## Vibrational Partition Function for Diatomic Ideal Gas Solution

STEP 0: Pre-Calculation Summary
Formula Used
Vibrational Partition Function = 1/(1-exp(-([hP]*Classical Frequency of Oscillation)/([BoltZ]*Temperature)))
qvib = 1/(1-exp(-([hP]*ν0)/([BoltZ]*T)))
This formula uses 2 Constants, 1 Functions, 3 Variables
Constants Used
[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23
[hP] - Planck constant Value Taken As 6.626070040E-34
Functions Used
exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)
Variables Used
Vibrational Partition Function - Vibrational Partition Function is the contribution to the total partition function due to vibrational motion.
Classical Frequency of Oscillation - (Measured in 1 Per Second) - Classical Frequency of Oscillation is the number of oscillations in the one-time unit, says in a second.
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.
STEP 1: Convert Input(s) to Base Unit
Classical Frequency of Oscillation: 26000000000000 1 Per Second --> 26000000000000 1 Per Second No Conversion Required
Temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
qvib = 1/(1-exp(-([hP]*ν0)/([BoltZ]*T))) --> 1/(1-exp(-([hP]*26000000000000)/([BoltZ]*300)))
Evaluating ... ...
qvib = 1.01586556322981
STEP 3: Convert Result to Output's Unit
1.01586556322981 --> No Conversion Required
1.01586556322981 1.015866 <-- Vibrational 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
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
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
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
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
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
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
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
Vibrational Partition Function = 1/(1-exp(-([hP]*Classical Frequency of Oscillation)/([BoltZ]*Temperature)))
Determination of Helmholtz Free Energy using Molecular PF for Distinguishable Particles
Helmholtz Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*ln(Molecular Partition Function)
Translational Partition Function
Translational Partition Function = Volume*((2*pi*Mass*[BoltZ]*Temperature)/([hP]^2))^(3/2)
Rotational Partition Function for Homonuclear Diatomic Molecules
Rotational Partition Function = Temperature/Symmetry Number*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2)
Rotational Partition Function for Heteronuclear Diatomic Molecule
Rotational Partition Function = Temperature*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2)
Mathematical Probability of Occurrence of Distribution
Probability of Occurrence = Number of Microstates in a Distribution/Total Number of Microstates
Boltzmann-Planck Equation
Entropy = [BoltZ]*ln(Number of Microstates in a Distribution)
Translational Partition Function using Thermal de Broglie Wavelength
Translational Partition Function = Volume/(Thermal de Broglie Wavelength)^3

## Vibrational Partition Function for Diatomic Ideal Gas Formula

Vibrational Partition Function = 1/(1-exp(-([hP]*Classical Frequency of Oscillation)/([BoltZ]*Temperature)))
qvib = 1/(1-exp(-([hP]*ν0)/([BoltZ]*T)))

## 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 Vibrational Partition Function for Diatomic Ideal Gas?

Vibrational Partition Function for Diatomic Ideal Gas calculator uses Vibrational Partition Function = 1/(1-exp(-([hP]*Classical Frequency of Oscillation)/([BoltZ]*Temperature))) to calculate the Vibrational Partition Function, The Vibrational Partition Function for Diatomic Ideal Gas formula is defined as the contribution to the total partition function due to vibrational motion. Vibrational Partition Function is denoted by qvib symbol.

How to calculate Vibrational Partition Function for Diatomic Ideal Gas using this online calculator? To use this online calculator for Vibrational Partition Function for Diatomic Ideal Gas, enter Classical Frequency of Oscillation 0) & Temperature (T) and hit the calculate button. Here is how the Vibrational Partition Function for Diatomic Ideal Gas calculation can be explained with given input values -> 2.7E+7 = 1/(1-exp(-([hP]*26000000000000)/([BoltZ]*300))).

### FAQ

What is Vibrational Partition Function for Diatomic Ideal Gas?
The Vibrational Partition Function for Diatomic Ideal Gas formula is defined as the contribution to the total partition function due to vibrational motion and is represented as qvib = 1/(1-exp(-([hP]*ν0)/([BoltZ]*T))) or Vibrational Partition Function = 1/(1-exp(-([hP]*Classical Frequency of Oscillation)/([BoltZ]*Temperature))). Classical Frequency of Oscillation is the number of oscillations in the one-time unit, says in a second & Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius or Kelvin.
How to calculate Vibrational Partition Function for Diatomic Ideal Gas?
The Vibrational Partition Function for Diatomic Ideal Gas formula is defined as the contribution to the total partition function due to vibrational motion is calculated using Vibrational Partition Function = 1/(1-exp(-([hP]*Classical Frequency of Oscillation)/([BoltZ]*Temperature))). To calculate Vibrational Partition Function for Diatomic Ideal Gas, you need Classical Frequency of Oscillation 0) & Temperature (T). With our tool, you need to enter the respective value for Classical Frequency of Oscillation & Temperature and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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