Question

compound x has a molar mass of 416.41 g·mol⁻¹ and the following composition: element mass % phosphorus 14.88% chlorine 85.12% write the molecular formula of x.

Explanation:

Step1: Calculate mass of each element in 1 - mole of compound

Assume we have 1 mole of compound \(X\) with a mass of \(m = 416.41\ g\).
The mass of phosphorus (\(P\)) in 1 - mole of compound \(X\) is \(m_P=416.41\ g\times0.1488 = 62.062\ g\).
The mass of chlorine (\(Cl\)) in 1 - mole of compound \(X\) is \(m_{Cl}=416.41\ g\times0.8512 = 354.348\ g\).

Step2: Calculate moles of each element

The molar mass of \(P\) is \(M_P = 30.97\ g/mol\), so the number of moles of \(P\), \(n_P=\frac{m_P}{M_P}=\frac{62.062\ g}{30.97\ g/mol}=2\ mol\).
The molar mass of \(Cl\) is \(M_{Cl}=35.45\ g/mol\), so the number of moles of \(Cl\), \(n_{Cl}=\frac{m_{Cl}}{M_{Cl}}=\frac{354.348\ g}{35.45\ g/mol}=10\ mol\).

Answer:

\(P_2Cl_{10}\)