Chemostat calculation: A chemostat of liquid volume 2 L is fed at 4 L·h^-1. What is the dilution rate D for this reactor?

Introduction / Context:Dilution rate (D) is the defining parameter of a chemostat, connecting feed flow and reactor volume. This item checks correct unit usage and the simple formula for D.

Given Data / Assumptions:

• Reactor volume V = 2 L.
• Feed flow F = 4 L·h^-1.
• Well-mixed, constant volume operation.

Concept / Approach:The dilution rate is defined as D = F / V with units of time^-1. It represents the fraction of reactor volume replaced per unit time.

Step-by-Step Solution:Compute D = F / V = 4 / 2 = 2 h^-1.Check units: (L·h^-1)/L = h^-1.Therefore, D = 2 h^-1.

Verification / Alternative check:Residence time τ = 1 / D = 0.5 h, consistent with a high-throughput chemostat replacing its content twice per hour.

Why Other Options Are Wrong:“2 litres” and “4 litres per hour” are not rates normalized by volume; they are volume or volumetric flow, not D.

“2 litres per hour” has wrong units; D must be in h^-1.

Common Pitfalls:

• Forgetting to normalize by reactor volume.
• Reporting D with incorrect units.

Final Answer:2 h^-1