Final answer:
To determine the empirical and molecular formulas of the substance, mass percentages of C, H, and N are converted to moles, the lowest whole number ratio is found, and then used to create the empirical formula. Here, the empirical formula is C5H14N2, which also turns out to be the molecular formula due to the molar mass matching that of the empirical formula.
Step-by-step explanation:
How to Find Empirical and Molecular Formulas
To find the empirical and molecular formulas of a substance, we need to convert the given mass percentages into moles and then determine the lowest whole number ratio of elements in the compound. In the given problem, we are told that a foul-smelling substance produced by the action of bacteria on meat contains 58.55% carbon, 13.81% hydrogen, and 27.40% nitrogen by mass, and its molar mass is 102.2 g/mol.
- Convert mass percentages to grams assuming 100 g of substance: 58.55 g C, 13.81 g H, 27.40 g N.
- Convert grams to moles using molar masses of elements (C: 12.01 g/mol, H: 1.008 g/mol, N: 14.01 g/mol): 4.88 mol C, 13.71 mol H, 1.955 mol N.
- Calculate the mole ratio by dividing by the smallest number of moles: C (4.88/1.955) = 2.5, H (13.71/1.955) = 7, N (1.955/1.955) = 1.
- Since we don't want fractional subscripts in our empirical formula, we multiply each mole ratio by 2 to get whole numbers: C5H14N2.
- Calculate the empirical formula mass: (5×12.01) + (14×1.008) + (2×14.01) ≈ 102 g/mol. Since the empirical formula mass is approximately equal to given molar mass we conclude that the empirical and molecular formulas are the same: C5H14N2, C5H14N2.