$\ln k = \ln A - E_a/RT$: Rate constant ($k$) increases exponentially with temperature ($T$) and inversely with activation energy ($E_a$).

$\mathbf{pH = - \log[H^+]}$ and $\mathbf{K_W = 10^{-14}}$: Used inversely to find concentration from $\mathbf{pH/pOH}$ or vice versa.

Units:
- Rate constant ($k$): $s^{-1}$ (for 1st order).
- Temperature ($T$): Must be in Kelvin for gas laws and Arrhenius equations.
Signs (+/-):
- $\Delta H$ is negative for exothermic reactions (heat released).
- $\Delta H$ is positive for endothermic reactions (heat absorbed).
- Slope of $\ln k$ vs $1/T$ is negative for calculating $E_a$.
Assumptions/Traps:
- Equilibrium: $K_P$ and $K_C$ are affected only by temperature. Pressure and catalysts do *not* change $K$.
- Le Chatelier's Principle: Increasing pressure favors the side with *fewer* moles of gas. Increasing temperature favors the *endothermic* reaction.
- $K_P/K_C$ (Heterogeneous): Solids and pure liquids (like $\text{H}_2\text{O}(l)$) are excluded from the equilibrium expressions.
- First Order: The half-life formula ($t_{1/2} = 0.693/k$) is applicable to all radioactive decay reactions, as they are universally first order.

High-Risk Error List:
- Failing to convert concentrations/pressures to the correct base unit (Molar, atm) for $K_P/K_C$ calculations.
- Misidentifying the change in gas moles ($\Delta n$) for $\Delta H$ and $K_P$ calculations, especially neglecting solids/liquids.
- Exothermic reactions (like $\mathbf{N_2 + 3H_2 \rightleftharpoons 2NH_3}$) are favored by low temperature and high pressure.
- Confusing bond breaking ($\mathbf{E_{break} > 0}$, endothermic) vs bond formation ($\mathbf{E_{form} < 0}$, exothermic).
- Incorrectly assigning the Henderson-Hasselbalch terms (Acid/Salt concentration ratio).
Instant Recall Formula Block:
- $K_P = K_C (RT)^{\Delta n}$
- $\Delta H = \Delta E + \Delta n RT$
- $\mathbf{pH = pK_a + \log \frac{[salt]}{[acid]}}$
- $t_{1/2} = \frac{0.693}{k} \text{ (1st Order)}$
- $\mathbf{K_W = 10^{-14}}$

Urea Production (General reaction): $2NH_3(g) + CO_2(g) \xrightarrow{\Delta, P} H_2NCONH_2$
Fermentation of Glucose: $C_6H_{12}O_6 \xrightarrow{Zymase} 2C_2H_5OH + 2CO_2$
Decarboxylation (Alkane prep.): $\mathbf{R - COONa + NaOH(CaO) \xrightarrow{\Delta} R - H + Na_2CO_3}$
Wurtz Reaction (Alkane prep.): $\mathbf{2R - X + 2Na \xrightarrow{\text{Dry} \ \text{ether}} R - R + 2NaX}$
Tollen's Test (Aldehyde Detection): $R-CHO + 2[Ag(NH_3)_2]OH \xrightarrow{\Delta} \mathbf{2Ag \downarrow} + RCOONH_4 + 3NH_3 + H_2O$
$K_{SP}$ calculation for $Al(OH)_3$: $K_{SP} = 27S^4$

Decarboxylation/Wurtz: Used to manipulate carbon chain length in alkanes. $\mathbf{CaO}$ acts as a dehydrating agent. Wurtz reaction yields higher alkanes with an even number of carbons.
Tollen's Test: The formation of $\mathbf{Ag \downarrow}$ (silver mirror) confirms the presence of the aldehyde group ($\mathbf{-CHO}$).
Fermentation: Catalyzed by $\mathbf{Zymase}$ (for Glucose to Ethanol) and $\mathbf{Inve