Reduced Mass of Reactants using Collision Frequency 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%
✖Collision Frequency is defined as the number of collisions per second per unit volume of the reacting mixture.ⓘ Collision Frequency [Z]			+10% -10%
✖Temperature in terms of Molecular Dynamics is the degree or intensity of heat present in a molecules during collision.ⓘ Temperature in terms of Molecular Dynamics [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 using Collision Frequency [μ_AB]

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Reduced Mass of Reactants using Collision Frequency

Formula

`"μ"_{"AB"} = (("n"_{"A"}*"n"_{"B"}*"σ"_{"AB"}/"Z")^2)*(8*"[BoltZ]"*"T"/pi)`

Example

`"0.000124kg"=(("18mmol/cm³"*"14mmol/cm³"*"5.66m²"/"7m³/s")^2)*(8*"[BoltZ]"*"85K"/pi)`

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Reduced Mass of Reactants using Collision Frequency Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
μ_AB = ((n_A*n_B*σ_AB/Z)^2)*(8*[BoltZ]*T/pi)
This formula uses 2 Constants, 6 Variables

Constants Used

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

Variables Used

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.
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.
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.
Temperature in terms of Molecular Dynamics - (Measured in Kelvin) - Temperature in terms of Molecular Dynamics is the degree or intensity of heat present in a molecules during collision.

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
Collision Frequency: 7 Cubic Meter per Second --> 7 Cubic Meter per Second No Conversion Required
Temperature in terms of Molecular Dynamics: 85 Kelvin --> 85 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

μ_AB = ((n_A*n_B*σ_AB/Z)^2)*(8*[BoltZ]*T/pi) --> ((18000*14000*5.66/7)^2)*(8*[BoltZ]*85/pi)

Evaluating ... ...

μ_AB = 0.000124073786307928

STEP 3: Convert Result to Output's Unit

0.000124073786307928 Kilogram --> No Conversion Required

FINAL ANSWER

0.000124073786307928 ≈ 0.000124 Kilogram <-- Reduced Mass of Reactants A and B

(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))

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)

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)

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)

Reduced Mass of Reactants using Collision Frequency 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 Reduced Mass of Reactants using Collision Frequency?

Reduced Mass of Reactants using Collision Frequency calculator uses 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) to calculate the Reduced Mass of Reactants A and B, The Reduced Mass of Reactants using Collision Frequency formula is defined as effective inertial mass appearing during collision of two reactant which calculated using collision frequency. Reduced Mass of Reactants A and B is denoted by μ_AB symbol.

How to calculate Reduced Mass of Reactants using Collision Frequency using this online calculator? To use this online calculator for Reduced Mass of Reactants using Collision Frequency, enter Number Density for A Molecules (n_A), Number Density for B Molecules (n_B), Collisional Cross Section (σ_AB), Collision Frequency (Z) & Temperature in terms of Molecular Dynamics (T) and hit the calculate button. Here is how the Reduced Mass of Reactants using Collision Frequency calculation can be explained with given input values -> 0.000124 = ((18000*14000*5.66/7)^2)*(8*[BoltZ]*85/pi).

FAQ

What is Reduced Mass of Reactants using Collision Frequency?

The Reduced Mass of Reactants using Collision Frequency formula is defined as effective inertial mass appearing during collision of two reactant which calculated using collision frequency and is represented as μ_AB = ((n_A*n_B*σ_AB/Z)^2)*(8*[BoltZ]*T/pi) or 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 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, Collision Frequency is defined as the number of collisions per second per unit volume of the reacting mixture & Temperature in terms of Molecular Dynamics is the degree or intensity of heat present in a molecules during collision.

How to calculate Reduced Mass of Reactants using Collision Frequency?

The Reduced Mass of Reactants using Collision Frequency formula is defined as effective inertial mass appearing during collision of two reactant which calculated using collision frequency is calculated using 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). To calculate Reduced Mass of Reactants using Collision Frequency, you need Number Density for A Molecules (n_A), Number Density for B Molecules (n_B), Collisional Cross Section (σ_AB), Collision Frequency (Z) & Temperature in terms of Molecular Dynamics (T). With our tool, you need to enter the respective value for Number Density for A Molecules, Number Density for B Molecules, Collisional Cross Section, Collision Frequency & Temperature in terms of Molecular Dynamics 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 Reduced Mass of Reactants A and B?

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

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

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