R = 8.314 J mol^{-1} K^{-1} =0.08206 L atmK^{-1} mol^{-1} = 0.08314 L bar K^{-1} mol^{-1} N_{A} = 6.022 x 10^{23} mol^{-1} k_{B} = 1.381 x 10^{-23} J K^{-1} h = 6.626 x 10^{-34} J s F = 96,485 C mol^{-1} c = 2.998 x 10^{8} m s^{-1} g = 9.81 m s^{-2} e = 1.6022 x 10^{-19 }C ε_{o} = 8.854 x 10^{-12} C^{2} J^{-1} m^{-1} B = 0.51 mol^{-1/2} dm^{3/2} (in H_{2}O, 25^{o}C) Other Units 1dm^{3 }=1 L 1dm^{3 }=1000 cm^{3} 1 J = 1 kg m^{2} s^{-2} 1 atm =1.01325 x 10^{5} Pa 1 atm = 760 mmHg 1 Torr = 1 mmHg 1 Torr = 133.322 Pa 1 bar = 10^{5} Pa E = hυ c =υλ PV =nRT (RT)/F = 25.6926 mV at 25^{o}C ln(x)/log_{10}(x) = 2.30259 for all x ln(1 - θ) = -θ if θ << 1 Quadratic equation: a x^{2} + b x + c = 0 solutions: x_{1,2} = (1/2a)[ - b ± (b^{2} - 4ac)^{1/2 }] RT/F = 25.70 mV(at 25^{o}C for ln) = 59.16 mV(at 25^{o}C for log_{10}) Michaelis - Menten equation: (1/R_{0})=(1/R_{max}) + (K_{m}/R_{max})x(1/[S]_{0}) Lindemann mechanism: k_{uni} = k_{1}k_{2}[M](k_{-1}[M] + k_{2})^{-1} Langmuir isotherm: θ = KP/(1 + KP) 1/R_{o} = 1/R_{max} + (K_{m}/R_{max}) (1/[S]_{o}) Sequential reactions: [B]=(k_{1}/(k_{2}-k_{-1})) f(t)[A]_{0} f(t)=exp(-k_{1}t)-exp(-k_{2}t) Note: Quantum yield/efficiency = Φ = moles of product formed / moles of photons absorbed | and Λ_{m} = Λ^{o}_{m} - K (c/c_{o})^{1/2 }(strong) 1/Λ_{m} = 1/Λ^{o}_{m} + cΛ_{m} /[(Λ^{o}_{m})^{2} K_{a} ] (weak) ΔG^{o}_{solvation} =(1/ε_{r} - 1)z^{2}e^{2}N_{A}/(8πε_{o}r) ΔG = -nFE and thus ΔG^{o} = -nFE^{o} ΔS = nF(dE/dt)_{P} a_{±}^{m+n} = a_{+}^{m}a_{-}^{n} for A_{m}B_{n} κ = [2e^{2}N_{A} x (1000 L m^{-3})/(ε_{o}k_{B}T)]^{1/2} x [ρ_{solvent} I/ε_{r}]^{1/2} E^{o}AgCl/Ag = +0.222 V k = A k = E_{a} = Δ^{≠}H^{o}-PΔ^{≠}V^{o} + RT (sol) = Δ^{≠}H^{o}-ΣνRT + RT (gas) ΔG^{# }= ΔH^{#}-TΔS^{#} t_{1/2} = (ln 2)/k (1^{st} order) fluorescence lifetime t_{f} = (k_{f} +k_{q}[Q])^{-1} R_{o} = k_{2}[S]_{o}[E]_{0}/([S]_{o} + K_{m}), K_{m} = (k_{-1} + k_{2})/k_{1} k_{2}[E]_{0} = R_{max} = V D = (1/3) v_{ave} λ κ = (1/3) (C_{V,m}/N_{A}) v_{ave} N_{p} λ PV = nRT = (N/N_{A})RT, (C_{V,m}/N_{A}) = (3/2) k_{B} η = (1/3) v_{ave}N_{p}λm f = 6πηr = k_{B}T/D v_{ave} = (8RT/(πM))^{1/2} N_{p}λ = 1/((√2)σ), λ = RT/(PN_{A}(√2)σ) Np = (N/V) = PN_{A}/(RT) σ = πd^{2} x_{rms} = √(2Dt) (1-Dimension) r_{rms} = √(6Dt) (3-Dimension) Poisseuille equation: (ΔV/Δt) = (πr^{4}/(8η)) ΔP/ ΔL Stokes-Einstein equation: D = k_{B}T/(6π ηr) if r(particle) >> r(solvent molecule) Ostwald viscosimeter: η = Aρt, Capillary rise: h = 2γ/(ρgr) |