High School Chemistry
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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$$ \large r = k[A]^x[B]^y $$
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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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$$ \large O_{reaction} = O_A + O_B $$
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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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$$ \large K_{sp} = [A^{y+}]^x[B^{x-}]^y $$
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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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$$ \large
E = h\nu = \frac{hc}{\lambda} $$
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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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$$ \large \Delta T_f = K_f m $$
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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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$$ \large \Delta H = \sum \Delta H_{products} - \sum \Delta H_{reactants} $$
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\(\\ {\Delta H} = change \hspace{4 pt} in \hspace{4 pt} enthalpy \hspace{4 pt} for \hspace{4 pt} the \\ \hspace{20 pt} reaction \hspace{4 pt} (J) \\ {\Delta H_{products}} = change \hspace{4 pt} in \hspace{4 pt} enthalpy \hspace{4 pt} of \hspace{4 pt} the \\ \hspace{58 pt} products \hspace{4 pt} (J) \\ {\Delta H_{reactants}} = change \hspace{4 pt} in \hspace{4 pt} enthalpy \hspace{4 pt} of \hspace{4 pt} the \\ \hspace{58 pt} reactants \hspace{4 pt} (J) \\\) |
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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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$$ \large P_T = P_1 + P_2 + P_3 + ... $$
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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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$$ \large PV = k $$
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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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$$ \large q = mc\Delta T = mH_f = mH_v $$
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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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