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Collision Cross Section in Ideal Gas Formula

GoCollisional Cross Section Formula

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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. Check FAQs

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

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

Collision Cross Section in Ideal Gas Example

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

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

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

6.4E-10 = (\frac{7}{18} \cdot 14) \cdot \sqrt{3.1416 \cdot \frac{30}{8} \cdot 1.4E-23 \cdot 85}

6.4E-10m² = (\frac{7m³/s}{18mmol/cm³} \cdot 14mmol/cm³) \cdot \sqrt{3.1416 \cdot \frac{30kg}{8} \cdot 1.4E-23J/K \cdot 85K}

6.4E-10 = (\frac{7}{18} \cdot 14) \cdot \sqrt{3.1416 \cdot \frac{30}{8} \cdot 1.4E-23 \cdot 85}

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Collision Cross Section in Ideal Gas Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

σ AB = (\frac{7m³/s}{18mmol/cm³} \cdot 14mmol/cm³) \cdot \sqrt{π \cdot \frac{30kg}{8} \cdot [BoltZ] \cdot 85K}

Next Step Substitute values of Constants

∴

σ AB = (\frac{7m³/s}{18mmol/cm³} \cdot 14mmol/cm³) \cdot \sqrt{3.1416 \cdot \frac{30kg}{8} \cdot 1.4E-23J/K \cdot 85K}

Next Step Convert Units

∴

σ AB = (\frac{7m³/s}{18000mol/m³} \cdot 14000mol/m³) \cdot \sqrt{3.1416 \cdot \frac{30kg}{8} \cdot 1.4E-23J/K \cdot 85K}

Next Step Prepare to Evaluate

∴

σ AB = (\frac{7}{18000} \cdot 14000) \cdot \sqrt{3.1416 \cdot \frac{30}{8} \cdot 1.4E-23 \cdot 85}

Next Step Evaluate

∴

σ AB = 6.40169780905547E-10m²

LAST Step Rounding Answer

∴

σ AB = 6.4E-10m²

Collision Cross Section in Ideal Gas Formula Elements

Variables

Constants

Functions

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.

Formulas to find Collisional Cross Section

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.

Formulas to find Collision Frequency

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.

Formulas to find Number Density for A Molecules

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.

Formulas to find Number Density for B Molecules

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.

Formulas to find Reduced Mass of Reactants A and B

Temperature in terms of Molecular Dynamics

Temperature in terms of Molecular Dynamics is the degree or intensity of heat present in a molecules during collision.

Symbol: T

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Temperature in terms of Molecular Dynamics

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)

Other Formulas to find Collisional Cross Section

Go Collisional Cross Section

σ AB = π \cdot ({(r A \cdot r B)}^{2})

Other formulas in Molecular Reaction Dynamics category

Go Number of Bimolecular Collision per Unit Time per Unit Volume

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

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]}

How to Evaluate Collision Cross Section in Ideal Gas?

Collision Cross Section in Ideal Gas evaluator 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 evaluate 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 evaluate Collision Cross Section in Ideal Gas using this online evaluator? To use this online evaluator 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.

FAQs on Collision Cross Section in Ideal Gas

What is the formula to find Collision Cross Section in Ideal Gas?

The formula of Collision Cross Section in Ideal Gas is expressed as 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). Here is an example- 6.4E-10 = (7/18000*14000)*sqrt(pi*30/8*[BoltZ]*85).

How to calculate Collision Cross Section in Ideal Gas?

With 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) we can find Collision Cross Section in Ideal Gas using the formula - 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). This formula also uses Boltzmann constant, Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Collisional Cross Section?

Here are the different ways to Calculate Collisional Cross Section-

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

Can the Collision Cross Section in Ideal Gas be negative?

No, the Collision Cross Section in Ideal Gas, measured in Area cannot be negative.

Which unit is used to measure Collision Cross Section in Ideal Gas?

Collision Cross Section in Ideal Gas is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Collision Cross Section in Ideal Gas can be measured.

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Collision Cross Section in Ideal Gas Formula

​GoCollisional Cross Section Formula

Collision Cross Section in Ideal Gas Example

Collision Cross Section in Ideal Gas Solution

Collision Cross Section in Ideal Gas Formula Elements

Other Formulas to find Collisional Cross Section

Other formulas in Molecular Reaction Dynamics category

How to Evaluate Collision Cross Section in Ideal Gas?

FAQs on Collision Cross Section in Ideal Gas

Variable Name

GoCollisional Cross Section Formula