## Determination of Gibbs Free Energy using Sackur-Tetrode Equation Solution

STEP 0: Pre-Calculation Summary
Formula Used
Gibbs Free Energy = -Universal Gas Constant*Temperature*ln(([BoltZ]*Temperature)/Pressure*((2*pi*Mass*[BoltZ]*Temperature)/[hP]^2)^(3/2))
G = -R*T*ln(([BoltZ]*T)/p*((2*pi*m*[BoltZ]*T)/[hP]^2)^(3/2))
This formula uses 3 Constants, 1 Functions, 5 Variables
Constants Used
[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23
[hP] - Planck constant Value Taken As 6.626070040E-34
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
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
Gibbs Free Energy - (Measured in Joule) - Gibbs Free Energy is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure-volume work at constant temperature and pressure.
Universal Gas Constant - Universal Gas Constant is a physical constant that appears in an equation defining the behavior of a gas under theoretically ideal conditions. Its unit is joule*kelvin−1*mole−1.
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.
Pressure - (Measured in Pascal) - Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Mass - (Measured in Kilogram) - Mass is the property of a body that is a measure of its inertia and that is commonly taken as a measure of the amount of material it contains and causes it to have weight in a gravitational field.
STEP 1: Convert Input(s) to Base Unit
Universal Gas Constant: 8.314 --> No Conversion Required
Temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
Pressure: 1.123 Atmosphere Technical --> 110128.6795 Pascal (Check conversion ​here)
Mass: 2.656E-26 Kilogram --> 2.656E-26 Kilogram No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
G = -R*T*ln(([BoltZ]*T)/p*((2*pi*m*[BoltZ]*T)/[hP]^2)^(3/2)) --> -8.314*300*ln(([BoltZ]*300)/110128.6795*((2*pi*2.656E-26*[BoltZ]*300)/[hP]^2)^(3/2))
Evaluating ... ...
G = -36589.0773818438
STEP 3: Convert Result to Output's Unit
-36589.0773818438 Joule -->-36.5890773818438 Kilojoule (Check conversion ​here)
-36.5890773818438 -36.589077 Kilojoule <-- Gibbs Free Energy
(Calculation completed in 00.020 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 Gibbs Free Energy using Sackur-Tetrode Equation Formula

Gibbs Free Energy = -Universal Gas Constant*Temperature*ln(([BoltZ]*Temperature)/Pressure*((2*pi*Mass*[BoltZ]*Temperature)/[hP]^2)^(3/2))
G = -R*T*ln(([BoltZ]*T)/p*((2*pi*m*[BoltZ]*T)/[hP]^2)^(3/2))

## 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 Gibbs Free Energy using Sackur-Tetrode Equation?

Determination of Gibbs Free Energy using Sackur-Tetrode Equation calculator uses Gibbs Free Energy = -Universal Gas Constant*Temperature*ln(([BoltZ]*Temperature)/Pressure*((2*pi*Mass*[BoltZ]*Temperature)/[hP]^2)^(3/2)) to calculate the Gibbs Free Energy, The Determination of Gibbs Free Energy using Sackur-Tetrode Equation formula is defined as the thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure-volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure. Gibbs Free Energy is denoted by G symbol.

How to calculate Determination of Gibbs Free Energy using Sackur-Tetrode Equation using this online calculator? To use this online calculator for Determination of Gibbs Free Energy using Sackur-Tetrode Equation, enter Universal Gas Constant (R), Temperature (T), Pressure (p) & Mass (m) and hit the calculate button. Here is how the Determination of Gibbs Free Energy using Sackur-Tetrode Equation calculation can be explained with given input values -> -0.036589 = -8.314*300*ln(([BoltZ]*300)/110128.6795*((2*pi*2.656E-26*[BoltZ]*300)/[hP]^2)^(3/2)).

### FAQ

What is Determination of Gibbs Free Energy using Sackur-Tetrode Equation?
The Determination of Gibbs Free Energy using Sackur-Tetrode Equation formula is defined as the thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure-volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure and is represented as G = -R*T*ln(([BoltZ]*T)/p*((2*pi*m*[BoltZ]*T)/[hP]^2)^(3/2)) or Gibbs Free Energy = -Universal Gas Constant*Temperature*ln(([BoltZ]*Temperature)/Pressure*((2*pi*Mass*[BoltZ]*Temperature)/[hP]^2)^(3/2)). Universal Gas Constant is a physical constant that appears in an equation defining the behavior of a gas under theoretically ideal conditions. Its unit is joule*kelvin−1*mole−1, Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius or Kelvin, Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed & Mass is the property of a body that is a measure of its inertia and that is commonly taken as a measure of the amount of material it contains and causes it to have weight in a gravitational field.
How to calculate Determination of Gibbs Free Energy using Sackur-Tetrode Equation?
The Determination of Gibbs Free Energy using Sackur-Tetrode Equation formula is defined as the thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure-volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure is calculated using Gibbs Free Energy = -Universal Gas Constant*Temperature*ln(([BoltZ]*Temperature)/Pressure*((2*pi*Mass*[BoltZ]*Temperature)/[hP]^2)^(3/2)). To calculate Determination of Gibbs Free Energy using Sackur-Tetrode Equation, you need Universal Gas Constant (R), Temperature (T), Pressure (p) & Mass (m). With our tool, you need to enter the respective value for Universal Gas Constant, Temperature, Pressure & Mass 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 Gibbs Free Energy?
In this formula, Gibbs Free Energy uses Universal Gas Constant, Temperature, Pressure & Mass. We can use 2 other way(s) to calculate the same, which is/are as follows -
• Gibbs Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*ln(Molecular Partition Function)+Pressure*Volume
• Gibbs Free Energy = -Number of Atoms or Molecules*[BoltZ]*Temperature*ln(Molecular Partition Function/Number of Atoms or Molecules)
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