## Translational Partition Function Solution

STEP 0: Pre-Calculation Summary
Formula Used
Translational Partition Function = Volume*((2*pi*Mass*[BoltZ]*Temperature)/([hP]^2))^(3/2)
qtrans = V*((2*pi*m*[BoltZ]*T)/([hP]^2))^(3/2)
This formula uses 3 Constants, 4 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
Variables Used
Translational Partition Function - Translational Partition Function is the contribution to the total partition function due to translational motion.
Volume - (Measured in Cubic Meter) - Volume is the amount of space that a substance or object occupies, or that is enclosed within a container.
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.
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.
STEP 1: Convert Input(s) to Base Unit
Volume: 0.02214 Cubic Meter --> 0.02214 Cubic Meter No Conversion Required
Mass: 2.656E-26 Kilogram --> 2.656E-26 Kilogram No Conversion Required
Temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
qtrans = V*((2*pi*m*[BoltZ]*T)/([hP]^2))^(3/2) --> 0.02214*((2*pi*2.656E-26*[BoltZ]*300)/([hP]^2))^(3/2)
Evaluating ... ...
qtrans = 1.3830186546575E+30
STEP 3: Convert Result to Output's Unit
1.3830186546575E+30 --> No Conversion Required
1.3830186546575E+30 1.4E+30 <-- Translational Partition Function
(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

## Translational Partition Function Formula

Translational Partition Function = Volume*((2*pi*Mass*[BoltZ]*Temperature)/([hP]^2))^(3/2)
qtrans = V*((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 Translational Partition Function?

Translational Partition Function calculator uses Translational Partition Function = Volume*((2*pi*Mass*[BoltZ]*Temperature)/([hP]^2))^(3/2) to calculate the Translational Partition Function, The Translational Partition Function formula is defined as the contribution to the total partition function due to translational motion. Translational Partition Function is denoted by qtrans symbol.

How to calculate Translational Partition Function using this online calculator? To use this online calculator for Translational Partition Function, enter Volume (V), Mass (m) & Temperature (T) and hit the calculate button. Here is how the Translational Partition Function calculation can be explained with given input values -> 1.4E+30 = 0.02214*((2*pi*2.656E-26*[BoltZ]*300)/([hP]^2))^(3/2).

### FAQ

What is Translational Partition Function?
The Translational Partition Function formula is defined as the contribution to the total partition function due to translational motion and is represented as qtrans = V*((2*pi*m*[BoltZ]*T)/([hP]^2))^(3/2) or Translational Partition Function = Volume*((2*pi*Mass*[BoltZ]*Temperature)/([hP]^2))^(3/2). Volume is the amount of space that a substance or object occupies, or that is enclosed within a container, 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 & Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius or Kelvin.
How to calculate Translational Partition Function?
The Translational Partition Function formula is defined as the contribution to the total partition function due to translational motion is calculated using Translational Partition Function = Volume*((2*pi*Mass*[BoltZ]*Temperature)/([hP]^2))^(3/2). To calculate Translational Partition Function, you need Volume (V), Mass (m) & Temperature (T). With our tool, you need to enter the respective value for Volume, Mass & Temperature 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 Translational Partition Function?
In this formula, Translational Partition Function uses Volume, Mass & Temperature. We can use 1 other way(s) to calculate the same, which is/are as follows -
• Translational Partition Function = Volume/(Thermal de Broglie Wavelength)^3
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