## Mathematical Probability of Occurrence of Distribution Solution

STEP 0: Pre-Calculation Summary
Formula Used
Probability of Occurrence = Number of Microstates in a Distribution/Total Number of Microstates
ρ = W/Wtot
This formula uses 3 Variables
Variables Used
Probability of Occurrence - Probability of Occurrence is the odds of a certain distribution occurring in the system.
Number of Microstates in a Distribution - Number of Microstates in a Distribution describes the precise positions and momenta of all the individual particles or components that make up the distribution.
Total Number of Microstates - Total Number of Microstates is the number of microstates present in all distributions.
STEP 1: Convert Input(s) to Base Unit
Number of Microstates in a Distribution: 30 --> No Conversion Required
Total Number of Microstates: 130 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ρ = W/Wtot --> 30/130
Evaluating ... ...
ρ = 0.230769230769231
STEP 3: Convert Result to Output's Unit
0.230769230769231 --> No Conversion Required
FINAL ANSWER
0.230769230769231 0.230769 <-- Probability of Occurrence
(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

## Mathematical Probability of Occurrence of Distribution Formula

Probability of Occurrence = Number of Microstates in a Distribution/Total Number of Microstates
ρ = W/Wtot

## 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 Mathematical Probability of Occurrence of Distribution?

Mathematical Probability of Occurrence of Distribution calculator uses Probability of Occurrence = Number of Microstates in a Distribution/Total Number of Microstates to calculate the Probability of Occurrence, The Mathematical Probability of Occurrence of Distribution formula is defined as the odds of a particular distribution to occur in the system. Probability of Occurrence is denoted by ρ symbol.

How to calculate Mathematical Probability of Occurrence of Distribution using this online calculator? To use this online calculator for Mathematical Probability of Occurrence of Distribution, enter Number of Microstates in a Distribution (W) & Total Number of Microstates (Wtot) and hit the calculate button. Here is how the Mathematical Probability of Occurrence of Distribution calculation can be explained with given input values -> 0.230769 = 30/130.

### FAQ

What is Mathematical Probability of Occurrence of Distribution?
The Mathematical Probability of Occurrence of Distribution formula is defined as the odds of a particular distribution to occur in the system and is represented as ρ = W/Wtot or Probability of Occurrence = Number of Microstates in a Distribution/Total Number of Microstates. Number of Microstates in a Distribution describes the precise positions and momenta of all the individual particles or components that make up the distribution & Total Number of Microstates is the number of microstates present in all distributions.
How to calculate Mathematical Probability of Occurrence of Distribution?
The Mathematical Probability of Occurrence of Distribution formula is defined as the odds of a particular distribution to occur in the system is calculated using Probability of Occurrence = Number of Microstates in a Distribution/Total Number of Microstates. To calculate Mathematical Probability of Occurrence of Distribution, you need Number of Microstates in a Distribution (W) & Total Number of Microstates (Wtot). With our tool, you need to enter the respective value for Number of Microstates in a Distribution & Total Number of Microstates 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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