## Determination of Helmholtz Free Energy using Molecular PF for Indistinguishable Particles Solution

STEP 0: Pre-Calculation Summary
Formula Used
Helmholtz Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*(ln(Molecular Partition Function/Number of Atoms or Molecules)+1)
A = -N*[BoltZ]*T*(ln(q/N)+1)
This formula uses 1 Constants, 1 Functions, 4 Variables
Constants Used
[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23
Functions Used
ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)
Variables Used
Helmholtz Free Energy - (Measured in Joule) - Helmholtz Free Energy is a concept in thermodynamics where the work of a closed system with constant temperature and volume is measured using thermodynamic potential.
Number of Atoms or Molecules - Number of Atoms or Molecules represents the quantitative value of the total atoms or molecules present in a substance.
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.
Molecular Partition Function - Molecular Partition Function enables us to calculate the probability of finding a collection of molecules with a given energy in a system.
STEP 1: Convert Input(s) to Base Unit
Number of Atoms or Molecules: 6.02E+23 --> No Conversion Required
Temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
Molecular Partition Function: 110.65 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
A = -N*[BoltZ]*T*(ln(q/N)+1) --> -6.02E+23*[BoltZ]*300*(ln(110.65/6.02E+23)+1)
Evaluating ... ...
A = 122299.225488437
STEP 3: Convert Result to Output's Unit
122299.225488437 Joule -->122.299225488438 Kilojoule (Check conversion βhere)
122.299225488438 β 122.2992 Kilojoule <-- Helmholtz Free Energy
(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

## Determination of Helmholtz Free Energy using Molecular PF for Indistinguishable Particles Formula

Helmholtz Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*(ln(Molecular Partition Function/Number of Atoms or Molecules)+1)
A = -N*[BoltZ]*T*(ln(q/N)+1)

## 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 Determination of Helmholtz Free Energy using Molecular PF for Indistinguishable Particles?

Determination of Helmholtz Free Energy using Molecular PF for Indistinguishable Particles calculator uses Helmholtz Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*(ln(Molecular Partition Function/Number of Atoms or Molecules)+1) to calculate the Helmholtz Free Energy, The Determination of Helmholtz Free Energy using Molecular PF for Indistinguishable Particles formula is defined as as the method in which the Helmholtz free energy for n- indistinguishable particles can be found using the molecular partition function. Helmholtz Free Energy is denoted by A symbol.

How to calculate Determination of Helmholtz Free Energy using Molecular PF for Indistinguishable Particles using this online calculator? To use this online calculator for Determination of Helmholtz Free Energy using Molecular PF for Indistinguishable Particles, enter Number of Atoms or Molecules (N), Temperature (T) & Molecular Partition Function (q) and hit the calculate button. Here is how the Determination of Helmholtz Free Energy using Molecular PF for Indistinguishable Particles calculation can be explained with given input values -> 0.122299 = -6.02E+23*[BoltZ]*300*(ln(110.65/6.02E+23)+1).

### FAQ

What is Determination of Helmholtz Free Energy using Molecular PF for Indistinguishable Particles?
The Determination of Helmholtz Free Energy using Molecular PF for Indistinguishable Particles formula is defined as as the method in which the Helmholtz free energy for n- indistinguishable particles can be found using the molecular partition function and is represented as A = -N*[BoltZ]*T*(ln(q/N)+1) or Helmholtz Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*(ln(Molecular Partition Function/Number of Atoms or Molecules)+1). Number of Atoms or Molecules represents the quantitative value of the total atoms or molecules present in a substance, Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius or Kelvin & Molecular Partition Function enables us to calculate the probability of finding a collection of molecules with a given energy in a system.
How to calculate Determination of Helmholtz Free Energy using Molecular PF for Indistinguishable Particles?
The Determination of Helmholtz Free Energy using Molecular PF for Indistinguishable Particles formula is defined as as the method in which the Helmholtz free energy for n- indistinguishable particles can be found using the molecular partition function is calculated using Helmholtz Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*(ln(Molecular Partition Function/Number of Atoms or Molecules)+1). To calculate Determination of Helmholtz Free Energy using Molecular PF for Indistinguishable Particles, you need Number of Atoms or Molecules (N), Temperature (T) & Molecular Partition Function (q). With our tool, you need to enter the respective value for Number of Atoms or Molecules, Temperature & Molecular Partition Function 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 Helmholtz Free Energy?
In this formula, Helmholtz Free Energy uses Number of Atoms or Molecules, Temperature & Molecular Partition Function. We can use 2 other way(s) to calculate the same, which is/are as follows -
• Helmholtz Free Energy = -Universal Gas Constant*Temperature*(ln(([BoltZ]*Temperature)/Pressure*((2*pi*Mass*[BoltZ]*Temperature)/[hP]^2)^(3/2))+1)
• Helmholtz Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*ln(Molecular Partition Function)
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