Ratio of Pre-Exponential Factor Calculator

Formula Used:

\[ \text{Ratio} = \frac{(D_1)^2 \times \sqrt{\mu_2}}{(D_2)^2 \times \sqrt{\mu_1}} \]

Collision Diameter 1 (D₁):

Collision Diameter 2 (D₂):

Reduced Mass 1 (μ₁):

kg/mol

Reduced Mass 2 (μ₂):

kg/mol

Ratio of Pre-Exponential Factor:

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1. What is Ratio of Pre-Exponential Factor?

Definition: The ratio compares the collision diameters and reduced masses of two different molecular collisions to determine their relative pre-exponential factors.

Purpose: This calculation is important in chemical kinetics to compare reaction rates between different molecular systems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Ratio} = \frac{(D_1)^2 \times \sqrt{\mu_2}}{(D_2)^2 \times \sqrt{\mu_1}} \]

Where:

\( D_1 \) — Collision diameter of first system (meters)
\( D_2 \) — Collision diameter of second system (meters)
\( \mu_1 \) — Reduced mass of first system (kg/mol)
\( \mu_2 \) — Reduced mass of second system (kg/mol)

Explanation: The ratio depends on the squares of the collision diameters and the square roots of the reduced masses.

3. Importance of This Calculation

Details: The pre-exponential factor is a key component in the Arrhenius equation that describes reaction rates. Comparing these factors helps predict relative reaction rates.

4. Using the Calculator

Tips: Enter the collision diameters (in meters) and reduced masses (in kg/mol) for both systems. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a collision diameter?
A: The distance between centers of two molecules at their closest approach during collision.

Q2: How is reduced mass calculated?
A: Reduced mass μ = (m₁ × m₂)/(m₁ + m₂), where m₁ and m₂ are the masses of the colliding molecules.

Q3: Why does diameter appear squared in the formula?
A: The collision cross-section (probability of collision) is proportional to the square of the collision diameter.

Q4: What does the ratio tell us?
A: It shows how much more likely collisions are in one system compared to another, all else being equal.

Q5: Can this be used for reactions with different temperatures?
A: This ratio only compares the pre-exponential factors. For complete rate comparisons, you would need to include the exponential (activation energy) terms.