AP \(^{\circledR}\) CHEMISTRY EQUATIONS AND CONSTANTS
Throughout the exam the following symbols have the definitions specified unless otherwise noted.
ATOMIC STRUCTURE
\[
\begin{aligned}
& E=h v \\
& c=\lambda v
\end{aligned}
\]
\[
\begin{aligned}
& E=\text { energy } \\
& \nu=\text { frequency } \\
& \lambda=\text { wavelength }
\end{aligned}
\]
ATOMIC STRUCTURE
Planck’s constant, \(h=6.626 \times 10^{-34} \mathrm{~J} \mathrm{~s}\)
Speed of light, \(c=2.998 \times 10^8 \mathrm{~m} \mathrm{~s}^{-1}\)
Avogadro’s number \(=6.022 \times 10^{23} \mathrm{~mol}^{-1}\)
Electron charge, \(e=-1.602 \times 10^{-19}\) coulomb
EQUILIBRIUM
\[
\begin{aligned}
K_c & =\frac{[\mathrm{C}]^c[\mathrm{D}]^d}{[\mathrm{~A}]^a[\mathrm{~B}]^b}, \text { where } a \mathrm{~A}+b \mathrm{~B} \rightleftarrows c \mathrm{C}+d \mathrm{D} \\
K_p & =\frac{\left(P_{\mathrm{C}}\right)^c\left(P_{\mathrm{D}}\right)^d}{\left(P_{\mathrm{A}}\right)^a\left(P_{\mathrm{B}}\right)^b} \\
K_a & =\frac{\left[\mathrm{H}^{+}\right]\left[\mathrm{A}^{-}\right]}{[\mathrm{HA}]} \\
K_b & =\frac{\left[\mathrm{OH}^{-}\right]\left[\mathrm{HB}^{+}\right]}{[\mathrm{B}]} \\
K_w & =\left[\mathrm{H}^{+}\right]\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-14} \text { at } 25^{\circ} \mathrm{C} \\
& =K_a \times K_b \\
\mathrm{pH} & =-\log \left[\mathrm{H}^{+}\right], \mathrm{pOH}=-\log \left[\mathrm{OH}^{-}\right] \\
14 & =\mathrm{pH}+\mathrm{pOH} \\
\mathrm{pH} & =\mathrm{p} K_a+\log \frac{\left[\mathrm{A}^{-}\right]}{[\mathrm{HA}]} \\
\mathrm{p} K_a & =-\log K_a, \mathrm{p} K_b=-\log K_b
\end{aligned}
\]
EQUILIBRIUM
Equilibrium Constants–
\(K_c\) (molar concentrations)
\(K_p\) (gas pressures)
\(K_a\) (weak acid)
\(K_b\) (weak base)
\(K_w\) (water)
KINETICS
\[
\begin{aligned}
\ln [\mathrm{A}]_t-\ln [\mathrm{A}]_0 & =-k t \\
\frac{1}{[\mathrm{~A}]_t}-\frac{1}{[\mathrm{~A}]_0} & =k t \\
t_{1 / 2} & =\frac{0.693}{k}
\end{aligned}
\]
KINETICS
\[
\begin{aligned}
k & =\text { rate constant } \\
t & =\text { time } \\
t_{1 / 2} & =\text { half-life }
\end{aligned}
\]
GASES, LIQUIDS, AND SOLUTIONS
\(\begin{aligned} P V & =n R T \\ P_A & =P_{\text {total }} \times X_{\mathrm{A}}, \text { where } X_{\mathrm{A}}=\frac{\text { moles A }}{\text { total moles }} \\ P_{\text {total }} & =P_{\mathrm{A}}+P_{\mathrm{B}}+P_{\mathrm{C}}+\ldots \\ n & =\frac{m}{M} \\ \mathrm{~K} & ={ }^{\circ} \mathrm{C}+273 \\ D & =\frac{m}{V} \\ K E \text { per molecule } & =\frac{1}{2} m v^2 \\ \text { Molarity, } M & =\text { moles of solute per liter of solution } \\ A & =a b c\end{aligned}\)
GASES, LIQUIDS, AND SOLUTIONS
\(P=\) pressure
\(V=\) volume
\(T=\) temperature
\(n=\) number of moles
\(m=\) mass
\(M=\) molar mass
\(D=\) density
\(K E=\) kinetic energy
\(v=\) velocity
\(A=\) absorbance
\(a=\) molar absorptivity
\(b=\) path length
\(c=\) concentration
Gas constant, \(R=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\)
\(=0.08206 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\)
\(=62.36 \mathrm{~L}^2\) torr \(\mathrm{mol}^{-1} \mathrm{~K}^{-1}\)
\(1 \mathrm{~atm}=760 \mathrm{~mm} \mathrm{Hg}=760\) torr
STP \(=273.15 \mathrm{~K}\) and \(1.0 \mathrm{~atm}\)
Ideal gas at STP \(=22.4 \mathrm{~L} \mathrm{~mol}^{-1}\)
THERMODYNAMICS / ELECTROCHEMISTRY
\[
\begin{aligned}
q & =m c \Delta T \\
\Delta S^{\circ} & =\sum S^{\circ} \text { products }-\sum S^{\circ} \text { reactants } \\
\Delta H^{\circ} & =\sum \Delta H_f^{\circ} \text { products }-\sum \Delta H_f^{\circ} \text { reactants } \\
\Delta G^{\circ} & =\sum \Delta G_f^{\circ} \text { products }-\sum \Delta G_f^{\circ} \text { reactants } \\
\Delta G^{\circ} & =\Delta H^{\circ}-T \Delta S^{\circ} \\
& =-R T \ln K \\
& =-n F E^{\circ} \\
I & =\frac{q}{t}
\end{aligned}
\]
THERMODYNAMICS / ELECTROCHEMISTRY
\[
\begin{aligned}
q & =\text { heat } \\
m & =\text { mass } \\
c & =\text { specific heat capacity } \\
T & =\text { temperature } \\
S^{\circ} & =\text { standard entropy } \\
H^{\circ} & =\text { standard enthalpy } \\
G^{\circ} & =\text { standard Gibbs free energy } \\
n & =\text { number of moles } \\
E^{\circ} & =\text { standard reduction potential } \\
I & =\text { current (amperes) } \\
q & =\text { charge (coulombs) } \\
t & =\text { time (seconds) }
\end{aligned}
\]
Faraday’s constant, \(F=96,485\) coulombs per mole of electrons
\[
1 \text { volt }=\frac{1 \text { joule }}{1 \text { coulomb }}
\]