Final answer:
To find the molecular formula of a compound given its percent composition and molecular mass, determine the empirical formula and the number of empirical formula units. Multiply the subscripts in the empirical formula by the number of empirical formula units to get the molecular formula.
Step-by-step explanation:
The molecular formula of a compound can be determined from its percent composition and molecular mass. To find the molecular formula of the compound with a percent composition of 49.47% C, 5.201% H, 28.84% N, and 16.48% O, and a molecular mass of 194.2 amu, first find the empirical formula. Convert the percent composition to grams, find the moles of each element, and divide by the smallest number of moles to get the empirical formula. Then, divide the molecular mass by the empirical formula mass to find the number of empirical formula units. Multiply the subscripts in the empirical formula by the number of empirical formula units to get the molecular formula.
For example, for the compound in question, if we assume a 100 g sample, we have 49.47 g C, 5.201 g H, 28.84 g N, and 16.48 g O. Converting these masses to moles, we have 4.120 moles C, 5.160 moles H, 2.071 moles N, and 1.030 moles O. Dividing these moles by the smallest number of moles (2.071), we get a ratio of approximately 2:2.5:1:0.5. We can multiply these ratios by a common factor to obtain whole numbers, which gives us an empirical formula of C4H5NO2. The empirical formula has a formula mass of 99.09 amu. Dividing the molecular mass (194.2 amu) by the empirical formula mass (99.09 amu) gives us approximately 1.96. Multiply the subscripts in the empirical formula by 2 to obtain the molecular formula, which is C8H10N2O4.