Vibrational Mode of Non-Linear Molecule Calculator

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Ratio of Molar Heat Capacity

Atomicity

Degree of Freedom

Molar Heat Capacity

Temperature

✖The Atomicity is defined as the total number of atoms present in a molecule or element.ⓘ Atomicity [N]

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-10%

✖The Number of Normal modes is the fundamental modes responsible for the vibrational motion.ⓘ Vibrational Mode of Non-Linear Molecule [N_vib]

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Formula

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Vibrational Mode of Non-Linear Molecule

Formula

`"N"_{"vib"} = (3*"N")-6`

Example

`"3"=(3*"3")-6`

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Vibrational Mode of Non-Linear Molecule Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Normal modes = (3*Atomicity)-6
N_vib = (3*N)-6
This formula uses 2 Variables

Variables Used

Number of Normal modes - The Number of Normal modes is the fundamental modes responsible for the vibrational motion.
Atomicity - The Atomicity is defined as the total number of atoms present in a molecule or element.

STEP 1: Convert Input(s) to Base Unit

Atomicity: 3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_vib = (3*N)-6 --> (3*3)-6

Evaluating ... ...

N_vib = 3

STEP 3: Convert Result to Output's Unit

3 --> No Conversion Required

FINAL ANSWER

3 <-- Number of Normal modes

(Calculation completed in 00.004 seconds)

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Home » Chemistry » Kinetic Theory of Gases » Equipartition Principle and Heat Capacity » Vibrational Mode of Non-Linear Molecule

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Created by Prerana Bakli

University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

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Verified by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

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< 24 Equipartition Principle and Heat Capacity Calculators

Internal Molar Energy of Non-Linear Molecule

Go Molar Internal Energy = ((3/2)*[R]*Temperature)+((0.5*Moment of Inertia along Y-axis*(Angular Velocity along Y-axis^2))+(0.5*Moment of Inertia along Z-axis*(Angular Velocity along Z-axis^2))+(0.5*Moment of Inertia along X-axis*(Angular Velocity along X-axis^2)))+((3*Atomicity)-6)*([R]*Temperature)

Average Thermal Energy of Non-linear Polyatomic Gas Molecule

Go Thermal Energy = ((3/2)*[BoltZ]*Temperature)+((0.5*Moment of Inertia along Y-axis*(Angular Velocity along Y-axis^2))+(0.5*Moment of Inertia along Z-axis*(Angular Velocity along Z-axis^2)))+((3*Atomicity)-6)*([BoltZ]*Temperature)

Average Thermal Energy of Linear Polyatomic Gas Molecule

Internal Molar Energy of Linear Molecule

Rotational Energy of Non-Linear Molecule

Go Rotational Energy = (0.5*Moment of Inertia along Y-axis*Angular Velocity along Y-axis^2)+(0.5*Moment of Inertia along Z-axis*Angular Velocity along Z-axis^2)+(0.5*Moment of Inertia along X-axis*Angular Velocity along X-axis^2)

Translational Energy

Go Translational Energy = ((Momentum along X-axis^2)/(2*Mass))+((Momentum along Y-axis^2)/(2*Mass))+((Momentum along Z-axis^2)/(2*Mass))

Rotational Energy of Linear Molecule

Go Rotational Energy = (0.5*Moment of Inertia along Y-axis*(Angular Velocity along Y-axis^2))+(0.5*Moment of Inertia along Z-axis*(Angular Velocity along Z-axis^2))

Vibrational Energy Modeled as Harmonic Oscillator

Go Vibrational Energy = ((Momentum of Harmonic Oscillator^2)/(2*Mass))+(0.5*Spring Constant*(Change in Position^2))

Average Thermal Energy of Non-linear polyatomic Gas Molecule given Atomicity

Go Thermal Energy given Atomicity = ((6*Atomicity)-6)*(0.5*[BoltZ]*Temperature)

Average Thermal Energy of Linear Polyatomic Gas Molecule given Atomicity

Go Thermal Energy given Atomicity = ((6*Atomicity)-5)*(0.5*[BoltZ]*Temperature)

Total Kinetic Energy

Go Total Energy = Translational Energy+Rotational Energy+Vibrational Energy

Specific Heat Capacity given heat capacity

Go Specific Heat Capacity = Heat Capacity/(Mass*Change in Temperature)

Internal Molar Energy of Non-Linear Molecule given Atomicity

Go Molar Internal Energy = ((6*Atomicity)-6)*(0.5*[R]*Temperature)

Internal Molar Energy of Linear Molecule given Atomicity

Go Molar Internal Energy = ((6*Atomicity)-5)*(0.5*[R]*Temperature)

Heat Capacity

Go Heat Capacity = Mass*Specific Heat Capacity*Change in Temperature

Molar Vibrational Energy of Non-Linear Molecule

Go Vibrational Molar Energy = ((3*Atomicity)-6)*([R]*Temperature)

Molar Vibrational Energy of Linear Molecule

Go Vibrational Molar Energy = ((3*Atomicity)-5)*([R]*Temperature)

Vibrational Energy of Non-Linear Molecule

Go Vibrational Energy = ((3*Atomicity)-6)*([BoltZ]*Temperature)

Vibrational Energy of Linear Molecule

Go Vibrational Energy = ((3*Atomicity)-5)*([BoltZ]*Temperature)

Heat Capacity given Specific Heat Capacity

Go Heat Capacity = Specific Heat Capacity*Mass

Number of Modes in Non-Linear Molecule

Go Number of Normal modes for Non Linear = (6*Atomicity)-6

Vibrational Mode of Non-Linear Molecule

Go Number of Normal modes = (3*Atomicity)-6

Vibrational Mode of Linear Molecule

Go Number of Normal modes = (3*Atomicity)-5

Number of Modes in Linear Molecule

Go Number of Modes = (6*Atomicity)-5

Vibrational Mode of Non-Linear Molecule Formula

Number of Normal modes = (3*Atomicity)-6
N_vib = (3*N)-6

What is the statement of Equipartition Theorem?

The original concept of equipartition was that the total kinetic energy of a system is shared equally among all of its independent parts, on the average, once the system has reached thermal equilibrium. Equipartition also makes quantitative predictions for these energies. The key point is that the kinetic energy is quadratic in the velocity. The equipartition theorem shows that in thermal equilibrium, any degree of freedom (such as a component of the position or velocity of a particle) which appears only quadratically in the energy has an average energy of 1⁄2kBT and therefore contributes 1⁄2kB to the system's heat capacity.

How to Calculate Vibrational Mode of Non-Linear Molecule?

Vibrational Mode of Non-Linear Molecule calculator uses Number of Normal modes = (3*Atomicity)-6 to calculate the Number of Normal modes, The Vibrational Mode of Non-Linear Molecule is the fundamental modes responsible for the vibrational motion. Number of Normal modes is denoted by N_vib symbol.

How to calculate Vibrational Mode of Non-Linear Molecule using this online calculator? To use this online calculator for Vibrational Mode of Non-Linear Molecule, enter Atomicity (N) and hit the calculate button. Here is how the Vibrational Mode of Non-Linear Molecule calculation can be explained with given input values -> 3 = (3*3)-6.

FAQ

What is Vibrational Mode of Non-Linear Molecule?

The Vibrational Mode of Non-Linear Molecule is the fundamental modes responsible for the vibrational motion and is represented as N_vib = (3*N)-6 or Number of Normal modes = (3*Atomicity)-6. The Atomicity is defined as the total number of atoms present in a molecule or element.

How to calculate Vibrational Mode of Non-Linear Molecule?

The Vibrational Mode of Non-Linear Molecule is the fundamental modes responsible for the vibrational motion is calculated using Number of Normal modes = (3*Atomicity)-6. To calculate Vibrational Mode of Non-Linear Molecule, you need Atomicity (N). With our tool, you need to enter the respective value for Atomicity 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 Number of Normal modes?

In this formula, Number of Normal modes uses Atomicity. We can use 1 other way(s) to calculate the same, which is/are as follows -

Number of Normal modes = (3*Atomicity)-5

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