Data and formulas

$C_P = \displaystyle\left.\frac{\partial H}{\partial T}\right\vert _P$

dS = dq_rev/T

G = H - TS

$\Delta\bar{G} = \Delta\bar{G}^\circ + RT\ln Q$

$\ln\left(\displaystyle\frac{K_1}{K_2}\right) = \displaystyle\frac{\Delta\bar{H}^\circ}{R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right)$

For liquids and solids, a=X. For solutes, $a=c/c^\circ$, where $c^\circ = 1\,\mathrm{mol/L}$ in the usual definition of the standard state. For gases, $a=P/P^\circ$, where $P^\circ=1\,\mathrm{bar}$.

E² = c²p² + m₀²c⁴

$c = \lambda\nu$

$E = h\nu$

$p = h/\lambda$

$E_K = \frac{1}{2}mv^2$

p = mv

$\Delta x\Delta p \ge \displaystyle\frac{h}{4\pi}$

$n\lambda = 2d\sin\theta$

For a hydrogenic atom, $E_n = -\displaystyle\frac{R_HZ^2}{n^2}$.

Vibrational absorption selection rule: $\Delta n = 1$; dipole moment must change during vibration.

Rotational energy: $E_J = \displaystyle\frac{J(J+1)\hbar^2}{2I}$

For a diatomic molecule, $I = \mu R^2$ and $\mu^{-1} = m_1^{-1} + m_2^{-1}$.

Rotational Raman transition selection rules: $\Delta J = \pm 2$; molecule must be anisotropic.

$1\,\mathrm{amu} = 1.660\,539\times 10^{-27}\,\mathrm{kg}$

$1\,\mathrm{cm}^3 = 1\,\mathrm{mL}$

$1\,\mathrm{pm} = 10^{-12}\,\mathrm{m}$

To convert degrees Celsius to Kelvin, add 273.15.

$c = 2.997\,925\times 10^8\,\mathrm{m/s}$

$h = 6.626\,069\times 10^{-34}\,\mathrm{J/Hz}$

$\hbar = \displaystyle\frac{h}{2\pi} = 1.054\,572\times 10^{-34}\,\mathrm{J\,s}$

$N_A=6.022\,142\times 10^{23}\,\mathrm{mol}^{-1}$

$R = 8.314\,510\,\mathrm{J\,K^{-1}mol^{-1}}$

Electron mass: $9.109\,382\times 10^{-31}\,\mathrm{kg}$

Specific heat capacity of water: $4.184\,\mathrm{J\,K^{-1}g^{-1}}$

Density of water:

T ($^\circ$C)	$\rho$ ( g/cm3)
4	1.0000
25	0.9971