Final answer:
The molecular formula of compound X with a molar mass of 416.48 g/mol and composed of 14.87% phosphorus and 85.13% chlorine is P2Cl10.
Step-by-step explanation:
To determine the molecular formula of compound X that has a molar mass of 416.48 g/mol and is composed of phosphorus and chlorine with mass percentages of 14.87% and 85.13% respectively, we follow these steps:
- Find the molar mass of individual elements: Phosphorus (P) = 30.97 g/mol and Chlorine (Cl) = 35.45 g/mol.
- Divide the mass percent of each element by its molar mass to find the mole ratio.
- Divide each obtained ratio by the smallest ratio to get whole numbers – these are the subscripts in the empirical formula.
- Divide the molar mass of compound X by the molar mass of the empirical formula to find the multiple, n.
- Multiply the subscripts in the empirical formula by n to get the molecular formula.
Converting the mass percentages to grams:
Phosphorus: (0.1487)(416.48 g/mol) = 61.941g Phosphorus
Chlorine: (0.8513)(416.48 g/mol) = 354.539g Chlorine
Now, convert grams to moles:
For Phosphorus: 61.941 g / 30.97 g/mol = 2 moles of P (approximately)
For Chlorine: 354.539 g / 35.45 g/mol = 10 moles of Cl (approximately)
The empirical formula is therefore P2Cl10.
To find the molecular formula, we compare the molar mass of the empirical formula to the given molar mass of compound X:
Molar mass of P2Cl10:
(2 mol x 30.97 g/mol) + (10 mol x 35.45 g/mol) = 415.47 g/mol (approximately)
Since the empirical formula mass is very close to the molar mass of compound X, the empirical formula P2Cl10 is also the molecular formula.