Strategy

Test which form of the integrated rate equation gives a straight line.

Three Diagnostic Graphs

Zero order: Plot [A] vs t

• Straight line? → Zero order
• Slope = −k (negative)
• Intercept = [A]_{0}

First order: Plot ln[A] vs t (or log[A] vs t)

• Straight line? → First order
• Slope of ln[A] vs t = −k
• Slope of log[A] vs t = −k/2.303
• Intercept = ln[A]{0} (or log[A]{0})

Second order: Plot 1/[A] vs t

• Straight line? → Second order
• Slope = +k (positive — note positive sign!)
• Intercept = 1/[A]_{0}

Diagnostic Key

If the problem says "which graph gives a straight line," use this table:

Arrhenius Graph

Plot ln k vs 1/T $\frac{or log k vs 1}{T}$:

• Always a straight line for reactions following Arrhenius behavior
• Slope = −Ea/R (from ln k) or −Ea/2.303R (from log k)
• Intercept = ln A (or log A)
• Steeper slope → higher Ea

Practical Application

If you're given [A] at various times, calculate [A], ln[A], and 1/[A] for each time point. Plot all three and see which gives the best straight line. That determines the order.