1. Confusing order with stoichiometry. Order exponents come from experiments, not from the balanced equation. For $2\text{NO} + \text{O}_2 \rightarrow 2\text{NO}_2$, the rate is $k[\text{NO}]^2[\text{O}_2]$ — but this is a coincidence; you cannot assume it in general.

2. Using Celsius instead of Kelvin in Arrhenius calculations. $T$ must be in Kelvin. At 27 °C, $T = 300\,K$. Substituting 27 instead of 300 gives wildly wrong $E_a$ values.

3. Assuming first-order behaviour for all reactions. Half-life is concentration-independent only for first-order. For zero order, $t_{1/2}$ doubles if $[A]_0$ doubles; for second order, $t_{1/2}$ halves.

4. Forgetting the stoichiometric factor when relating rate to concentration change. Rate of reaction $\neq$ rate of change of any species unless the stoichiometric coefficient is 1. For $2\text{H}_2\text{O}_2 \rightarrow 2\text{H}_2\text{O} + \text{O}_2$: rate $= -\frac{1}{2}\frac{d[\text{H}_2\text{O}_2]}{dt}$.

5. Thinking a catalyst changes $\Delta H$ or $K$. A catalyst speeds up the reaction by lowering $E_a$; $\Delta H$ and $K$ are thermodynamic quantities that remain unchanged.

6. Confusing $E_a(\text{forward})$ with the net $\Delta H$. $\Delta H = E_a(\text{forward}) - E_a(\text{backward})$, not equal to either alone.

7. Misidentifying the graph for each order.

• Zero order: linear $[A]$ vs $t$
• First order: linear $\ln[A]$ vs $t$
• Second order: linear $1/[A]$ vs $t$

8. Assuming molecularity equals order. For a complex reaction the overall order comes from the rate-determining step, which may give an order entirely different from the overall stoichiometry.

9. Applying $t_{1/2} = 0.693/k$ to zero- or second-order reactions. This formula is exclusive to first-order kinetics.

10. Getting the sign wrong in the two-temperature Arrhenius form. It is $(1/T_1 - 1/T_2)$ with $T_1 < T_2$. If you write $(1/T_2 - 1/T_1)$, the sign of the result flips and $E_a$ appears negative — a nonsensical answer.