Environmental Chemistry
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EQUATIONS
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INFORMATION
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$$ \large H = \frac{RT}{mg} $$
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\(\\ \textbf{H} = atmospheric \hspace{4 pt} scale \hspace{4 pt} height \hspace{4 pt} (m) \\ \textbf{R} = universal \hspace{4 pt} gas \hspace{4 pt} constant \\ \hspace{8 pt} (8.314 \hspace{2 pt} J \hspace{2 pt} mol^{-1} \hspace{2 pt} K^{-1}) \\ \textbf{T} = mean \hspace{4 pt} atmospheric \hspace{4 pt} temperature \hspace{4 pt} (K)\\ \textbf{m} = mean \hspace{4 pt} molecular \hspace{4 pt} mass \hspace{4 pt} of \hspace{4 pt} dry \\ \hspace{9 pt} air \hspace{4 pt} (kg) \\ \textbf{g} = acceleration \hspace{4 pt} due \hspace{4 pt} to \hspace{4 pt} gravity \\ \hspace{4 pt} (9.81 \hspace{4 pt} m \hspace{2 pt} s^{-1})\) |
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$$ \large p_z = p_\circ e^{\frac{-z}{H}} $$
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\(\\ {p_z} = pressure \hspace{4 pt} at \hspace{4 pt} altitude \hspace{4 pt} z \hspace{4 pt} (Pa) \\ {p_\circ} = ground \hspace{4 pt} level \hspace{4 pt} pressure \hspace{4 pt} (Pa)\\ \textbf{z} = altitude \hspace{4 pt} (m) \\ \textbf{H} = atmospheric \hspace{4 pt} scale \hspace{4 pt} height \hspace{4 pt} (m)\) |
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$$ \large P_T = P_1 + P_2 + P_3 + ... $$
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\( P_T = total \hspace{4 pt} pressure \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} mixture \hspace{4 pt} (Pa) \\ P_{\#} = partial \hspace{4 pt} pressure \hspace{4 pt} of \hspace{4 pt} gas \hspace{4 pt} \# \hspace{4 pt} (Pa) \) |
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$$ \large K = \frac{[C]^x [D]^y}{[A]^n [B]^m} $$
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\(\\ for \hspace{4 pt} equation \hspace{4 pt} of \hspace{4 pt} type: \\ nA + mB \rightleftharpoons xC + yD \\ \\ \textbf{K} = equilibrium \hspace{4 pt} constant \hspace{4 pt} of \hspace{4 pt} the \\ \hspace{9 pt} reaction \\ \textbf{[#]} = concentration \hspace{4 pt} of \hspace{4 pt} substance \\ \hspace{18 pt} \# \hspace{4 pt} (M) \\ \textbf{x, y, n, m} = formula \hspace{4 pt} coefficients \\\) |
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$$ \large K_a = \frac{[A^-][H^+]}{[HA]} $$
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\(\\ for \hspace{4 pt} equation \hspace{4 pt} of \hspace{4 pt} type: \\ HA \rightleftharpoons A^- + H^+ \\ \\ {K_a} = acid \hspace{4 pt} dissociation \hspace{4 pt} constant \\ \textbf{[#]} = concentration \hspace{4 pt} of \hspace{4 pt} \# \hspace{4 pt} (M) \\ \textbf{HA} = generic \hspace{4 pt} acid \\ {A^-} = conjugate \hspace{4 pt} base \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} acid \\ {H^+} = hydrogen \hspace{4 pt} ion\) |
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$$ \large K_b = \frac{[HB^+][OH^-]}{[B]} $$
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\(\\ for \hspace{4 pt} equation \hspace{4 pt} of \hspace{4 pt} type: \\ B + H_2 O \rightleftharpoons HB^+ + OH^- \\ \\ {K_b} = base \hspace{4 pt} dissociation \hspace{4 pt} constant \\ \textbf{[#]} = concentration \hspace{4 pt} of \hspace{4 pt} \# \hspace{4 pt} (M) \\ {HB^+} = conjugate \hspace{4 pt} acid \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} base \\ {OH^-} = hydroxide \hspace{4 pt} ion \hspace{4 pt} \\ \textbf{B} = generic \hspace{4 pt} base\) |
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$$ \large K_{eq} = \frac{[H_3 O^+] [OH^-]}{[H_2 O]^2} $$
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\(\\ for \hspace{4 pt} equation \hspace{4 pt} of \hspace{4 pt} type: \\ H_2 O + H_2 O \rightleftharpoons H_3 O^+ + OH^- \\ \\ {K_{eq}} = self \hspace{4 pt} ionization \hspace{4 pt} constant \\ \textbf{[#]} = concentration \hspace{4 pt} of \hspace{4 pt} \# \hspace{4 pt} (M) \\ {H_3O^+} = hydronium \\ {OH^-} = hydroxide \hspace{4 pt} ion \\ {H_2 O} = water\) |
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$$ \large K_H = \frac{P}{C} $$
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\(\\ {K_H} = Henry's \hspace{4 pt} Law \hspace{4 pt} constant \hspace{4 pt} (Pa \hspace{2 pt} M^{-1}) \\ \textbf{P} = vapor \hspace{4 pt} pressure \hspace{4 pt} of \hspace{4 pt} solute \hspace{4 pt} (Pa) \\ \textbf{C} = concentration \hspace{4 pt} of \hspace{4 pt} solute \hspace{4 pt} in \\ \hspace{8 pt} the \hspace{4 pt} solution \hspace{4 pt} (M) \) |
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$$ \large \Delta G ^{\circ} + RT \hspace{2 pt} ln \hspace{2 pt} Q $$
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\( \Delta G = free - energy \hspace{4 pt} change \hspace{4 pt}(J \hspace{2 pt} mol^{-1} ) \\ \Delta G^{\circ} = standard \hspace{4 pt} free - energy \hspace{4 pt} change \\ \hspace{8 pt} (J \hspace{2 pt} mol^{-1}) \\ \textbf{R} = universal \hspace{4 pt} gas \hspace{4 pt} law \\ \hspace{8 pt} (8.314 \hspace{2 pt} J \hspace{2 pt} mol^{-1} K^{-1}) \\ \textbf{T} = temperature \hspace{4 pt} (K) \\ \textbf{Q} = reaction \hspace{4 pt} quotient \) |
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$$ \large \Delta G = - nFE $$
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\( \\ {\Delta G} = standard \hspace{4 pt} reduction \hspace{4 pt} potential \\ \hspace{20 pt} (J \hspace{4 pt} mol ^{-1})\\ {n} = number \hspace{4 pt} of \hspace{4 pt} moles \hspace{4 pt} of \hspace{4 pt} electrons \\ \hspace{8 pt} per \hspace{4 pt} mole \hspace{4 pt} of \hspace{4 pt} product \hspace{4 pt} (mol) \\ \textbf{F} = Faraday \hspace{4 pt} constant \\ \hspace{7 pt} (9.649 \hspace{2 pt} \times 10^4 \hspace{2 pt} C \hspace{2 pt} mol^{-1}) \\ \textbf{E} = standard \hspace{4 pt} reduction \hspace{4 pt} potential \hspace{4 pt} (V)\) |
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$$ \large K_{sp} = [B^+]^x[C^-]^y $$
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\(\\ for \hspace{4 pt} equation \hspace{4 pt} of \hspace{4 pt} form: \\ A \rightarrow xB^+ + yC^- \\ \\ {K_{sp}} = solubility \hspace{4 pt} product \hspace{4 pt} constant \hspace{4 pt} (M^{x+y}) \\ \textbf{[#]} = concentration \hspace{4 pt} of \hspace{4 pt} \# \hspace{4 pt} (M) \\\) |
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$$ \large \Omega = \frac{IAP}{K_{sp}} $$
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\(\\ {\Omega} = saturation \hspace{4 pt} index \\ \textbf{IAP} = ion \hspace{4 pt} activity \hspace{4 pt} product \hspace{4 pt} (M^x) \\ {K_{sp}} = solubility \hspace{4 pt} product \hspace{4 pt} constant \hspace{4 pt} (M^x) \\ \\ *where \hspace{4 pt} x \hspace{4 pt} equals \hspace{4 pt} the \hspace{4 pt} number \hspace{4 pt} of \hspace{4 pt} products\) |
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$$ \large CIA = \frac{Al_2 O_3}{Al_2 O_3 + Na_2O + K_2O + CaO^*} \times 100 $$
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\(\\ \textbf{CIA} = chemical \hspace{4 pt} index \hspace{4 pt} of \hspace{4 pt} alteration \\ {Al_2 O_3} = moles \hspace{4 pt} of \hspace{4 pt} Al_2 O_3 \hspace{4 pt} (mol) \\ {Na_2 O} = moles \hspace{4 pt} of \hspace{4 pt} Na_2 O \hspace{4 pt} (mol) \\ {K_2 O} = moles \hspace{4 pt} of \hspace{4 pt} K_2 O \hspace{4 pt} (mol) \\ {CaO^*} = CaO \hspace{4 pt} content \hspace{4 pt} of \hspace{4 pt} silicate \\ \hspace{28 pt} minerals \hspace{4 pt} (mol) \\\) |
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$$ \large I = \frac{1}{2} \sum ^n _{i=1} c_i z_i ^2 $$
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\(\\ \textbf{I} = ionic \hspace{4 pt} strength \hspace{4 pt} (M) \\ {c_i} = concentration \hspace{4 pt} of \hspace{4 pt} ion \hspace{4 pt} i \hspace{4 pt} (M) \\ {z_i} = charge \hspace{4 pt} number \hspace{4 pt} of \hspace{4 pt} ion \hspace{4 pt} i \hspace{4 pt} (mol) \\\) |
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$$ \large \delta = \left(\frac{R_{sample} - R_{standard}}{R_{standard}} \right ) \times 1000 $$
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\(\\ {\delta} = delta \hspace{4 pt} notation \hspace{4 pt} for \hspace{4 pt} expressing \\ \hspace{4 pt} stable \hspace{4 pt} isotope \hspace{4 pt} ratio \hspace{4 pt} values \\ {R_{sample}} = stable \hspace{4 pt} isotope \hspace{4 pt} ratio \hspace{4 pt} of \\ \hspace{8 pt} the \hspace{4 pt} sample \\ {R_{standard}} = stable \hspace{4 pt} isotope \hspace{4 pt} ratio \hspace{4 pt} of \\ \hspace{8 pt} the \hspace{4 pt} standard \) |
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