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Determination of Helmholtz Free Energy using Molecular PF for Distinguishable Particles Calculator

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✖Number of Atoms or Molecules represents the quantitative value of the total atoms or molecules present in a substance.ⓘ Number of Atoms or Molecules [N]			+10% -10%
✖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%
✖Molecular Partition Function enables us to calculate the probability of finding a collection of molecules with a given energy in a system.ⓘ Molecular Partition Function [q]			+10% -10%

✖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.ⓘ Determination of Helmholtz Free Energy using Molecular PF for Distinguishable Particles [A]

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Determination of Helmholtz Free Energy using Molecular PF for Distinguishable Particles

Formula

`"A" = -"N"*"[BoltZ]"*"T"*ln("q")`

Example

`"-11.735109KJ"=-"6.02E^23"*"[BoltZ]"*"300K"*ln("110.65")`

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Determination of Helmholtz Free Energy using Molecular PF for Distinguishable Particles Solution

STEP 0: Pre-Calculation Summary

Formula Used

Helmholtz Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*ln(Molecular Partition Function)
A = -N*[BoltZ]*T*ln(q)
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) --> -6.02E+23*[BoltZ]*300*ln(110.65)

Evaluating ... ...

A = -11735.1092044904

STEP 3: Convert Result to Output's Unit

-11735.1092044904 Joule -->-11.7351092044904 Kilojoule (Check conversion here)

FINAL ANSWER

-11.7351092044904 ≈ -11.735109 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

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

Determination of Helmholtz Free Energy using Molecular PF for Distinguishable Particles Formula

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

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 Distinguishable Particles?

Determination of Helmholtz Free Energy using Molecular PF for Distinguishable Particles calculator uses Helmholtz Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*ln(Molecular Partition Function) to calculate the Helmholtz Free Energy, Determination of Helmholtz Free Energy using Molecular PF for Distinguishable Particles formula is defined as the method in which we can calculate the Helmholtz free energy from the molecular partition function. Helmholtz Free Energy is denoted by A symbol.

How to calculate Determination of Helmholtz Free Energy using Molecular PF for Distinguishable Particles using this online calculator? To use this online calculator for Determination of Helmholtz Free Energy using Molecular PF for Distinguishable 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 Distinguishable Particles calculation can be explained with given input values -> -0.011735 = -6.02E+23*[BoltZ]*300*ln(110.65).

FAQ

What is Determination of Helmholtz Free Energy using Molecular PF for Distinguishable Particles?

Determination of Helmholtz Free Energy using Molecular PF for Distinguishable Particles formula is defined as the method in which we can calculate the Helmholtz free energy from the molecular partition function and is represented as A = -N*[BoltZ]*T*ln(q) or Helmholtz Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*ln(Molecular Partition Function). 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 Distinguishable Particles?

Determination of Helmholtz Free Energy using Molecular PF for Distinguishable Particles formula is defined as the method in which we can calculate the Helmholtz free energy from the molecular partition function is calculated using Helmholtz Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*ln(Molecular Partition Function). To calculate Determination of Helmholtz Free Energy using Molecular PF for Distinguishable 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/Number of Atoms or Molecules)+1)

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