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

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Indistinguishable Particles Distinguishable Particles

✖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_A]			+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 Indistinguishable Particles [A]

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Formula

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Determination of Helmholtz Free Energy using Molecular PF for Indistinguishable Particles

Formula

A = - N A \cdot [BoltZ] \cdot T \cdot (\ln (\frac{q}{N A}) + 1)

Example

122.2992 KJ = - 6.02E+23 \cdot [BoltZ] \cdot 300 K \cdot (\ln (\frac{110.65}{6.02E+23}) + 1)

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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_A*[BoltZ]*T*(ln(q/N_A)+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_A*[BoltZ]*T*(ln(q/N_A)+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 here)

FINAL ANSWER

122.299225488438 ≈ 122.2992 Kilojoule <-- Helmholtz Free Energy

(Calculation completed in 00.004 seconds)

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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)

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)

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_A*[BoltZ]*T*(ln(q/N_A)+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_A), 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 -> 0.407664 = -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_A*[BoltZ]*T*(ln(q/N_A)+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_A), 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.

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