Determine the molecular formula of a compound that contains $26.7 \% \mathrm{P}, 12.1 \% \mathrm{N},\( and \)61.2 \% \mathrm{Cl},$ and has a molar mass of 580 \(\mathrm{g} / \mathrm{mol}\)

First, we need to calculate the moles of each element present in the compound. The given percentages of the compound are: - P: 26.7% - N: 12.1% - Cl: 61.2% Since we are given a molar mass of 580 g/mol, we can use these percentages to calculate the grams of each element present. - Mass of P: (\(0.267 \times 580\text{g/mol}\)) = 154.86 g/mol - Mass of N: (\(0.121 \times 580\text{g/mol}\)) = 70.18 g/mol - Mass of Cl: (\(0.612 \times 580\text{g/mol}\)) = 354.96 g/mol Next, divide the mass of each element by its respective molar mass to determine the moles: - Moles of P: (\(\frac{154.86\text{g/mol}}{30.97\text{g/mol}}\)) = 5.0 mol - Moles of N: (\(\frac{70.18\text{g/mol}}{14.01\text{g/mol}}\)) = 5.0 mol - Moles of Cl: (\(\frac{354.96\text{g/mol}}{35.45\text{g/mol}}\)) = 10.0 mol

To find the mole ratio of the elements in the compound, we'll divide the moles of each element by the smallest number of moles: - P: \(\frac{5.0}{5.0}\) = 1 - N: \(\frac{5.0}{5.0}\) = 1 - Cl: \(\frac{10.0}{5.0}\) = 2 Thus, the mole ratio of P:N:Cl in the compound is 1:1:2.

Following the mole ratio obtained in the previous step, the molecular formula for the given compound is P1N1Cl2, or simply PCl₂N.