Molar Vibrational Energy of Non-Linear Molecule Solution

STEP 0: Pre-Calculation Summary
Formula Used
Vibrational Molar Energy = ((3*Atomicity)-6)*([R]*Temperature)
Eviv = ((3*N)-6)*([R]*T)
This formula uses 1 Constants, 3 Variables
Constants Used
[R] - Universal gas constant Value Taken As 8.31446261815324
Variables Used
Vibrational Molar Energy - (Measured in Joule Per Mole) - Vibrational Molar Energy is the energy responsible for vibration motion of particles.
Atomicity - The Atomicity is defined as the total number of atoms present in a molecule or element.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.
STEP 1: Convert Input(s) to Base Unit
Atomicity: 3 --> No Conversion Required
Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Eviv = ((3*N)-6)*([R]*T) --> ((3*3)-6)*([R]*85)
Evaluating ... ...
Eviv = 2120.18796762908
STEP 3: Convert Result to Output's Unit
2120.18796762908 Joule Per Mole --> No Conversion Required
FINAL ANSWER
2120.18796762908 2120.188 Joule Per Mole <-- Vibrational Molar Energy
(Calculation completed in 00.004 seconds)

Credits

Created by Prerana Bakli
University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA
Prerana Bakli has created this Calculator and 800+ more calculators!
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
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)-5)*([BoltZ]*Temperature)
Internal Molar Energy of 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)))+((3*Atomicity)-5)*([R]*Temperature)
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

20 Important Formulae on 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)
Internal Molar Energy of 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)))+((3*Atomicity)-5)*([R]*Temperature)
Atomicity given Molar Heat Capacity at Constant Pressure and Volume of Linear Molecule
Go Atomicity = ((2.5*( Molar Specific Heat Capacity at Constant Pressure/Molar Specific Heat Capacity at Constant Volume))-1.5)/((3*(Molar Specific Heat Capacity at Constant Pressure/Molar Specific Heat Capacity at Constant Volume))-3)
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))
Molar Heat Capacity at Constant Pressure given Compressibility
Go Molar Specific Heat Capacity at Constant Pressure = (Isothermal Compressibility/Isentropic Compressibility)*Molar Specific Heat Capacity at Constant Volume
Ratio of Molar Heat Capacity of Linear Molecule
Go Ratio of Molar Heat Capacity = ((((3*Atomicity)-2.5)*[R])+[R])/(((3*Atomicity)-2.5)*[R])
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
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)
Atomicity given Molar Vibrational Energy of Non-Linear Molecule
Go Atomicity = ((Molar Vibrational Energy/([R]*Temperature))+6)/3
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)
Atomicity given Ratio of Molar Heat Capacity of Linear Molecule
Go Atomicity = ((2.5*Ratio of Molar Heat Capacity)-1.5)/((3*Ratio of Molar Heat Capacity)-3)
Number of Modes in Non-Linear Molecule
Go Number of Normal modes for Non Linear = (6*Atomicity)-6
Ratio of Molar Heat Capacity given Degree of Freedom
Go Ratio of Molar Heat Capacity = 1+(2/Degree of Freedom)
Degree of Freedom given Ratio of Molar Heat Capacity
Go Degree of Freedom = 2/(Ratio of Molar Heat Capacity-1)
Vibrational Mode of Linear Molecule
Go Number of Normal modes = (3*Atomicity)-5
Atomicity given Vibrational Degree of Freedom in Non-Linear Molecule
Go Atomicity = (Degree of Freedom+6)/3

Molar Vibrational Energy of Non-Linear Molecule Formula

Vibrational Molar Energy = ((3*Atomicity)-6)*([R]*Temperature)
Eviv = ((3*N)-6)*([R]*T)

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 Molar Vibrational Energy of Non-Linear Molecule?

Molar Vibrational Energy of Non-Linear Molecule calculator uses Vibrational Molar Energy = ((3*Atomicity)-6)*([R]*Temperature) to calculate the Vibrational Molar Energy, The Molar Vibrational Energy of Non-Linear Molecule formula is defined as the kinetic energy an object has due to its vibrational motion. Vibrational Molar Energy is denoted by Eviv symbol.

How to calculate Molar Vibrational Energy of Non-Linear Molecule using this online calculator? To use this online calculator for Molar Vibrational Energy of Non-Linear Molecule, enter Atomicity (N) & Temperature (T) and hit the calculate button. Here is how the Molar Vibrational Energy of Non-Linear Molecule calculation can be explained with given input values -> 2120.188 = ((3*3)-6)*([R]*85).

FAQ

What is Molar Vibrational Energy of Non-Linear Molecule?
The Molar Vibrational Energy of Non-Linear Molecule formula is defined as the kinetic energy an object has due to its vibrational motion and is represented as Eviv = ((3*N)-6)*([R]*T) or Vibrational Molar Energy = ((3*Atomicity)-6)*([R]*Temperature). The Atomicity is defined as the total number of atoms present in a molecule or element & Temperature is the degree or intensity of heat present in a substance or object.
How to calculate Molar Vibrational Energy of Non-Linear Molecule?
The Molar Vibrational Energy of Non-Linear Molecule formula is defined as the kinetic energy an object has due to its vibrational motion is calculated using Vibrational Molar Energy = ((3*Atomicity)-6)*([R]*Temperature). To calculate Molar Vibrational Energy of Non-Linear Molecule, you need Atomicity (N) & Temperature (T). With our tool, you need to enter the respective value for Atomicity & 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 Vibrational Molar Energy?
In this formula, Vibrational Molar Energy uses Atomicity & Temperature. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Vibrational Molar Energy = ((3*Atomicity)-5)*([R]*Temperature)
  • Vibrational Molar Energy = ((3*Atomicity)-5)*([R]*Temperature)
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