You're on a roll — here are the key formulas in Physical Chemistry for advanced level: 1. Thermodynamics First Law of Thermodynamics: $$\Delta U = Q - W$$ (where $W$ is work done by the system) Enthalpy Change: $$\Delta H = \Delta U + P\Delta V$$ $$\Delta H = Q_p \quad \text{(at constant pressure)}$$ Entropy Change: $$\Delta S = \frac{Q_{rev}}{T}$$ $$\Delta S_{total} = \Delta S_{sys} + \Delta S_{surr} \ge 0$$ Gibbs Free Energy Change: $$\Delta G = \Delta H - T\Delta S$$ $$\Delta G = -RT \ln K \quad \text{(at equilibrium)}$$ $$\Delta G = \Delta G^\circ + RT \ln Q$$ 2. Chemical Kinetics Rate Law: $$\text{Rate} = k[A]^m[B]^n$$ Integrated Rate Laws: First Order: $$\ln[A]_t = \ln[A]_0 - kt$$ $$t_{1/2} = \frac{\ln 2}{k}$$ Second Order: $$\frac{1}{[A]_t} = \frac{1}{[A]_0} + kt$$ $$t_{1/2} = \frac{1}{k[A]_0}$$ Arrhenius Equation: $$k = A e^{-E_a/RT}$$ $$\ln k = \ln A - \frac{E_a}{RT}$$ 3. Chemical Equilibrium Equilibrium Constant: $$K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$$ $$K_p = K_c(RT)^{\Delta n}$$ Van't Hoff Equation: $$\ln\left(\frac{K_2}{K_1}\right) = -\frac{\Delta H^\circ}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)$$ 4. Electrochemistry Nernst Equation: $$E = E^\circ - \frac{RT}{nF}\ln Q$$ Relationship between $\Delta G^\circ$ and $E^\circ$: $$\Delta G^\circ = -nFE^\circ$$ Faraday's Law of Electrolysis: $$Q = It = nF$$ (where $n$ is moles of electrons, $F$ is Faraday constant) 5. Quantum Chemistry (Basic) Planck's Equation: $$E = hf = \frac{hc}{\lambda}$$ De Broglie Wavelength: $$\lambda = \frac{h}{p} = \frac{h}{mv}$$ Got more? Send 'em!