Question

The Damköhler number (Da) relates:

• A. Reaction rate to diffusion rate
• B. Heat transfer to mass transfer
• C. Reactor volume to flow rate
• D. Pressure to temperature

Hint:

Remember: Damköhler number indicates whether a process is reaction-limited or diffusion-limited — high Da implies mass transfer control.

Answer 1

The Correct Option is A

The Damköhler number (Da) is a dimensionless number widely used in chemical reaction engineering and mass transfer studies.
It represents the ratio of the chemical reaction rate to the rate of transport phenomena (usually mass transport such as diffusion).
For mass-transfer-limited systems, it is typically defined as:
\[ Da = \frac{\text{Reaction rate}}{\text{Diffusion rate}} \]
Interpretation:
- If $Da \gg 1$, the reaction is much faster than diffusion, and diffusion limits the overall process.
- If $Da \ll 1$, diffusion is faster than the reaction, and the kinetics of the reaction control the overall rate.
Now evaluating the other options:
- (2) Heat transfer to mass transfer: This is typically described by the Lewis number, not Damköhler number.
- (3) Reactor volume to flow rate: This ratio defines residence time, not the Damköhler number.
- (4) Pressure to temperature: This relation is not relevant to Damköhler; it’s more related to gas laws.
Hence, the Damköhler number directly compares reaction rate to diffusion rate.