Microbial destruction during saturated-steam sterilization is commonly modeled as which kinetic order with respect to the surviving population?

Introduction:
Predicting microbial lethality in thermal processes relies on kinetic models that relate time–temperature exposure to survivor counts. For many microorganisms under isothermal conditions, survivor curves are approximately log-linear, leading to first-order kinetics with respect to the number of survivors.

Given Data / Assumptions:

• Isothermal exposure in a steam environment (e.g., 121 °C).
• No protective clumping or tailing effects assumed.
• Population is homogeneous with respect to heat resistance.

Concept / Approach:
First-order death kinetics state dN/dt = -k * N, where N is the number of survivors and k is a temperature-dependent rate constant. The solution N = N0 * exp(-k t) yields a straight line when plotting log(N) vs time, which forms the basis for D-value (time for 1-log reduction) and z-value calculations used in sterilization validation and process design.

Step-by-Step Solution:

Verification / Alternative check:
Experimental survivor curves for vegetative cells and many spores approximate straight lines on semi-log plots in the absence of strong protection or tailing, supporting first-order modeling for design purposes.

Why Other Options Are Wrong:

• Zero order: Would predict a constant kill rate independent of N, not observed generally.
• Second order: Requires bimolecular dependence, not appropriate for simple thermal death.
• None: Incorrect since first-order is widely adopted.

Common Pitfalls:
Ignoring deviations such as shoulders/tailing due to clumping or resistant subpopulations; conservative safety factors may be needed in real processes.

Final Answer:
first order chemical reaction