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Collision Frequency in Ideal Gas Formula

GoNumber of Bimolecular Collision per Unit Time per Unit Volume Formula

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Collision Frequency is defined as the number of collisions per second per unit volume of the reacting mixture. Check FAQs

Z = n A \cdot n B \cdot σ AB \cdot \sqrt{(8 \cdot [BoltZ] \cdot \frac{t}{π} \cdot μ AB)}

Z - Collision Frequency?n_A - Number Density for A Molecules?n_B - Number Density for B Molecules?σ_AB - Collisional Cross Section?t - Time in terms of Ideal Gas?μ_AB - Reduced Mass of Reactants A and B?[BoltZ] - Boltzmann constant?π - Archimedes' constant?

Collision Frequency in Ideal Gas Example

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Here is how the Collision Frequency in Ideal Gas equation looks like with Values.

Here is how the Collision Frequency in Ideal Gas equation looks like with Units.

Here is how the Collision Frequency in Ideal Gas equation looks like.

415.5343 = 18 \cdot 14 \cdot 5.66 \cdot \sqrt{(8 \cdot 1.4E-23 \cdot \frac{2.55}{3.1416} \cdot 30)}

415.5343m³/s = 18mmol/cm³ \cdot 14mmol/cm³ \cdot 5.66m² \cdot \sqrt{(8 \cdot 1.4E-23J/K \cdot \frac{2.55Year}{3.1416} \cdot 30kg)}

415.5343 = 18 \cdot 14 \cdot 5.66 \cdot \sqrt{(8 \cdot 1.4E-23 \cdot \frac{2.55}{3.1416} \cdot 30)}

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Home » Chemistry » Quantum » Molecular Reaction Dynamics » Collision Frequency in Ideal Gas

Collision Frequency in Ideal Gas Solution

Follow our step by step solution on how to calculate Collision Frequency in Ideal Gas?

FIRST Step Consider the formula

Z = n A \cdot n B \cdot σ AB \cdot \sqrt{(8 \cdot [BoltZ] \cdot \frac{t}{π} \cdot μ AB)}

Next Step Substitute values of Variables

∴

Z = 18mmol/cm³ \cdot 14mmol/cm³ \cdot 5.66m² \cdot \sqrt{(8 \cdot [BoltZ] \cdot \frac{2.55Year}{π} \cdot 30kg)}

Next Step Substitute values of Constants

∴

Z = 18mmol/cm³ \cdot 14mmol/cm³ \cdot 5.66m² \cdot \sqrt{(8 \cdot 1.4E-23J/K \cdot \frac{2.55Year}{3.1416} \cdot 30kg)}

Next Step Convert Units

∴

Z = 18000mol/m³ \cdot 14000mol/m³ \cdot 5.66m² \cdot \sqrt{(8 \cdot 1.4E-23J/K \cdot \frac{8E+7s}{3.1416} \cdot 30kg)}

Next Step Prepare to Evaluate

∴

Z = 18000 \cdot 14000 \cdot 5.66 \cdot \sqrt{(8 \cdot 1.4E-23 \cdot \frac{8E+7}{3.1416} \cdot 30)}

Next Step Evaluate

∴

Z = 415.53426078593m³/s

LAST Step Rounding Answer

∴

Z = 415.5343m³/s

Collision Frequency in Ideal Gas Formula Elements

Variables

Constants

Functions

Collision Frequency

Collision Frequency is defined as the number of collisions per second per unit volume of the reacting mixture.

Symbol: Z

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Number Density for A Molecules

Number Density for A Molecules is expressed as a number of moles per unit volume (and thus called molar concentration).

Symbol: n_A

Measurement: Molar ConcentrationUnit: mmol/cm³

Note: Value should be greater than 0.

Number Density for B Molecules

Number Density for B Molecules is expressed as a number of moles per unit volume (and thus called molar concentration) of B molecules.

Symbol: n_B

Measurement: Molar ConcentrationUnit: mmol/cm³

Note: Value should be greater than 0.

Collisional Cross Section

Collisional Cross Section is defined as the area around a particle in which the center of another particle must be in order for a collision to occur.

Symbol: σ_AB

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Time in terms of Ideal Gas

Time in terms of Ideal Gas is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future.

Symbol: t

Measurement: TimeUnit: Year

Note: Value can be positive or negative.

Reduced Mass of Reactants A and B

Reduced Mass of Reactants A and B is inertial mass appearing in the two-body problem of Newtonian mechanics.

Symbol: μ_AB

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

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

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Credits

Created by Soupayan banerjee

National University of Judicial Science (NUJS), Kolkata

Soupayan banerjee has created this Formula and 200+ more formulas!

Verified by Prerana Bakli

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

Prerana Bakli has verified this Formula and 1600+ more formulas!

Other Formulas to find Collision Frequency

Go Number of Bimolecular Collision per Unit Time per Unit Volume

Z = n A \cdot n B \cdot v beam \cdot A

Other formulas in Molecular Reaction Dynamics category

Go Number Density for A Molecules using Collision Rate Constant

n A = \frac{Z}{v beam \cdot n B \cdot A}

Go Cross Sectional Area using Rate of Molecular Collisions

A = \frac{Z}{v beam \cdot n B \cdot n A}

Go Vibrational Frequency given Boltzmann's Constant

v vib = \frac{[BoltZ] \cdot T}{[hP]}

Go Reduced Mass of Reactants A and B

μ AB = \frac{m B \cdot m B}{m A + m B}

How to Evaluate Collision Frequency in Ideal Gas?

Collision Frequency in Ideal Gas evaluator uses Collision Frequency = Number Density for A Molecules*Number Density for B Molecules*Collisional Cross Section*sqrt((8*[BoltZ]*Time in terms of Ideal Gas/pi*Reduced Mass of Reactants A and B)) to evaluate the Collision Frequency, The Collision Frequency in Ideal Gas formula is defined as the average rate in which two reactants collide for a given system and is used to express the average number of collisions per unit of time in a defined system. Collision Frequency is denoted by Z symbol.

How to evaluate Collision Frequency in Ideal Gas using this online evaluator? To use this online evaluator for Collision Frequency in Ideal Gas, enter Number Density for A Molecules (n_A), Number Density for B Molecules (n_B), Collisional Cross Section (σ_AB), Time in terms of Ideal Gas (t) & Reduced Mass of Reactants A and B (μ_AB) and hit the calculate button.

FAQs on Collision Frequency in Ideal Gas

What is the formula to find Collision Frequency in Ideal Gas?

The formula of Collision Frequency in Ideal Gas is expressed as Collision Frequency = Number Density for A Molecules*Number Density for B Molecules*Collisional Cross Section*sqrt((8*[BoltZ]*Time in terms of Ideal Gas/pi*Reduced Mass of Reactants A and B)). Here is an example- 415.5343 = 18000*14000*5.66*sqrt((8*[BoltZ]*80470227.6/pi*30)).

How to calculate Collision Frequency in Ideal Gas?

With Number Density for A Molecules (n_A), Number Density for B Molecules (n_B), Collisional Cross Section (σ_AB), Time in terms of Ideal Gas (t) & Reduced Mass of Reactants A and B (μ_AB) we can find Collision Frequency in Ideal Gas using the formula - Collision Frequency = Number Density for A Molecules*Number Density for B Molecules*Collisional Cross Section*sqrt((8*[BoltZ]*Time in terms of Ideal Gas/pi*Reduced Mass of Reactants A and B)). This formula also uses Boltzmann constant, Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Collision Frequency?

Here are the different ways to Calculate Collision Frequency-

Collision Frequency=Number Density for A Molecules*Number Density for B Molecules*Velocity of Beam Molecules*Cross Sectional Area for Quantum

Can the Collision Frequency in Ideal Gas be negative?

No, the Collision Frequency in Ideal Gas, measured in Volumetric Flow Rate cannot be negative.

Which unit is used to measure Collision Frequency in Ideal Gas?

Collision Frequency in Ideal Gas is usually measured using the Cubic Meter per Second[m³/s] for Volumetric Flow Rate. Cubic Meter per Day[m³/s], Cubic Meter per Hour[m³/s], Cubic Meter per Minute[m³/s] are the few other units in which Collision Frequency in Ideal Gas can be measured.

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Collision Frequency in Ideal Gas Formula

​GoNumber of Bimolecular Collision per Unit Time per Unit Volume Formula

Collision Frequency in Ideal Gas Example

Collision Frequency in Ideal Gas Solution

Collision Frequency in Ideal Gas Formula Elements

Credits

Other Formulas to find Collision Frequency

Other formulas in Molecular Reaction Dynamics category

How to Evaluate Collision Frequency in Ideal Gas?

FAQs on Collision Frequency in Ideal Gas

Variable Name

GoNumber of Bimolecular Collision per Unit Time per Unit Volume Formula