Order: does speed depend on concentration?
The reaction order answers one question: as the drug is used up, does the degradation slow down? In zero-order decay it does not — the drug disappears at a steady amount per unit time, no matter how much is left. In first-order decay it does — the rate is proportional to how much drug remains, so it tapers off as the drug runs low. Most degradation in solution behaves first-order; suspensions of poorly soluble drugs often look zero-order because the dissolved concentration stays fixed.
The rate constant and the lines it draws
Each reaction has a rate constant, written k, that fixes the speed at a given temperature. It is the slope of the straight line above. For zero-order, k has units like mg/mL per month; for first-order, k has units of “per month” (a fractional loss). The bigger the k, the faster the degradation and the shorter the shelf life.
Two landmarks come straight from k. The half-life (t½) is the time to lose half the drug. The t₉₀ is the time to lose 10% — and for stability work t₉₀ is the star, because the common shelf-life limit is 90% of label. For a first-order reaction both depend only on k, not on the starting amount, which is a wonderfully convenient fact.
First-order shelf-life worked example
A drug in solution degrades by first order.
Measured rate constant at 25 C: k = 0.0050 per month
For first order, the time to lose 10% (t90):
t90 = 0.105 / k
t90 = 0.105 / 0.0050
t90 = 21 months
Half-life for comparison:
t1/2 = 0.693 / k
t1/2 = 0.693 / 0.0050
t1/2 = 139 months
=> Shelf life is governed by t90 (21 months),
reached long before half the drug is gone.
(The 0.105 comes from ln(100/90) = ln(1.111).)Why order matters for the formulator
Knowing the order is not academic. It tells you how the expiry will behave if you change the dose: double the strength of a first-order product and t₉₀ is unchanged, but double a zero-order suspension and it lasts twice as long in percentage terms. It also tells you whether a single measured k lets you read off shelf life directly, or whether you must integrate. Get the order right first; everything downstream depends on it.