PHARM/PCS V5 · Procedure 21 Drug Decay and Binding
First-Order Drug Decay
Get the first-order rate constant k for a decomposing drug from concentration-time data, and with it a half-life or shelf-life.
What it computes
Determines the first-order rate constant k for drug decomposition from concentration-time data. The first entry must be the initial concentration at time 0. Subsequent entries are (time, concentration). The procedure computes ln(a0 / (a0 − x)) at each time point and fits a regression line through the origin (Procedure 4): slope = k.
Inputs and outputs
You provide
- The initial concentration at time 0, entered first
- Time and concentration for each later point, one pair per line
PHARM/PCS reports
- The first-order rate constant k, from the slope of a line fitted through the origin
- A plot of ln(a0/C) against time
When to use it
For stability or degradation studies where a drug decomposes by first-order kinetics and you want the rate constant (and, from it, a half-life or shelf-life). It's the decomposition analog of the general exponential fit in Procedure 24.
Reading the results
The through-origin fit (Procedure 4) assumes clean first-order behavior; curvature in the transformed points signals a different order or a mixed process, and forcing a line through it would report a k that isn't real. Getting a0 right is critical, since every transformed value depends on it.
Check for curvature
The fit is forced through the origin, which assumes clean first-order behavior. Curvature in the transformed points means a different order or a mixed process, and the k reported for such data would not be real. The initial concentration matters most of all, since every transformed value depends on it.
This page describes the procedure. Calculations run inside the licensed PHARM/PCS V5 application. PHARM/PCS is a trademark of MCS Scientific LLC.