Section 2: First-Order Reaction Kinetics & Comparative Metrics

First-Order Reaction Metric

Characterized by a reaction type where the absolute loss of drug is directly proportional to the concentration remaining.

First-Order Degradation Rule

A constant percentage or fraction of the active drug molecule is systematically degraded per unit time.

First-Order Prevalence

Represents the baseline degradation pathway common for the vast majority of all standard pharmaceutical products.

First-Order Exponential Equation

Represented fundamentally in exponential form as: Ct = Co * e^(-kt).

First-Order Natural Log Equation

Represented in natural log format as: In(Ct) - In(Co) = -kt.

First-Order Base-10 Log Equation

Represented in standard base-10 log format as: log(Ct) = log(Co) - (kt / 2.303).

First-Order Direct Plot Profile

Plotting direct concentration remaining versus time on a standard regular graph produces a non-linear, curved profile.

First-Order Log Plot Profile

Plotting log concentration remaining versus time produces a perfectly straight, linear line on a semilog graph.

First-Order Linear Plot Metrics

The y-axis charts log concentration remaining, the x-axis charts time, the y-intercept equals log(Co), and the slope equals -k / 2.303.

First-Order Half-Life Behavior

It remains completely constant and is entirely independent of the initial drug concentration.

First-Order Half-Life Equation

Calculated using the constant mathematical formula: t0.50 = 0.693 / k.

First-Order Shelf-Life Equation

Calculated using the explicit mathematical formula: t0.90 = 0.105 / k.

Zero-Order Rate Constant Unit

Expressed strictly in metric units of Concentration divided by Time (e.g., mg/mL/hr).

First-Order Rate Constant Unit

Expressed strictly as reciprocal time or 1/Time (e.g., hr⁻¹ or day⁻¹).

Zero-Order Kinetics Formulation Examples

Most commonly observed inside pharmaceutical suspensions or specialized controlled-release delivery platforms.

First-Order Kinetics Rate Constant Formula

Calculated across intervals using the equation: k = (2.303 * (log(C1) - log(C2))) / (t2 - t1).