Question

Determine the molecular formula of a compound that contains 26.7% P, 12.1% N, and 61.2% CI,and has a molar mass of 580 g/mol.

Short answer

The molecular formula of a compound is$P_5{N}_{5}C{l}_{10}$

Step-by-step solution

Finding moles and empirical formula

The moles of each compound can be expressed as,

$\begin{array}{rcl}\mathrm{P}& =& \frac{26.7\mathrm{g}}{30.97{\displaystyle \raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mol}$}\right.}}\\ & =& 0.86\mathrm{moles}\\ \mathrm{N}& =& \frac{12.1\mathrm{g}}{14.01{\displaystyle \raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mol}$}\right.}}\\ & =& 0.86\mathrm{moles}\\ \mathrm{Cl}& =& \frac{61.2\mathrm{g}}{35.45{\displaystyle \raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mol}$}\right.}}\\ & =& 1.73\mathrm{moles}\end{array}$

On dividing,

$\begin{array}{rcl}P& =& \frac{0.86}{0.86}\\ \mathrm{P}& =& 1\\ \mathrm{N}& =& \frac{0.86}{0.86}\\ & =& 1\\ \mathrm{Cl}& =& \frac{1.73}{0.86}\\ & =& 2\end{array}$

The empirical formula is$PNC{l}_2$.

Finding empirical formula mass

The mass of empirical formula can be denoted as,

$$\begin{gathered} =\mathrm{Mass}\mathrm{of}\mathrm{P}+\mathrm{Mass}\mathrm{of}\mathrm{N}+2\left(\mathrm{Mass}\mathrm{of}\mathrm{Cl}\right) \\ =30.97\raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mol}$}\right.+14.01\raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mol}$}\right.+2\left(35.45\raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mol}$}\right.\right) \\ =115.88\raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mol}$}\right. \end{gathered}$$