General College Chemistry
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EQUATIONS
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INFORMATION
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$$ \large c_{\%} = \frac{m_{pt}}{m_{wh}} \cdot 100\% $$
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\(\\ {c_{\%}} = percent \hspace{4 pt} composition \hspace{4 pt} by \hspace{4 pt} mass \\ {m_{pt}} = mass \hspace{4 pt} of \hspace{4 pt} part \hspace{4 pt} / \hspace{4 pt} component \hspace{4 pt} (g) \\ {m_{wh}} = mass \hspace{4 pt} of \hspace{4 pt} whole \hspace{4 pt} / \hspace{4 pt} compound \hspace{4 pt} (g)\) |
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$$ \large PPM = \frac{m_{solute}}{m_{solution}} \cdot 1,000,000 $$
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\( \textbf{PPM} = parts \hspace{4 pt} per \hspace{4 pt} million \\ {m_{solute}} = mass \hspace{4 pt} of \hspace{4 pt} solute \hspace{4 pt} (g) \\ {m_{solution}} = mass \hspace{4 pt} of \hspace{4 pt} solution \hspace{4 pt} (g)\) |
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$$ \large \frac{R_1}{R_2} = \sqrt{\frac{M_2}{M_1}} $$
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\( {R_\#} = rate \hspace{4 pt} of \hspace{4 pt} effusion \hspace{4 pt} of \hspace{4 pt} gas \hspace{4 pt} \# \hspace{4 pt} (m \hspace{2 pt} s^{-1})\\ {M_\#} = molar \hspace{4 pt} mass \hspace{4 pt} of \hspace{4 pt} gas \hspace{4 pt} \# \hspace{4 pt} (kg \hspace{4 pt} mol^{-1})\) |
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$$ \large
K_w \hspace{1 pt} = [H_3 O^+][OH^-] = [H^+][OH^-] \\
= 1.00 \times 10^{-14} $$
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\( {K_w} = equilibrium \hspace{4 pt} constant \hspace{4 pt} for \hspace{4 pt} the \\ \hspace{16 pt} self - ionization \hspace{4 pt} of \hspace{4 pt} water\\ \textbf{[#]} = concentration \hspace{4 pt} of \hspace{4 pt} \# \hspace{4 pt} (M) \\\) |
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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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$$ \large I_\% = \frac{[H^+]_{eq}}{[HA]_i} \times 100 \% $$
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\( {I_\%} = percent \hspace{4 pt} ionization \hspace{4 pt} \\ {[H^+]_{eq}} = concentration \hspace{4 pt} of \hspace{4 pt} H^+ \hspace{4 pt} at \\ \hspace{32 pt} equilibrium \hspace{4 pt} (M) \\ \textbf{[HA]} = initial \hspace{4 pt} acid \hspace{4 pt} concentration\hspace{4 pt} (M)\) |
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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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$$ \large
r = -\frac{1}{a} \frac{\Delta [A]}{\Delta t} = -\frac{1}{b} \frac{\Delta [B]}{\Delta t} = $$ $$ \large
-\frac{1}{c} \frac{\Delta [C]}{\Delta t} = -\frac{1}{d} \frac{\Delta [D]}{\Delta t} $$
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\(\\ for \hspace{4 pt} equation \hspace{4 pt} of \hspace{4 pt} type: \\ aA + bB \rightarrow cC +dD \\ \\ \textbf{r} = rate \hspace{4 pt} of \hspace{4 pt} reaction \hspace{4 pt} (M \hspace{4 pt} s^{-1}) \\ \textbf{a,b,c,d} = formula \hspace{4 pt} coefficients \\ {\Delta [\#]} = change \hspace{4 pt} in \hspace{4 pt} concentration \hspace{4 pt} of \hspace{4 pt} \# \hspace{4 pt} (M) \\ {\Delta t} = change \hspace{4 pt} in \hspace{4 pt} time \hspace{4 pt} (s)\) |
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$$ \large r = k[A]^x[B]^y $$
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\( for \hspace{4 pt} equation \hspace{4 pt} of \hspace{4 pt} type: \\ aA + bB \rightarrow C \\ \\ \textbf{r} = rate \hspace{4 pt} of \hspace{4 pt} reaction \hspace{4 pt} (M \hspace{2 pt} s^{-1}) \\ \textbf{k} = specific \hspace{4 pt} rate \hspace{4 pt} constant \hspace{4 pt} (M^{-1} \hspace{2 pt} s^{-1}) \\ \textbf{[#]} = concentration \hspace{4 pt} (M) \\ \textbf{x,y} = experimentally \hspace{4 pt} determined \\ \hspace{17 pt} variables\\ \textbf{a,b} = formula \hspace{4 pt} coefficients\) |
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$$ \large {ln} \frac{[A]_t}{[A]_0} = -kt $$
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\( for \hspace{4 pt} equation \hspace{4 pt} of \hspace{4 pt} type: \\ A \rightarrow products \\ \\ {[A]_t} = concentration \hspace{4 pt} of \hspace{4 pt} A \hspace{4 pt} at \\ \hspace{18 pt} time \hspace{4 pt} t \hspace{4 pt} (M) \\ {[A]_0} = initial \hspace{4 pt} concentration \hspace{4 pt} of \hspace{4 pt} A \hspace{4 pt} (M) \\ \textbf{k} = reaction \hspace{4 pt} rate \hspace{4 pt} coefficient \hspace{4 pt} (s^{-1}) \\ \textbf{t} = reaction \hspace{4 pt} time \hspace{4 pt} (s)\) |
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$$ \large \frac{1}{[A]_t} = kt + \frac{1}{[A]_t} $$
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\(\\ for \hspace{4 pt} equation \hspace{4 pt} of \hspace{4 pt} type: \\ A \rightarrow products \\ \\ {[A]_t} = concentration \hspace{4 pt} of \hspace{4 pt} A \hspace{4 pt} at \\ \hspace{18 pt} time \hspace{4 pt} t \hspace{4 pt} (M) \\ {[A]_0} = initial \hspace{4 pt} concentration \hspace{4 pt} of \hspace{4 pt} A \hspace{4 pt} (M) \\ \textbf{k} = reaction \hspace{4 pt} rate \hspace{4 pt} coefficient \hspace{4 pt} (s^{-1}) \\ \textbf{t} = reaction \hspace{4 pt} time \hspace{4 pt} (s)\) |
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$$ \large k = Ae^{ ^{-\left(\frac{E_a}{RT} \right )}} $$
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\(\\ \textbf{k} = reaction \hspace{4 pt} rate \hspace{4 pt} coefficient \hspace{4 pt} (s^{-1}) \\ \textbf{A} = pre-exponential \hspace{4 pt} factor \hspace{4 pt} (M \hspace{2 pt} s^{-1}) \\ {E_a} = activation \hspace{4 pt} energy \hspace{4 pt} (J \hspace{2 pt} mol^{-1}) \\ \textbf{R} = universal \hspace{4 pt} gas \hspace{4 pt} constant \\ \hspace{9 pt} (8.314 \hspace{2 pt} J \hspace{2 pt} K^{-1} \hspace{2 pt} mol^{-1}) \\ \textbf{T} = temperature \hspace{4 pt} (K)\) |
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$$ \large {ln} \hspace{2 pt} k = -\frac{E_a}{RT} + {ln} \hspace{2 pt} A $$
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\(\\ \textbf{k} = reaction \hspace{4 pt} rate \hspace{4 pt} coefficient \hspace{4 pt} (s^{-1}) \\ \textbf{A} = pre-exponential \hspace{4 pt} factor \hspace{4 pt} (M \hspace{2 pt} s^{-1}) \\ {E_a} = activation \hspace{4 pt} energy \hspace{4 pt} (J \hspace{2 pt} mol^{-1}) \\ \textbf{R} = universal \hspace{4 pt} gas \hspace{4 pt} constant \\ \hspace{9 pt} (8.314 \hspace{2 pt} J \hspace{2 pt} K^{-1} \hspace{2 pt} mol^{-1}) \\ \textbf{T} = temperature \hspace{4 pt} (K)\) |
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$$ \large O_{reaction} = O_A + O_B $$
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\(\\ for \hspace{4 pt} equation \hspace{4 pt} of \hspace{4 pt} type: \\ aA + bB \rightarrow C \\ \\ {O_{reaction}} = order \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} reaction \\ {O_{\#}} = order \hspace{4 pt} of \hspace{4 pt} substance \hspace{4 pt} \#\) |
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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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$$ \large K_p = \frac{{p_C}^x {p_D}^y}{{p_A}^n {p_B}^m} $$
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\(\\ for \hspace{4 pt} equation \hspace{4 pt} of \hspace{4 pt} type: \\ nA + mB \rightleftharpoons xC + yD \\ \\ {K_p} = equilibrium \hspace{4 pt} constant \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} reaction \\ \hspace{13 pt} computed \hspace{4 pt} with \hspace{4 pt} partial \hspace{4 pt} pressures \\ {p_\#} = partial \hspace{4 pt} pressure \hspace{4 pt} of \hspace{4 pt} \# \hspace{4 pt} (Pa) \\ \textbf{x,y,n,m} = formula \hspace{4 pt} coefficients \) |
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$$ \large K_p = K \times (RT)^{\Delta n}
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\(\\ {K_p} = equilibrium \hspace{4 pt} constant \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} reaction \\ \hspace{14 pt} computed \hspace{4 pt} with \hspace{4 pt} partial \hspace{4 pt} pressures \\ \textbf{K} = equilibrium \hspace{4 pt} constant \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} reaction \\ \hspace{14 pt} computed \hspace{4 pt} with \hspace{4 pt} molar \hspace{4 pt} concentrations \\ \textbf{R} = universal \hspace{4 pt} gas \hspace{4 pt} constant \hspace{4 pt} \\ \hspace{8 pt} (8.314 \hspace{2 pt} J \hspace{2 pt} mol^{-1} \hspace{2 pt} K^{-1}) \\ \textbf{T} = temperature \hspace{4 pt} (K) \\ {\Delta n} = change \hspace{4 pt} in \hspace{4 pt} amount \hspace{4 pt} of \hspace{4 pt} molecules \\ \hspace{15 pt} between \hspace{4 pt} reactants \hspace{4 pt} and \hspace{4 pt} products \hspace{4 pt}(mol) \) |
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$$ \large Q = \frac{[C]^x [D]^y}{[A]^n [B]^m} $$
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\(\\ for \hspace{4 pt} equation \hspace{4 pt} of \hspace{4 pt} type: \\ nA + mB \rightleftharpoons xC + yD \\ \\ \textbf{Q} = reaction \hspace{4 pt} quotient \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} reaction \\ \textbf{[#]} = concentration \hspace{4 pt} of \hspace{4 pt} \# \hspace{4 pt} (M) \\ \textbf{x,y,n,m} = formula \hspace{4 pt} coefficients\) |
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$$ \large K_{sp} = [A^{y+}]^x[B^{x-}]^y $$
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\(\\ for \hspace{4 pt} equation \hspace{4 pt} of \hspace{4 pt} type: \\ A_xB_y(s) \rightarrow xA^{y+} (aq) + yB^{x-} \\ \\ {K_{sp}} = solubility \hspace{4 pt} product \hspace{4 pt} constant \\ \textbf{[#]} = concentration \hspace{4 pt} of \hspace{4 pt} substance \\ \hspace{14 pt} \# \hspace{4 pt} (M) \\ \textbf{x, y} = formula \hspace{4 pt} coefficients\) |
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$$ \large M_AV_A = M_BV_B $$
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\(\\ {M_A} = molarity \hspace{4 pt} of \hspace{4 pt} H^+ \hspace{4 pt} (M) \\ {V_A} = volume \hspace{4 pt} of \hspace{4 pt} acid \hspace{4 pt} (m^3) \\ {M_B} = molarity \hspace{4 pt} of \hspace{4 pt} OH^{-} \hspace{4 pt} (M) \\ {V_B} = volume \hspace{4 pt} of \hspace{4 pt} base \hspace{4 pt} (m^3)\) |
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$$ \large E^\circ _{cell} = E^\circ _{cathode} - E^\circ _{anode} $$
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\(\\ {E^\circ _{cell}} = electrode \hspace{4 pt} potential \hspace{4 pt} (V) \\ {E^\circ _{cathode}} = cathode \hspace{4 pt} potential \hspace{4 pt} (V)\\ {E^\circ _{anode}} = anode \hspace{4 pt} potential \hspace{4 pt} (V)\) |
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$$ \large
c = \nu \lambda $$
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\(\\ \textbf{c} = speed \hspace{4 pt} of \hspace{4 pt} light \hspace{4 pt} (3.00 \hspace{2 pt} m \hspace{2 pt} s^{-2}) \\ {\nu} = frequency \hspace{4 pt} of \hspace{4 pt} light \hspace{4 pt} (Hz) \\ {\lambda} = wavelength \hspace{4 pt} of \hspace{4 pt} light \hspace{4 pt} (m)\) |
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$$ \large \Delta x \Delta p \geq \frac{h}{4 \pi} $$
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\(\\ {\Delta x} = uncertainty \hspace{4 pt} in \hspace{4 pt} position \hspace{4 pt} (m)\\ {\Delta p} = uncertainty \hspace{4 pt} in \hspace{4 pt} the \\ \hspace{18 pt} momentum \hspace{4 pt} (m) \\ \textbf{h} = Planck's \hspace{4 pt} constant \hspace{4 pt} \\ \hspace{4 pt} (6.626 \times 10^{-34} \hspace{2 pt} m^2 \hspace{2 pt} kg \hspace{2 pt} s^{-1})\) |
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$$ \large Z_{eff} = Z - S $$
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\(\\ {Z_{eff}} = effective \hspace{4 pt} nuclear \hspace{4 pt} charge \\ \textbf{Z} = number \hspace{4 pt} of \hspace{4 pt} protons \hspace{4 pt} in \hspace{4 pt} the \\ \hspace{7 pt} nucleus \\ \textbf{S} = average \hspace{4 pt} number \hspace{4 pt} of \hspace{4 pt} electrons \\ \hspace{5 pt} between \hspace{4 pt} the \hspace{4 pt} nucleus \hspace{4 pt} and \hspace{4 pt} the \\ \hspace{5 pt} particular \hspace{4 pt} electron\) |
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$$ \large
E = h\nu = \frac{hc}{\lambda} $$
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\( \textbf{E} = energy \hspace{4 pt} of \hspace{4 pt} a \hspace{4 pt} photon \hspace{4 pt} (J) \\ \textbf{h} = Planck's \hspace{4 pt} constant \hspace{4 pt} (6.625 \hspace{2 pt}x \hspace{2 pt} 10^{-34} J \hspace{2 pt} s ) \\ {\nu} = frequency \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} light \hspace{4 pt}(Hz) \\ \textbf{c} = speed \hspace{4 pt} of \hspace{4 pt} light \hspace{4 pt} (3.0 \hspace{2 pt} x \hspace{2 pt} 10^8 \hspace{4 pt} m \hspace{2 pt} s^{-1}) \\ {\lambda} = wavelength \hspace{4 pt} (m) \) |
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$$ \large K = \frac{1}{2} m{\bar{v}}^2 $$
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\(\\ \textbf{K} = kinetic \hspace{4 pt} energy \hspace{4 pt} (J) \\ \textbf{m} = mass \hspace{4 pt} (kg) \\ \textbf{v} = velocity \hspace{4 pt} (m \hspace{2 pt} s^{-1}) \\ \textbf{k} = Boltzmann \hspace{4 pt} constant \\ \hspace{5 pt} (1.38 \hspace{2 pt} x 10^{-23} \hspace{2 pt} m^2 \hspace{2 pt} kg \hspace{2 pt} s^{-2} \hspace{2 pt} K^{-1}) \\ \textbf{T} = temperature \hspace{2 pt} (K)\) |
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$$ \large U = \frac{\kappa q_1 q_2}{r} $$
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\(\\ \textbf{U} = electric \hspace{4 pt} potential \hspace{4 pt} energy \hspace{4 pt} (J) \\ {\kappa} = Couloumb's \hspace{4 pt} constant \hspace{4 pt} \\ \hspace{4 pt} (8.988 \times 10^9 \hspace{2 pt} N \hspace{2 pt} m^2 \hspace{2 pt} C^{-2}) \\ {q_{\#}} = charge \hspace{4 pt} of \hspace{4 pt} particle \hspace{4 pt} \# \hspace{4 pt} (C) \\ \textbf{r} = distance \hspace{4 pt} between \hspace{4 pt} charges \hspace{4 pt} (m) \) |
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$$ \large \mu = Qr $$
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\(\\ {\mu} = dipole \hspace{4 pt} (C \hspace{2 pt} m) \\ \textbf{Q} = magnitude \hspace{4 pt} of \hspace{4 pt} charges \hspace{4 pt} creating \\ \hspace{10 pt} the \hspace{4 pt} dipole \hspace{4 pt} (C) \\ \textbf{r} = distance \hspace{4 pt} between \hspace{4 pt} charges \hspace{4 pt} (m) \) |
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$$ \large \Delta E = E_{final} - E_{initial} $$
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\({\Delta E} = change \hspace{4 pt} in \hspace{4 pt} internal \hspace{4 pt} energy \hspace{4 pt} (J)\\ {E_{final}} = final \hspace{4 pt} internal \hspace{4 pt} energy \hspace{4 pt} (J) \\ {E_{initial}} = initial \hspace{4 pt} internal \hspace{4 pt} energy \hspace{4 pt} (J)\) |
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$$ \large q = mc\Delta T = mH_f = mH_v $$
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\(\\ \textbf{q} = heat \hspace{4 pt} (J) \\ \textbf{m} = mass \hspace{4 pt} (kg) \\ \textbf{c} = specific \hspace{4 pt} heat \hspace{4 pt} capacity \hspace{4 pt} (J \hspace{2 pt} kg^{-1} \hspace{4 pt} K^{-1}) \\ {\Delta T} = change \hspace{4 pt} in \hspace{4 pt} temperature \hspace{4 pt} (K) \\ {H_f} = heat \hspace{4 pt} of \hspace{4 pt} fusion \hspace{4 pt} (J \hspace{2 pt} kg^{-1}) \\ {H_v} = heat \hspace{4 pt} of \hspace{4 pt} vaporization \hspace{4 pt} (J \hspace{2 pt} kg^{-1})\) |
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$$ \large \Delta E = q + w $$
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\(\\ {\Delta E} = change \hspace{4 pt} in \hspace{4 pt} internal \hspace{4 pt} energy \hspace{4 pt} (J)\\ \textbf{q} = heat \hspace{4 pt} transfer \hspace{4 pt} in \hspace{4 pt} to /out \hspace{4 pt} of \\ \hspace{6 pt} the \hspace{4 pt} system \hspace{4 pt} (J) \\ \textbf{w} = work \hspace{4 pt} done \hspace{4 pt} by/on \hspace{4 pt} the \hspace{4 pt} system \hspace{4 pt} (J)\) |
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$$ \large
Reversible \hspace{4 pt} process: \\ $$ $$ \large
\Delta S_{univ} = \Delta S_{sys} +\Delta S_{surr} = 0 \\ $$ $$ \large
Irreversible \hspace{4 pt} process: $$ $$ \large
\Delta S_{univ} = \Delta S_{sys} +\Delta S_{surr} > 0 $$
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\(\\ {\Delta S_{univ}} = change \hspace{4 pt} in \hspace{4 pt} the \hspace{4 pt} entropy \\ \hspace{38 pt} of \hspace{4 pt} the \hspace{4 pt} universe \hspace{4 pt} (J \hspace{2 pt} K^{-1}) \\ {\Delta S_{sys}} = change \hspace{4 pt} in \hspace{4 pt} the \hspace{4 pt} entropy \\ \hspace{31 pt} of \hspace{4 pt} the \hspace{4 pt} system \hspace{4 pt} (J \hspace{2 pt} K^{-1}) \\ {\Delta S_{surr}} = change \hspace{4 pt} in \hspace{4 pt} the \hspace{4 pt} entropy \\ \hspace{36 pt} of \hspace{4 pt} the \hspace{4 pt} surroundings \hspace{4 pt} (J \hspace{2 pt} K^{-1}) \\\) |
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$$ \large \Delta S = \frac{q_{rev}}{T} $$
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\(\\ {\Delta S} = change \hspace{4 pt} in \hspace{4 pt} entropy \hspace{4 pt} (J \hspace{2 pt} K^{-1}) \\ {q_{rev}} = reversible \hspace{4 pt} exchange \hspace{4 pt} of \hspace{4 pt} heat \hspace{4 pt} (J)\\ \textbf{T} = temperature \hspace{4 pt} (K)\) |
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$$ \large S = k \hspace{2 pt} {ln} \hspace{2 pt} \Omega $$
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\(\\ \textbf{S} = entropy \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} system \hspace{4 pt} (J \hspace{2 pt} K^{-1}) \\ \textbf{k} = Boltzmann \hspace{4 pt} constant \\ \hspace{6 pt} (1.381 \times 10^{-23} \hspace{2 pt} m^2 \hspace{2 pt} kg \hspace{2 pt} s^{-2} \hspace{2 pt} K^{-1}) \\ {\Omega} = number \hspace{4 pt} of \hspace{4 pt} microstates \) |
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$$ \large \Delta H = \sum \Delta H_{products} - \sum \Delta H_{reactants} $$
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\(\\ {\Delta H} = change \hspace{4 pt} in \hspace{4 pt} enthalpy \hspace{4 pt} for \hspace{4 pt} the \\ \hspace{20 pt} reaction \hspace{4 pt} (J) \\ {\Delta H_{products}} = change \hspace{4 pt} in \hspace{4 pt} enthalpy \hspace{4 pt} of \hspace{4 pt} the \\ \hspace{20 pt} products \hspace{4 pt} (J) \\ {\Delta H_{reactants}} = change \hspace{4 pt} in \hspace{4 pt} enthalpy \hspace{4 pt} of \hspace{4 pt} the \\ \hspace{20 pt} reactants \hspace{4 pt} (J) \\\) |
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$$ \large \Delta S_{surr} = - \frac{\Delta H_{sys}}{T} $$
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\(\\ {\Delta S_{surr}} = change \hspace{4 pt} in \hspace{4 pt} the \hspace{4 pt} entropy \\ \hspace{35 pt} of \hspace{4 pt} the \hspace{4 pt} surroundings \hspace{4 pt} (J \hspace{2 pt} K^{-1}) \\ {\Delta H_{sys}} = enthalpy \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} reaction \hspace{4 pt} (J) \\ \textbf{T} = temperature \hspace{4 pt} (K)\) |
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$$ \large \Delta G = \Delta H - T \Delta S_{int} $$
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\(\\ {\Delta G} = Gibbs \hspace{4 pt} free \hspace{4 pt} energy \hspace{4 pt} change \\ \hspace{18 pt} (J \hspace{2 pt} mol^{-1}) \\ {\Delta H} = change \hspace{4 pt} in \hspace{4 pt} enthalpy \hspace{4 pt} (J \hspace{2 pt} mol^{-1}) \\ \textbf{T} = temperature \hspace{4 pt} (K)\\ {\Delta S_{int}} = change \hspace{4 pt} in \hspace{4 pt} internal \\ \hspace{28 pt} entropy \hspace{4 pt} (J \hspace{2 pt} mol^{-1} K^{-1})\) |
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$$ \large \Delta G^{\circ} = \sum \Delta G^ {\circ} _{f, products} - \sum \Delta G^ {\circ} _{f, reactants} $$
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\(\\ {\Delta G^{\circ}} = Standard - State \hspace{4 pt} Free \\ \hspace{24 pt} Energy \hspace{4 pt} of \hspace{4 pt} Formation \hspace{4 pt} (J \hspace{2 pt} mol^{-1}) \\ {\Delta G^ {\circ} _{f, products}} = standard - state \hspace{4 pt} free \\ \hspace{8 pt} energy \hspace{4 pt} of \hspace{4 pt} the \\ \hspace{8 pt} products \hspace{4 pt} (J \hspace{2 pt} mol^{-1}) \\ {\Delta G^ {\circ} _{f, reactants}} = standard - state \hspace{4 pt} free \\ \hspace{8 pt} energy \hspace{4 pt} of \hspace{4 pt} the \\ \hspace{8 pt} reactants \hspace{4 pt} (J \hspace{2 pt} mol^{-1}) \) |
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$$ \large \Delta G = -w_{max} $$
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\(\\ {\Delta G} = free-energy \hspace{4 pt} change \hspace{4 pt} (J \hspace{2 pt} mol^{-1}) \\ {w_{max}} = maximum \hspace{4 pt} work \hspace{4 pt} that \hspace{4 pt} can \hspace{4 pt} be \\ \hspace{26 pt} performed \hspace{4 pt} by \hspace{4 pt} a \hspace{4 pt} process \hspace{4 pt} (J \hspace{2 pt} mol^{-1}) \) |
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$$ \large \Delta G = \Delta G ^ {\circ} + RT \hspace{2 pt} {ln} \hspace{2 pt} Q $$
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\(\\ {\Delta G} = free - energy \hspace{4 pt} change \hspace{4 pt} (J \hspace{2 pt} mol^{-1}) \\ {\Delta G ^ {\circ}} = standard \hspace{4 pt} free - energy \hspace{4 pt} change \hspace{4 pt} (J \hspace{2 pt} mol^{-1}) \\ \textbf{R} = universal \hspace{4 pt} gas \hspace{4 pt} law \\ \hspace{9 pt} (8.314 \hspace{2 pt} J \hspace{2 pt} mol^{-1} \hspace{2 pt} K^{-1}) \\ \textbf{T} = temperature \hspace{4 pt} (K) \\ \textbf{Q} = reaction \hspace{4 pt} quotient\) |
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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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\( \Delta G^{\circ} = standard \hspace{4 pt} free - energy \hspace{4 pt} change \\ \hspace{8 pt} (J \hspace{2 pt} mol^{-1}) \\ \textbf{n} = number \hspace{4 pt} of \hspace{4 pt} moles \hspace{4 pt} of \hspace{4 pt} electrons \\ \hspace{8 pt} per \hspace{4 pt} mole \hspace{4 pt} of \hspace{4 pt} product \hspace{4 pt} (mol) \\ \textbf{F} = Faraday \hspace{4 pt} constant \\ \hspace{8 pt} (9.649 \hspace{2 pt} x \hspace{2 pt} 10^4 \hspace{2 pt} C \hspace{2 pt} mol^{-1}) \\ \textbf{E} = standard \hspace{4 pt} reduction \hspace{4 pt} potential \hspace{4 pt} (V) \) |
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$$ \large E = E^{\circ} - \frac{0.0592 \hspace{2 pt} V}{n} \hspace{2 pt} {log} \hspace{2 pt} Q $$
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\(\\ \textbf{E} = potential \hspace{4 pt} difference \hspace{4 pt} (V) \\ {E^{\circ}} = standard \hspace{4 pt} potential \hspace{4 pt} difference \hspace{4 pt} (V) \\ \textbf{n} = number \hspace{4 pt} of \hspace{4 pt} electrons \hspace{4 pt} transferred \\ \hspace{6 pt} in \hspace{4 pt} the \hspace{4 pt} reaction \\ \textbf{Q} = reaction \hspace{4 pt} quotient\) |
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$$ \large w = -P \Delta V $$
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\(\\ \textbf{w} = work \hspace{4 pt} done \hspace{4 pt} by \hspace{4 pt} gas \hspace{4 pt} (J)\\ \textbf{P} = pressure \hspace{4 pt} (Pa) \\ {\Delta V} = change \hspace{4 pt} in \hspace{4 pt} the \hspace{4 pt} volume \hspace{4 pt} of \\ \hspace{21 pt} the \hspace{4 pt} system \hspace{4 pt} (m^3)\) |
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$$ \large \Delta T_f = K_f m $$
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\(\\ {\Delta T_f} = freezing-point \hspace{4 pt} depression \hspace{4 pt} (K) \\ {K_f} = freezing-point \hspace{4 pt} constant \hspace{4 pt} (^\circ C \hspace{4 pt} m^{-1})\\ \textbf{b} = molality \hspace{4 pt} amount \hspace{4 pt} (mol \hspace{4 pt} kg^{-1})\) |
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$$ \large \Delta T_b = K_b \hspace{2 pt} b $$
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\( \Delta T_b = boiling - point \hspace{4 pt} elevation \hspace{4 pt} (K) \\ K_b = boiling - point \hspace{4 pt} constant \hspace{4 pt} ( ^{\circ} C \hspace{2 pt} m^{-1}) \\ \textbf{b} = molality \hspace{4 pt} (mol \hspace{2 pt} kg^{-1}) \) |
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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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$$ \large P_1 = \left(\frac{n_1}{n_{tot}} \right ) P_{tot} = X_1 P_{tot} $$
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\(\\ {P_\#} = partial \hspace{4 pt} pressure \hspace{4 pt} of \hspace{4 pt} gas \hspace{4 pt} \# \hspace{4 pt} (Pa) \\ {{n_{\#}}} = amount \hspace{4 pt} of \hspace{4 pt} gas \hspace{4 pt} \# \hspace{4 pt} (mol) \\ {n_{tot}} = total \hspace{4 pt} amount \hspace{4 pt} of \hspace{4 pt} gas \hspace{4 pt} (mol) \\ {P_{tot}} = total \hspace{4 pt} pressure \hspace{4 pt} (Pa) \\ {X_{\#}} = mole \hspace{4 pt} fraction \hspace{4 pt} of \hspace{4 pt} gas \hspace{4 pt} \# \) |
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$$ \large PV = k $$
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\( \textbf{P} = pressure \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} system \hspace{4 pt} (Pa) \\ \textbf{V} = volume \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} gas \hspace{4 pt} (m^3) \\ \textbf{k} = constant \hspace{4 pt} value \hspace{4 pt} (N \hspace{2 pt} m) \) |
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$$ \large \frac{P}{T} = k $$
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\( \textbf{P} = pressure \hspace{4 pt} of \hspace{4 pt} system \hspace{4 pt} (Pa) \\ \textbf{T} = temperature \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} gas \hspace{4 pt} (K) \\ \textbf{k} = constant \hspace{4 pt} value \hspace{4 pt} (N \hspace{2 pt} m^{-2} \hspace{2 pt} K) \) |
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$$ \large \frac{V_1}{n_1} = k $$
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\( V_{\#} = volume \hspace{4 pt} of \hspace{4 pt} gas \hspace{4 pt} \# \hspace{4 pt} (m^3) \\ n_{\#} = number \hspace{4 pt} of \hspace{4 pt} moles \hspace{4 pt} of \hspace{4 pt} gas \hspace{4 pt} (mol) \\ \textbf{k} = constant \hspace{4 pt} value \hspace{4 pt} (m^3 \hspace{2 pt} mol^{-1}) \) |
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$$ \large \frac{P_1 V_1 }{T_1} = \frac{P_2 V_2}{T_2} = k $$
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\( P_{\#} = pressure \hspace{4 pt} of \hspace{4 pt} system \hspace{4 pt} \# \hspace{4 pt} (Pa) \\ V_{\#} = volume \hspace{4 pt} of \hspace{4 pt} gas \hspace{4 pt} \# \hspace{4 pt} (m^3) \\ T_{\#} = temperature \hspace{4 pt} of \hspace{4 pt} gas \hspace{4 pt} \# \hspace{4 pt} (K) \\ \textbf{k} = constant \hspace{4 pt} value \hspace{4 pt} (N \hspace{2 pt} m \hspace{2 pt} K^{-1}) \) |
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$$ \large PV = nRT = NkT $$
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\( \textbf{P} = pressure \hspace{4 pt} (Pa) \\ \textbf{V} = volume \hspace{4 pt} (m^3) \\ \textbf{n} = number \hspace{4 pt} of \hspace{4 pt} moles \hspace{4 pt} of \hspace{4 pt} gas \hspace{4 pt} (mol) \\ \textbf{R} = gas \hspace{4 pt} constant \hspace{4 pt} (8.314 \hspace{4 pt} J \hspace{2 pt} K^{-1} \hspace{2 pt} mole^{-1}) \\ \textbf{T} = temperature \hspace{4 pt} (K) \\ \textbf{N} = number \hspace{4 pt} of \hspace{4 pt} particles \\ \textbf{k} = Boltzmann \hspace{4 pt} constant \\ \hspace{8 pt} (1.38 \hspace{2 pt} x \hspace{2 pt} 10^{-23} \hspace{2 pt} m^2 \hspace{2 pt} kg \hspace{2 pt} s^{-2} \hspace{2 pt} K^{-1}) \) |
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$$ \large d = \frac{P\textbf{M}}{RT}
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\(\\ \textbf{d} = density \hspace{4 pt} of \hspace{4 pt} a \hspace{4 pt} gas \hspace{4 pt} (kg \hspace{2 pt} m^{-3}) \\ \textbf{P} = pressure \hspace{4 pt} (Pa) \\ \textbf{M} = molar \hspace{4 pt} mass \hspace{4 pt} (kg \hspace{2 pt} mol^{-1}) \\ \textbf{R} = universal \hspace{4 pt} gas \hspace{4 pt} constant \\ \hspace{10 pt} (8.314 J \hspace{2 pt} mol^{-1} K^{-1}) \\ \textbf{T} = temperature \hspace{4 pt} (K)\) |
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$$ \large v_{rms} = \sqrt{\frac{3RT}{\textbf{M}}} $$
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\( {v_{rms}} = root - mean - square \hspace{4 pt} speed \hspace{4 pt} of \\ \hspace{23 pt} gas \hspace{4 pt} molecules \hspace{4 pt} (m \hspace{2 pt} s^{-1}) \\ \textbf{R} = universal \hspace{4 pt} gas \hspace{4 pt} constant \\ \hspace{10 pt} (8.314 J \hspace{2 pt} mol^{-1} K^{-1}) \\ \textbf{T} = temperature \hspace{4 pt} of \hspace{4 pt} the \hspace{4 pt} gas \hspace{4 pt} (K) \\ \textbf{M} = molar \hspace{4 pt} mass \hspace{4 pt} (kg \hspace{2 pt} mol^{-1}) \\\) |
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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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$$ \large \Pi = \left( \frac{n}{V} \right ) RT = MRT $$
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\(\\ {\Pi} = osmotic \hspace{4 pt} pressure \hspace{4 pt} (Pa) \\ \textbf{n} = amount \hspace{4 pt} of \hspace{4 pt} solute\hspace{4 pt} (mol) \\ \textbf{V} = volume \hspace{4 pt} of \hspace{4 pt} solution \hspace{4 pt} (m^3) \\ \textbf{R} = universal \hspace{4 pt} gas \hspace{4 pt} constant \\ \hspace{10 pt} (8.314 J \hspace{2 pt} mol^{-1} K^{-1}) \\ \textbf{T} = temperature \hspace{4 pt} of \hspace{4 pt} solution \hspace{4 pt} (K)\) |
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$$ \large {ln} \frac{N_t}{N_{\circ}} = - \lambda t $$
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\(\\ {N_t} = radioactive \hspace{4 pt} material \hspace{4 pt} \hspace{4 pt} at \hspace{4 pt} time \hspace{4 pt} t \hspace{4 pt} (kg) \\ {N_{\circ}} = initial \hspace{4 pt} mass \hspace{4 pt} of \hspace{4 pt} radioactive \hspace{4 pt} \\ \hspace{14 pt} material \hspace{4 pt}(kg) \\ {\lambda} = decay \hspace{4 pt} constant \hspace{4 pt} (s^{-1})\\ \textbf{t} = time \hspace{4 pt} (s)\) |
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