Collision Cross Section in Ideal Gas Calculator

Collisional Cross Section Formula:

\[ \sigma_{AB} = \frac{Z}{n_A \cdot n_B} \cdot \sqrt{\frac{\pi \cdot \mu_{AB}}{8 \cdot k_B \cdot T}} \]

Collision Frequency (Z):

m³/s

Number Density for A (n_A):

mol/m³

Number Density for B (n_B):

mol/m³

Reduced Mass (μ_AB):

Temperature (T):

Collisional Cross Section (σ_AB):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Collisional Cross Section?

Definition: 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.

Purpose: It helps in understanding molecular interactions, reaction rates, and gas dynamics in physical chemistry and molecular physics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \sigma_{AB} = \frac{Z}{n_A \cdot n_B} \cdot \sqrt{\frac{\pi \cdot \mu_{AB}}{8 \cdot k_B \cdot T}} \]

Where:

\( \sigma_{AB} \) — Collisional Cross Section (m²)
\( Z \) — Collision Frequency (m³/s)
\( n_A \) — Number Density for A Molecules (mol/m³)
\( n_B \) — Number Density for B Molecules (mol/m³)
\( \mu_{AB} \) — Reduced Mass of Reactants A and B (kg)
\( k_B \) — Boltzmann constant (1.38 × 10⁻²³ J/K)
\( T \) — Temperature (K)

Explanation: The formula relates collision frequency to molecular densities and incorporates temperature-dependent molecular motion.

3. Importance of Collisional Cross Section

Details: Understanding collision cross sections is crucial for predicting reaction rates, studying gas kinetics, and designing chemical processes.

4. Using the Calculator

Tips: Enter all required parameters in appropriate units. Ensure all values are positive. The calculator uses Boltzmann constant (1.38 × 10⁻²³ J/K) and π (3.1416) as constants.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical meaning of collision cross section?
A: It represents the effective target area that one molecule presents to another for collision.

Q2: How does temperature affect collision cross section?
A: Higher temperatures generally lead to smaller effective cross sections due to faster molecular motion.

Q3: What are typical values for collision cross sections?
A: For simple molecules, typically in the range of 10⁻¹⁹ to 10⁻²⁰ m².

Q4: How is reduced mass calculated?
A: \( \mu_{AB} = \frac{m_A \cdot m_B}{m_A + m_B} \), where m_A and m_B are the masses of the molecules.

Q5: Can this be used for non-ideal gases?
A: This calculator assumes ideal gas behavior. For real gases, additional corrections may be needed.