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Rotational Partition Function for Heteronuclear Diatomic Molecule Calculator

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✖Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius or Kelvin.ⓘ Temperature [T]			+10% -10%
✖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.ⓘ Moment of Inertia [I]			+10% -10%

✖Rotational Partition Function is the rotational contribution to the total partition function.ⓘ Rotational Partition Function for Heteronuclear Diatomic Molecule [q_rot]

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Formula

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Rotational Partition Function for Heteronuclear Diatomic Molecule

Formula

`"q"_{"rot"} = "T"*((8*pi^2*"I"*"[BoltZ]")/"[hP]"^2)`

Example

`"145.2502"="300K"*((8*pi^2*"1.95E^-46kg·m²"*"[BoltZ]")/"[hP]"^2)`

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Rotational Partition Function for Heteronuclear Diatomic Molecule Solution

STEP 0: Pre-Calculation Summary

Formula Used

Rotational Partition Function = Temperature*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2)
q_rot = T*((8*pi^2*I*[BoltZ])/[hP]^2)
This formula uses 3 Constants, 3 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.
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
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

q_rot = T*((8*pi^2*I*[BoltZ])/[hP]^2) --> 300*((8*pi^2*1.95E-46*[BoltZ])/[hP]^2)

Evaluating ... ...

q_rot = 145.250182156806

STEP 3: Convert Result to Output's Unit

145.250182156806 --> No Conversion Required

FINAL ANSWER

145.250182156806 ≈ 145.2502 <-- 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 Heteronuclear Diatomic Molecule Formula

Rotational Partition Function = Temperature*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2)
q_rot = T*((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 Heteronuclear Diatomic Molecule?

Rotational Partition Function for Heteronuclear Diatomic Molecule calculator uses Rotational Partition Function = Temperature*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2) to calculate the Rotational Partition Function, The Rotational Partition Function for Heteronuclear Diatomic Molecule formula is defined as the contribution to the total partition function due to rotational motion. Rotational Partition Function is denoted by q_rot symbol.

How to calculate Rotational Partition Function for Heteronuclear Diatomic Molecule using this online calculator? To use this online calculator for Rotational Partition Function for Heteronuclear Diatomic Molecule, enter Temperature (T) & Moment of Inertia (I) and hit the calculate button. Here is how the Rotational Partition Function for Heteronuclear Diatomic Molecule calculation can be explained with given input values -> 145.2502 = 300*((8*pi^2*1.95E-46*[BoltZ])/[hP]^2).

FAQ

What is Rotational Partition Function for Heteronuclear Diatomic Molecule?

The Rotational Partition Function for Heteronuclear Diatomic Molecule formula is defined as the contribution to the total partition function due to rotational motion and is represented as q_rot = T*((8*pi^2*I*[BoltZ])/[hP]^2) or Rotational Partition Function = Temperature*((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 & 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 Heteronuclear Diatomic Molecule?

The Rotational Partition Function for Heteronuclear Diatomic Molecule formula is defined as the contribution to the total partition function due to rotational motion is calculated using Rotational Partition Function = Temperature*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2). To calculate Rotational Partition Function for Heteronuclear Diatomic Molecule, you need Temperature (T) & Moment of Inertia (I). With our tool, you need to enter the respective value for Temperature & 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 & Moment of Inertia. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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