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Rotational Partition Function for Homonuclear Diatomic Molecules Formula

GoRotational Partition Function for Heteronuclear Diatomic Molecule Formula

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Rotational Partition Function is the rotational contribution to the total partition function. Check FAQs

q rot = \frac{T}{σ} \cdot (\frac{8 \cdot π^{2} \cdot I \cdot [BoltZ]}{{[hP]}^{2}})

q_rot - Rotational Partition Function?T - Temperature?σ - Symmetry Number?I - Moment of Inertia?[BoltZ] - Boltzmann constant?[hP] - Planck constant?π - Archimedes' constant?

Rotational Partition Function for Homonuclear Diatomic Molecules Example

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Here is how the Rotational Partition Function for Homonuclear Diatomic Molecules equation looks like with Values.

Here is how the Rotational Partition Function for Homonuclear Diatomic Molecules equation looks like with Units.

Here is how the Rotational Partition Function for Homonuclear Diatomic Molecules equation looks like.

72.6251 = \frac{300}{2} \cdot (\frac{8 \cdot {3.1416}^{2} \cdot 2E-46 \cdot 1.4E-23}{{6.6E-34}^{2}})

72.6251 = \frac{300K}{2} \cdot (\frac{8 \cdot {3.1416}^{2} \cdot 2E-46kg·m² \cdot 1.4E-23J/K}{{6.6E-34}^{2}})

72.6251 = \frac{300}{2} \cdot (\frac{8 \cdot {3.1416}^{2} \cdot 2E-46 \cdot 1.4E-23}{{6.6E-34}^{2}})

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Rotational Partition Function for Homonuclear Diatomic Molecules Solution

Follow our step by step solution on how to calculate Rotational Partition Function for Homonuclear Diatomic Molecules?

FIRST Step Consider the formula

q rot = \frac{T}{σ} \cdot (\frac{8 \cdot π^{2} \cdot I \cdot [BoltZ]}{{[hP]}^{2}})

Next Step Substitute values of Variables

∴

q rot = \frac{300K}{2} \cdot (\frac{8 \cdot π^{2} \cdot 2E-46kg·m² \cdot [BoltZ]}{{[hP]}^{2}})

Next Step Substitute values of Constants

∴

q rot = \frac{300K}{2} \cdot (\frac{8 \cdot {3.1416}^{2} \cdot 2E-46kg·m² \cdot 1.4E-23J/K}{{6.6E-34}^{2}})

Next Step Prepare to Evaluate

∴

q rot = \frac{300}{2} \cdot (\frac{8 \cdot {3.1416}^{2} \cdot 2E-46 \cdot 1.4E-23}{{6.6E-34}^{2}})

Next Step Evaluate

∴

q rot = 72.6250910784032

LAST Step Rounding Answer

∴

q rot = 72.6251

Rotational Partition Function for Homonuclear Diatomic Molecules Formula Elements

Variables

Constants

Rotational Partition Function

Rotational Partition Function is the rotational contribution to the total partition function.

Symbol: q_rot

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Rotational Partition Function

Temperature

Temperature is the measure of hotness or coldness expressed in terms of any of several scales, including Fahrenheit and Celsius or Kelvin.

Symbol: T

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Temperature

Symmetry Number

Symmetry Number or symmetry order of an object is the number of different but indistinguishable arrangements of the object, that is, it is the order of its symmetry group.

Symbol: σ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Symmetry Number

Moment of Inertia

Moment of Inertia is the quantitative measure of the rotational inertia of a body or the opposition that the body exhibits to having its speed of rotation about an axis altered by torque.

Symbol: I

Measurement: Moment of InertiaUnit: kg·m²

Note: Value can be positive or negative.

Formulas to find Moment of Inertia

Boltzmann constant

Boltzmann constant relates the average kinetic energy of particles in a gas with the temperature of the gas and is a fundamental constant in statistical mechanics and thermodynamics.

Symbol: [BoltZ]

Value: 1.38064852E-23 J/K

Planck constant

Planck constant is a fundamental universal constant that defines the quantum nature of energy and relates the energy of a photon to its frequency.

Symbol: [hP]

Value: 6.626070040E-34

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Rotational Partition Function

Go Rotational Partition Function for Heteronuclear Diatomic Molecule

q rot = T \cdot (\frac{8 \cdot π^{2} \cdot I \cdot [BoltZ]}{{[hP]}^{2}})

Other formulas in Distinguishable Particles category

Go Total Number of Microstates in All Distributions

W tot = \frac{(N' + E - 1)!}{(N' - 1)! \cdot (E!)}

Go Translational Partition Function

q trans = V \cdot {(\frac{2 \cdot π \cdot m \cdot [BoltZ] \cdot T}{{[hP]}^{2}})}^{\frac{3}{2}}

Go Translational Partition Function using Thermal de Broglie Wavelength

q trans = \frac{V}{{(Λ)}^{3}}

Go Determination of Entropy using Sackur-Tetrode Equation

S° m = R \cdot (- 1.154 + (\frac{3}{2}) \cdot \ln (A r) + (\frac{5}{2}) \cdot \ln (T) - \ln (\frac{p}{p°}))

How to Evaluate Rotational Partition Function for Homonuclear Diatomic Molecules?

Rotational Partition Function for Homonuclear Diatomic Molecules evaluator uses Rotational Partition Function = Temperature/Symmetry Number*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2) to evaluate the Rotational Partition Function, The Rotational Partition Function for Homonuclear Diatomic Molecules formula is defined as the contribution to the molecular partition function due to rotational motion for diatomic molecule. Rotational Partition Function is denoted by q_rot symbol.

How to evaluate Rotational Partition Function for Homonuclear Diatomic Molecules using this online evaluator? To use this online evaluator for Rotational Partition Function for Homonuclear Diatomic Molecules, enter Temperature (T), Symmetry Number (σ) & Moment of Inertia (I) and hit the calculate button.

FAQs on Rotational Partition Function for Homonuclear Diatomic Molecules

What is the formula to find Rotational Partition Function for Homonuclear Diatomic Molecules?

The formula of Rotational Partition Function for Homonuclear Diatomic Molecules is expressed as Rotational Partition Function = Temperature/Symmetry Number*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2). Here is an example- 242.0836 = 300/2*((8*pi^2*1.95E-46*[BoltZ])/[hP]^2).

How to calculate Rotational Partition Function for Homonuclear Diatomic Molecules?

With Temperature (T), Symmetry Number (σ) & Moment of Inertia (I) we can find Rotational Partition Function for Homonuclear Diatomic Molecules using the formula - Rotational Partition Function = Temperature/Symmetry Number*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2). This formula also uses Boltzmann constant, Planck constant, Archimedes' constant .

What are the other ways to Calculate Rotational Partition Function?

Here are the different ways to Calculate Rotational Partition Function-

Rotational Partition Function=Temperature*((8*pi^2*Moment of Inertia*[BoltZ])/[hP]^2)

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Rotational Partition Function for Homonuclear Diatomic Molecules Formula

​GoRotational Partition Function for Heteronuclear Diatomic Molecule Formula

Rotational Partition Function for Homonuclear Diatomic Molecules Example

Rotational Partition Function for Homonuclear Diatomic Molecules Solution

Rotational Partition Function for Homonuclear Diatomic Molecules Formula Elements

Other Formulas to find Rotational Partition Function

Other formulas in Distinguishable Particles category

How to Evaluate Rotational Partition Function for Homonuclear Diatomic Molecules?

FAQs on Rotational Partition Function for Homonuclear Diatomic Molecules

Variable Name

GoRotational Partition Function for Heteronuclear Diatomic Molecule Formula