Determine the empirical and molecular formulas of each of the following substances: (b) Cadaverine, a foul-smelling substance produced by the action of bacteria on meat, contains 58.55% C, 13.81% H, and 27.40% N by mass; its molar mass is 102.2 g/mol.

Verified step by step guidance

1. Assume a 100 g sample of cadaverine. This assumption simplifies the calculation as the percentages can be directly converted to grams. Thus, you have 58.55 g of carbon (C), 13.81 g of hydrogen (H), and 27.40 g of nitrogen (N).
2. Convert the mass of each element to moles by using the atomic masses (C = 12.01 g/mol, H = 1.008 g/mol, N = 14.01 g/mol). Calculate the moles of each element by dividing the mass of each element by its atomic mass.
3. Determine the simplest whole number ratio of the moles of each element. Divide the number of moles of each element by the smallest number of moles calculated in the previous step.
4. Write the empirical formula by using the whole number ratios as subscripts for each element. If any of the subscripts are not whole numbers, multiply all subscripts by the smallest factor that converts all subscripts to whole numbers.
5. Calculate the molecular formula using the empirical formula and the given molar mass of cadaverine (102.2 g/mol). First, calculate the molar mass of the empirical formula. Then, divide the molar mass of cadaverine by the molar mass of the empirical formula to find the factor by which to multiply the subscripts in the empirical formula.

Key Concepts

Empirical Formula

The empirical formula represents the simplest whole-number ratio of the elements in a compound. To determine it, the percentage composition of each element is converted to moles, and then the mole ratios are simplified to the smallest integers. This formula provides insight into the basic composition of the substance without indicating the actual number of atoms in a molecule.

Molecular Formula

The molecular formula indicates the actual number of atoms of each element in a molecule of the compound. It can be derived from the empirical formula by multiplying the subscripts by a whole number, which is determined by dividing the compound's molar mass by the empirical formula mass. This formula gives a complete picture of the molecular structure and composition.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms in a molecule based on its molecular formula. Knowing the molar mass is essential for converting between grams and moles, which is crucial for determining both empirical and molecular formulas.