地球化學

公式總表

公式總表

閱讀時間 // 約 2 分鐘

考前最後 30 分鐘看這一節就好。

主題公式
Hubble 年齡t=1/H0=d/vt = 1/H_0 = d/v
結合能BE=Nmn+Zmp+Zme−M\mathrm{BE} = N m_n + Z m_p + Z m_e - M；每核子 BE/A\mathrm{BE}/A
分配係數D=Cs/CLD = C_s/C_L；Dˉ=∑xiDi\bar D = \sum x_i D_i
Batch meltingCL/C0=1/[D(1−F)+F]C_L/C_0 = 1/[D(1-F)+F]；F→0F \to 0 時為 1/D1/D
第一定律dU=dQ+dW=T dS−P dVdU = dQ + dW = T\,dS - P\,dV
熵dS=dQrev/TdS = dQ_{\text{rev}}/T；S=kln⁡ΩS = k\ln\Omega
焓H=U+PVH = U + PV；ΔH=∫CP dT\Delta H = \int C_P\,dT；ΔS=∫(CP/T) dT\Delta S = \int (C_P/T)\,dT
GibbsG=H−TSG = H - TS；dG=V dP−S dTdG = V\,dP - S\,dT
G 對 P、T(∂ΔG/∂P)T=ΔV(\partial \Delta G/\partial P)_T = \Delta V；(∂ΔG/∂T)P=−ΔS(\partial \Delta G/\partial T)_P = -\Delta S
ClapeyrondP/dT=ΔS/ΔV=ΔH/(TΔV)dP/dT = \Delta S/\Delta V = \Delta H/(T\Delta V)
相律f=c−φ+2f = c - \varphi + 2；c=n−rc = n - r
化學勢μi=μi∘+RTln⁡ai\mu_i = \mu_i^\circ + RT\ln a_i
平衡常數ΔG∘=−RTln⁡K\Delta G^\circ = -RT\ln K；ΔG=ΔG∘+RTln⁡Q\Delta G = \Delta G^\circ + RT\ln Q
van't Hoffln⁡K=−ΔH∘/RT+ΔS∘/R\ln K = -\Delta H^\circ/RT + \Delta S^\circ/R
一階動力學[A]=[A]0e−kt[\mathrm{A}] = [\mathrm{A}]_0 e^{-kt}；t1/2=ln⁡2/kt_{1/2} = \ln 2/k
Arrheniusk=A e−Ea/RTk = A\,e^{-E_a/RT}
碳酸常數（25 °C）KCO2=10−1.47K_{\mathrm{CO_2}} = 10^{-1.47}；K1=10−6.35K_1 = 10^{-6.35}；K2=10−10.33K_2 = 10^{-10.33}；Kw=10−14K_w = 10^{-14}
鹼度Alk=[HCO3−]+2[CO32−]+[OH−]−[H+]\text{Alk} = [\mathrm{HCO_3^-}] + 2[\mathrm{CO_3^{2-}}] + [\mathrm{OH^-}] - [\mathrm{H^+}]
緩衝強度β=dCB/d pH\beta = dC_B/d\,\mathrm{pH}
KspK_{sp} 溶解度AB：x=Kspx = \sqrt{K_{sp}}；AB₂：x=(Ksp/4)1/3x = (K_{sp}/4)^{1/3}
滯留時間τ=M/F\tau = M/F
NernstE=E∘−(0.0592/z)log⁡QE = E^\circ - (0.0592/z)\log Q；ΔG=−zFE\Delta G = -zFE
E∘E^\circ 與 KKE∘=(0.0592/z)log⁡KE^\circ = (0.0592/z)\log K
pεpε=−log⁡ae−=E/0.0592p\varepsilon = -\log a_{e^-} = E/0.0592；pε∘=(1/n)log⁡Kp\varepsilon^\circ = (1/n)\log K
水的穩定範圍上界 pε=20.75−pHp\varepsilon = 20.75 - \mathrm{pH}；下界 pε=−pHp\varepsilon = -\mathrm{pH}
常數R=8.314 J/(mol⋅K)R = 8.314\ \mathrm{J/(mol\cdot K)}；F=96,485 C/molF = 96{,}485\ \mathrm{C/mol}
換算1 cm3=1 J/MPa1\ \mathrm{cm^3} = 1\ \mathrm{J/MPa}；2.303RT/F=0.0592 V2.303RT/F = 0.0592\ \mathrm{V}（25 °C）

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