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Vibrational Partition Function for Diatomic Ideal Gas Formula

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Vibrational Partition Function is the contribution to the total partition function due to vibrational motion. Check FAQs

q vib = \frac{1}{1 - \exp (- \frac{[hP] \cdot ν 0}{[BoltZ] \cdot T})}

q_vib - Vibrational Partition Function?ν₀ - Classical Frequency of Oscillation?T - Temperature?[hP] - Planck constant?[BoltZ] - Boltzmann constant?

Vibrational Partition Function for Diatomic Ideal Gas Example

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Here is how the Vibrational Partition Function for Diatomic Ideal Gas equation looks like with Values.

Here is how the Vibrational Partition Function for Diatomic Ideal Gas equation looks like with Units.

Here is how the Vibrational Partition Function for Diatomic Ideal Gas equation looks like.

1.0159 = \frac{1}{1 - \exp (- \frac{6.6E-34 \cdot 2.6E+13}{1.4E-23 \cdot 300})}

1.0159 = \frac{1}{1 - \exp (- \frac{6.6E-34 \cdot 2.6E+13s⁻¹}{1.4E-23J/K \cdot 300K})}

1.0159 = \frac{1}{1 - \exp (- \frac{6.6E-34 \cdot 2.6E+13}{1.4E-23 \cdot 300})}

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Vibrational Partition Function for Diatomic Ideal Gas Solution

Follow our step by step solution on how to calculate Vibrational Partition Function for Diatomic Ideal Gas?

FIRST Step Consider the formula

q vib = \frac{1}{1 - \exp (- \frac{[hP] \cdot ν 0}{[BoltZ] \cdot T})}

Next Step Substitute values of Variables

∴

q vib = \frac{1}{1 - \exp (- \frac{[hP] \cdot 2.6E+13s⁻¹}{[BoltZ] \cdot 300K})}

Next Step Substitute values of Constants

∴

q vib = \frac{1}{1 - \exp (- \frac{6.6E-34 \cdot 2.6E+13s⁻¹}{1.4E-23J/K \cdot 300K})}

Next Step Prepare to Evaluate

∴

q vib = \frac{1}{1 - \exp (- \frac{6.6E-34 \cdot 2.6E+13}{1.4E-23 \cdot 300})}

Next Step Evaluate

∴

q vib = 1.01586556322981

LAST Step Rounding Answer

∴

q vib = 1.0159

Vibrational Partition Function for Diatomic Ideal Gas Formula Elements

Variables

Constants

Functions

Vibrational Partition Function

Vibrational Partition Function is the contribution to the total partition function due to vibrational motion.

Symbol: q_vib

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Vibrational Partition Function

Classical Frequency of Oscillation

Classical Frequency of Oscillation is the number of oscillations in the one-time unit, says in a second.

Symbol: ν₀

Measurement: First Order Reaction Rate ConstantUnit: s⁻¹

Note: Value can be positive or negative.

Formulas to find Classical Frequency of Oscillation

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

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

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

exp

n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable.

Syntax: exp(Number)

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 Vibrational Partition Function for Diatomic Ideal Gas?

Vibrational Partition Function for Diatomic Ideal Gas evaluator uses Vibrational Partition Function = 1/(1-exp(-([hP]*Classical Frequency of Oscillation)/([BoltZ]*Temperature))) to evaluate the Vibrational Partition Function, The Vibrational Partition Function for Diatomic Ideal Gas formula is defined as the contribution to the total partition function due to vibrational motion. Vibrational Partition Function is denoted by q_vib symbol.

How to evaluate Vibrational Partition Function for Diatomic Ideal Gas using this online evaluator? To use this online evaluator for Vibrational Partition Function for Diatomic Ideal Gas, enter Classical Frequency of Oscillation (ν₀) & Temperature (T) and hit the calculate button.

FAQs on Vibrational Partition Function for Diatomic Ideal Gas

What is the formula to find Vibrational Partition Function for Diatomic Ideal Gas?

The formula of Vibrational Partition Function for Diatomic Ideal Gas is expressed as Vibrational Partition Function = 1/(1-exp(-([hP]*Classical Frequency of Oscillation)/([BoltZ]*Temperature))). Here is an example- 1.40279 = 1/(1-exp(-([hP]*26000000000000)/([BoltZ]*300))).

How to calculate Vibrational Partition Function for Diatomic Ideal Gas?

With Classical Frequency of Oscillation (ν₀) & Temperature (T) we can find Vibrational Partition Function for Diatomic Ideal Gas using the formula - Vibrational Partition Function = 1/(1-exp(-([hP]*Classical Frequency of Oscillation)/([BoltZ]*Temperature))). This formula also uses Planck constant, Boltzmann constant and Exponential Growth (exp) function(s).

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Vibrational Partition Function for Diatomic Ideal Gas Formula

Vibrational Partition Function for Diatomic Ideal Gas Example

Vibrational Partition Function for Diatomic Ideal Gas Solution

Vibrational Partition Function for Diatomic Ideal Gas Formula Elements

Other formulas in Distinguishable Particles category

How to Evaluate Vibrational Partition Function for Diatomic Ideal Gas?

FAQs on Vibrational Partition Function for Diatomic Ideal Gas

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