Essential Formulas at a Glance

Rate Law: $\text{rate} = k[A]^m[B]^n; \quad \text{overall order} = m + n$

Integrated Equations: $[A] = [A]_0 - kt \quad \text{(zero)}$ $k = \frac{2.303}{t}\log\frac{[A]_0}{[A]} \quad \text{(first)}$ $\frac{1}{[A]} = \frac{1}{[A]_0} + kt \quad \text{(second)}$

Half-Lives: $t_{1/2}^{(0)} = \frac{[A]_0}{2k}, \quad t_{1/2}^{(1)} = \frac{0.693}{k}, \quad t_{1/2}^{(2)} = \frac{1}{k[A]_0}$

Units of k: $(\text{mol/L})^{1-n} \cdot \text{s}^{-1}$

Arrhenius: $\log\frac{k_2}{k_1} = \frac{E_a}{2.303R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)$

Ea relationship: $E_a(\text{fwd}) - E_a(\text{bwd}) = \Delta H$

Key NEET Points (Must Know)

1. First-order t_{1}/{2} is independent of [A]{0}
2. Zero-order t_{1}/{2} is proportional to [A]{0}
3. Catalyst lowers Ea but does NOT change $\Delta H$ or K
4. Order can be 0 or fractional; molecularity cannot
5. Units of k: zero = mol/L/s; first = $s^{-1}$; second = L/mol/s
6. Temperature in Arrhenius must be in Kelvin
7. Slope of ln k vs 1/T = −Ea/R (negative)
8. Pseudo first-order: one reactant in large excess

First-Order Completion Times (t_{1}/_{2} = t)