Question

compound $x$ has a molar mass of $416.41 g mol^{-1}$ and the following composition:

element	mass %
chlorine	85.12%

write the molecular formula of $x$.

Explanation:

Step1: Calculate the mass of each element in 1 mole of compound X

Assume we have 1 mole of compound X with a mass of 416.41 g.
Mass of phosphorus ($m_{P}$) = $416.41\ g\times14.88\%=416.41\ g\times0.1488 = 62.06\ g$
Mass of chlorine ($m_{Cl}$) = $416.41\ g\times85.12\%=416.41\ g\times0.8512 = 354.35\ g$

Step2: Calculate the number of moles of each element

The molar - mass of phosphorus ($M_{P}$) is 30.97 g/mol, and the molar - mass of chlorine ($M_{Cl}$) is 35.45 g/mol.
Number of moles of phosphorus ($n_{P}$) = $\frac{m_{P}}{M_{P}}=\frac{62.06\ g}{30.97\ g/mol}=2\ mol$
Number of moles of chlorine ($n_{Cl}$) = $\frac{m_{Cl}}{M_{Cl}}=\frac{354.35\ g}{35.45\ g/mol}=10\ mol$

Answer:

$P_{2}Cl_{10}$