Stability Kinetics

Shelf Life: t₉₀

t₉₀ = the time during which a product retains at least 90% of its labeled amount of active ingredient.

• Shelf life calculation depends on the order of the degradation reaction.

• It is commonly determined through accelerated stability studies, such as exposure to:

  • High temperature

  • High humidity

Pharmacist Responsibilities

Pharmacists help maintain drug stability by:

• Dispensing the oldest stock first and checking expiration dates.

• Storing products according to USP monographs and product labeling.

• Watching for signs of instability.

• Using the proper container and closure.

• Properly labeling products that are repackaged, diluted, or mixed.

• Educating patients about proper storage, use, and disposal of expired medications.

Pharmacist Responsibilities

Pharmacists help maintain drug stability by:

• Dispensing the oldest stock first and checking expiration dates.

• Storing products according to USP monographs and product labeling.

• Watching for signs of instability.

• Using the proper container and closure.

• Properly labeling products that are repackaged, diluted, or mixed.

• Educating patients about proper storage, use, and disposal of expired medications.

Why Estimate Shelf Life?

Shelf-life estimates help answer questions such as:

• How much longer will a product last if refrigerated?

• How long can a refrigerated product remain at room temperature?

• What percent degradation occurs after heating or autoclaving a product?

Kinetics

Kinetics is the study of the rate of chemical change and the factors that affect it.

Factors that can affect reaction rate include:

• Drug/reactant concentration

• Product concentration

• Other chemicals present

• Solvent

• Pressure

• Temperature

Reaction Kinetics in Drug Stability

To determine a pharmaceutical product’s stability, we need to know its:

• Reaction order

• Reaction rate

• Rate constant (k)

Reaction order is determined experimentally by measuring how the drug concentration changes over time.

Rate of Reaction

For a reaction:

Drug A → Product B

• Drug A decreases over time:

• Product B increases over time:

Order of Reaction

Reaction order describes how the concentration of a reactant affects the reaction rate.

Zero-Order Kinetics

In a zero-order reaction, the degradation rate is constant and does not depend on drug concentration.

Key Features

• Drug concentration decreases linearly with time.

• The same amount of drug is lost per unit time.

• A plot of drug concentration vs. time is linear.

• There is no constant half-life; half-life depends on the starting concentration.

• Drug concentration decreases linearly with time.

• The same amount of drug is lost per unit time.

• A plot of drug concentration vs. time is linear.

• There is no constant half-life; half-life depends on the starting concentration.

Equations

\[ \text{Rate} = k \]\[ C = C_0 - kt \]

• C = drug concentration at time t

• C₀ = initial drug concentration

• k = zero-order rate constant

• t = time

First-Order Kinetics

Most biological processes and many drug-degradation reactions follow first-order kinetics.

In a first-order reaction, the degradation rate depends on the amount of drug present.

Key Features

• Drug concentration decreases exponentially with time.

• The greater the drug concentration, the faster the degradation rate.

• A plot of ln[drug] vs. time is linear.

• The slope of the line is −k.

• The half-life is constant, regardless of the initial drug concentration.

Equations

\[ \text{Rate} = kC \]\[ \frac{dC}{dt} = -kC \]\[ C = C_0e^{-kt} \]\[ \ln[C] = -kt + \ln[C_0] \]\[ t_{1/2} = \frac{0.693}{k} \]

• k has units of reciprocal time, such as month⁻¹.

Zero-Order vs. First-Order Comparison