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Collision Cross Section in Ideal Gas Calculator

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✖Collision Frequency is defined as the number of collisions per second per unit volume of the reacting mixture.ⓘ Collision Frequency [Z]			+10% -10%
✖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%
✖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%
✖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%

✖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 Cross Section in Ideal Gas [σ_AB]

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Collision Cross Section in Ideal Gas Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

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

Functions Used

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., sqrt(Number)

Variables Used

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.
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.
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.
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

Collision Frequency: 7 Cubic Meter per Second --> 7 Cubic Meter per Second No Conversion Required
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)
Reduced Mass of Reactants A and B: 30 Kilogram --> 30 Kilogram 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

σ_AB = (Z/n_A*n_B)*sqrt(pi*μ_AB/8*[BoltZ]*T) --> (7/18000*14000)*sqrt(pi*30/8*[BoltZ]*85)

Evaluating ... ...

σ_AB = 6.40169780905547E-10

STEP 3: Convert Result to Output's Unit

6.40169780905547E-10 Square Meter --> No Conversion Required

FINAL ANSWER

6.40169780905547E-10 ≈ 6.4E-10 Square Meter <-- Collisional Cross Section

(Calculation completed in 00.004 seconds)

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< Molecular Reaction Dynamics Calculators

Number Density for A Molecules using Collision Rate Constant

LaTeX 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

LaTeX 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

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

Vibrational Frequency given Boltzmann's Constant

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

Collision Cross Section in Ideal Gas Formula

LaTeX Go

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 Cross Section in Ideal Gas?

Collision Cross Section in Ideal Gas calculator uses 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) to calculate the Collisional Cross Section, The Collision Cross Section in Ideal Gas formula is defined as the area around a particle A in which the center of another particle B must be in order for a collision to occur in ideal gas. Collisional Cross Section is denoted by σ_AB symbol.

How to calculate Collision Cross Section in Ideal Gas using this online calculator? To use this online calculator for Collision Cross Section in Ideal Gas, enter Collision Frequency (Z), Number Density for A Molecules (n_A), Number Density for B Molecules (n_B), Reduced Mass of Reactants A and B (μ_AB) & Temperature in terms of Molecular Dynamics (T) and hit the calculate button. Here is how the Collision Cross Section in Ideal Gas calculation can be explained with given input values -> 6.4E-10 = (7/18000*14000)*sqrt(pi*30/8*[BoltZ]*85).

FAQ

What is Collision Cross Section in Ideal Gas?

The Collision Cross Section in Ideal Gas formula is defined as the area around a particle A in which the center of another particle B must be in order for a collision to occur in ideal gas and is represented as σ_AB = (Z/n_A*n_B)*sqrt(pi*μ_AB/8*[BoltZ]*T) or 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 is defined as the number of collisions per second per unit volume of the reacting mixture, 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, Reduced Mass of Reactants A and B is inertial mass appearing in the two-body problem of Newtonian mechanics & Temperature in terms of Molecular Dynamics is the degree or intensity of heat present in a molecules during collision.

How to calculate Collision Cross Section in Ideal Gas?

The Collision Cross Section in Ideal Gas formula is defined as the area around a particle A in which the center of another particle B must be in order for a collision to occur in ideal gas is calculated using 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). To calculate Collision Cross Section in Ideal Gas, you need Collision Frequency (Z), Number Density for A Molecules (n_A), Number Density for B Molecules (n_B), Reduced Mass of Reactants A and B (μ_AB) & Temperature in terms of Molecular Dynamics (T). With our tool, you need to enter the respective value for Collision Frequency, Number Density for A Molecules, Number Density for B Molecules, Reduced Mass of Reactants A and B & 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 Collisional Cross Section?

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

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

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