Collision Frequency in Ideal Gas Calculator

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✖Number Density for A Molecules is expressed as a number of moles per unit volume (and thus called molar concentration).ⓘ Number Density for A Molecules [n_A]			+10% -10%
✖Number Density for B Molecules is expressed as a number of moles per unit volume (and thus called molar concentration) of B molecules.ⓘ Number Density for B Molecules [n_B]			+10% -10%
✖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.ⓘ Collisional Cross Section [σ_AB]			+10% -10%
✖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.ⓘ Time in terms of Ideal Gas [t]			+10% -10%
✖Reduced Mass of Reactants A and B is inertial mass appearing in the two-body problem of Newtonian mechanics.ⓘ Reduced Mass of Reactants A and B [μ_AB]			+10% -10%

✖Collision Frequency is defined as the number of collisions per second per unit volume of the reacting mixture.ⓘ Collision Frequency in Ideal Gas [Z]

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Formula

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Collision Frequency in Ideal Gas

Formula

`"Z" = "n"_{"A"}*"n"_{"B"}*"σ"_{"AB"}*sqrt((8*"[BoltZ]"*"t"/pi*"μ"_{"AB"}))`

Example

`"415.5343m³/s"="18mmol/cm³"*"14mmol/cm³"*"5.66m²"*sqrt((8*"[BoltZ]"*"2.55Year"/pi*"30kg"))`

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Collision Frequency in Ideal Gas Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
Z = n_A*n_B*σ_AB*sqrt((8*[BoltZ]*t/pi*μ_AB))
This formula uses 2 Constants, 1 Functions, 6 Variables

Constants Used

[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23 Joule/Kelvin
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - Square root function, sqrt(Number)

Variables Used

Collision Frequency - (Measured in Cubic Meter per Second) - Collision Frequency is defined as the number of collisions per second per unit volume of the reacting mixture.
Number Density for A Molecules - (Measured in Mole per Cubic Meter) - Number Density for A Molecules is expressed as a number of moles per unit volume (and thus called molar concentration).
Number Density for B Molecules - (Measured in Mole per Cubic Meter) - Number Density for B Molecules is expressed as a number of moles per unit volume (and thus called molar concentration) of B molecules.
Collisional Cross Section - (Measured in Square Meter) - 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.
Time in terms of Ideal Gas - (Measured in Second) - 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.
Reduced Mass of Reactants A and B - (Measured in Kilogram) - Reduced Mass of Reactants A and B is inertial mass appearing in the two-body problem of Newtonian mechanics.

STEP 1: Convert Input(s) to Base Unit

Number Density for A Molecules: 18 Millimole per Cubic Centimeter --> 18000 Mole per Cubic Meter (Check conversion here)
Number Density for B Molecules: 14 Millimole per Cubic Centimeter --> 14000 Mole per Cubic Meter (Check conversion here)
Collisional Cross Section: 5.66 Square Meter --> 5.66 Square Meter No Conversion Required
Time in terms of Ideal Gas: 2.55 Year --> 80470227.6 Second (Check conversion here)
Reduced Mass of Reactants A and B: 30 Kilogram --> 30 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Z = n_A*n_B*σ_AB*sqrt((8*[BoltZ]*t/pi*μ_AB)) --> 18000*14000*5.66*sqrt((8*[BoltZ]*80470227.6/pi*30))

Evaluating ... ...

Z = 415.53426078593

STEP 3: Convert Result to Output's Unit

415.53426078593 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

415.53426078593 ≈ 415.5343 Cubic Meter per Second <-- Collision Frequency

(Calculation completed in 00.004 seconds)

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National University of Judicial Science (NUJS), Kolkata

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< 19 Molecular Reaction Dynamics Calculators

Collision Cross Section in Ideal Gas

Go Collisional Cross Section = (Collision Frequency/Number Density for A Molecules*Number Density for B Molecules)*sqrt(pi*Reduced Mass of Reactants A and B/8*[BoltZ]*Temperature in terms of Molecular Dynamics)

Collision Frequency in Ideal Gas

Go 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))

Reduced Mass of Reactants using Collision Frequency

Go Reduced Mass of Reactants A and B = ((Number Density for A Molecules*Number Density for B Molecules*Collisional Cross Section/Collision Frequency)^2)*(8*[BoltZ]*Temperature in terms of Molecular Dynamics/pi)

Number of Collisions per Second in Equal Size Particles

Go Number of Collisions per Second = ((8*[BoltZ]*Temperature in terms of Molecular Dynamics*Concentration of Equal Size Particle in Solution)/(3*Viscosity of Fluid in Quantum))

Temperature of Molecular Particle using Collision Rate

Go Temperature in terms of Molecular Dynamics = (3*Viscosity of Fluid in Quantum*Number of Collisions per Second)/(8* [BoltZ]*Concentration of Equal Size Particle in Solution)

Concentration of Equal Size Particle in Solution using Collision Rate

Go Concentration of Equal Size Particle in Solution = (3*Viscosity of Fluid in Quantum*Number of Collisions per Second)/(8*[BoltZ]*Temperature in terms of Molecular Dynamics)

Viscosity of Solution using Collision Rate

Go Viscosity of Fluid in Quantum = (8*[BoltZ]*Temperature in terms of Molecular Dynamics*Concentration of Equal Size Particle in Solution)/(3*Number of Collisions per Second)

Number Density for A Molecules using Collision Rate Constant

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

Cross Sectional Area using Rate of Molecular Collisions

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

Number of Bimolecular Collision per Unit Time per Unit Volume

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

Reduced Mass of Reactants A and B

Go Reduced Mass of Reactants A and B = (Mass of Reactant B*Mass of Reactant B)/(Mass of Reactant A+Mass of Reactant B)

Miss Distance between Particles in Collision

Go Miss Distance = sqrt(((Interparticle Distance Vector^2)*Centrifugal Energy)/Total Energy Before Collision)

Interparticle Distance Vector in Molecular Reaction Dynamics

Go Interparticle Distance Vector = sqrt(Total Energy Before Collision*(Miss Distance^2)/Centrifugal Energy)

Centrifugal Energy in Collision

Go Centrifugal Energy = Total Energy Before Collision*(Miss Distance^2)/(Interparticle Distance Vector^2)

Total Energy before Collision

Go Total Energy Before Collision = Centrifugal Energy*(Interparticle Distance Vector^2)/(Miss Distance^2)

Vibrational Frequency given Boltzmann's Constant

Go Vibrational Frequency = ([BoltZ]*Temperature in terms of Molecular Dynamics)/[hP]

Collisional Cross Section

Go Collisional Cross Section = pi*((Radius of Molecule A*Radius of Molecule B)^2)

Largest Charge Seperation in Collision

Go Largest Charge Seperation = sqrt(Reaction Cross Section/pi)

Reaction Cross Section in Collision

Go Reaction Cross Section = pi*(Largest Charge Seperation^2)

Collision Frequency in Ideal Gas Formula

What is Collision Theory?

Collision theory states that when suitable particles of the reactant hit each other with correct orientation, only a certain amount of collisions result in a perceptible or notable change; these successful changes are called successful collisions. The successful collisions must have enough energy, also known as activation energy, at the moment of impact to break the pre-existing bonds and form all new bonds.

How to Calculate Collision Frequency in Ideal Gas?

Collision Frequency in Ideal Gas calculator 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 calculate 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 calculate Collision Frequency in Ideal Gas using this online calculator? To use this online calculator 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. Here is how the Collision Frequency in Ideal Gas calculation can be explained with given input values -> 415.5343 = 18000*14000*5.66*sqrt((8*[BoltZ]*80470227.6/pi*30)).

FAQ

What is Collision Frequency in Ideal Gas?

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 and is represented as Z = n_A*n_B*σ_AB*sqrt((8*[BoltZ]*t/pi*μ_AB)) or 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)). Number Density for A Molecules is expressed as a number of moles per unit volume (and thus called molar concentration), Number Density for B Molecules is expressed as a number of moles per unit volume (and thus called molar concentration) of B molecules, 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, 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 & Reduced Mass of Reactants A and B is inertial mass appearing in the two-body problem of Newtonian mechanics.

How to calculate Collision Frequency in Ideal Gas?

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 is calculated using 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 calculate Collision Frequency in Ideal Gas, you need 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). With our tool, you need to enter the respective value for Number Density for A Molecules, Number Density for B Molecules, Collisional Cross Section, Time in terms of Ideal Gas & Reduced Mass of Reactants A and B 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 Collision Frequency?

In this formula, Collision Frequency uses Number Density for A Molecules, Number Density for B Molecules, Collisional Cross Section, Time in terms of Ideal Gas & Reduced Mass of Reactants A and B. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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