Other Homeless Equations¶
Mole Fraction (\(\chi_l\))¶
Is the molar concentration of the solute, as a ratio over the molar concentration of all constituents in the sample.
\[
\chi_l=\frac{n_i}{n_{total}}
\]
Density/Molarity/Molar Mass¶
\[
M_x\:(mol/L)=\frac{\rho_x\:(g/L)}{mm_x\:(g/mol)}
\]
Wavenumber to energy (\(\bar\nu \to \kjmol\))¶
\[
\begin{align}
\nu_{Hz}&=\frac{c\cdot100}{\bar\nu^{-1}}\\
E_J&=h\nu\\
E_{\kjmol}&=\frac{E_J\cdot N_A}{1000}\\\\
\end{align}
\]
Example
To convert \(\bar\nu=404\:cm^{-1}\) to \(\kjmol\)
\[
\begin{align}
\nu_{Hz}&=\frac{(3\e{8}\:m\cdot s^{-1})\cdot(100\:cm)}{\frac{1}{404\:cm^{-1}}}=1.212\e{13}\:s^{-1}\\\\
E_J&=(6.626\e{−34}\:J\cdot s)(1.212\e{13}\:s^{-1})=8.030712\e{-21}\:J\\\\
E_{\kjmol}&=\frac{(8.030712\e{-21}\:J)(6.022\e{23}\:mol^{-1})}{1000\:J^{-1}}=4.84\:\kjmol\\
\end{align}
\]