Temperature, Symmetry Number & Moment of Inertia. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Rotational Partition Function = Temperature*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2)
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