An 84-mg sample of a compound is found to contain 36 mg of carbon, 3 mg of hydrogen, 21 mg of nitrogen, and 24 mg of oxygen. If the compound has a molecular weight of 112 g/mol, what is its molecular formula?

Question

An 84-mg sample of a compound is found to contain 36 mg of carbon, 3 mg of hydrogen, 21 mg of nitrogen, and 24 mg of oxygen.  If the compound has a molecular weight of 112 g/mol, what is its molecular formula?

Quizplus · Accepted Answer

11ecba2d_11bf_0a83_a3bf_f5f5e73f5db1_MD0008_00 The composition of chemical compounds can be described in several ways, including the empirical, molecular, and structural formulae. The empirical formula describes only the ratios of each unique atom in a compound, whereas the molecular formula describes the actual number of each type of atom. The structural formula describes how the atoms are bonded to one another. An empirical formula may be calculated from the known mass of each type of atom in a compound sample by calculating the number of moles of each. Dividing each mass given in the question by the atomic mass of the atom yields the number of moles. For these calculations, grams and moles are scaled down to milligrams and millimoles: Carbon: 11ecba2d_11bf_3194_a3bf_69f1f3cd942a_MD0008_00 Hydrogen: 11ecba2d_11bf_3195_a3bf_7dc42e32efd0_MD0008_00 Nitrogen: 11ecba2d_11bf_3196_a3bf_dd457f494650_MD0008_00 Oxygen: 11ecba2d_11bf_3197_a3bf_9d8d7b801be6_MD0008_00 Dividing each molar amount by the smallest molar amount (1.5 mmol) yields the relative ratios of each type of atom: C:H:N:O = 2:2:1:1. Therefore, the empirical formula of the compound is C₂H₂NO (Choice A). However, the question states that the compound has a molecular weight of 112 g/mol. A compound with a molecular formula of C₂H₂NO would only have a molecular weight of 56 g/mol, or half the observed molecular weight. Doubling the number of each atom (a two-fold multiple of the lowest whole-number ratio) yields the correct molecular formula C₄H₄N₂O₂, which is consistent with the compound composition. (Choices B and C) C₄H₆N₃O and C₅H₆NO₂ have the correct molecular weight but the wrong ratios of each type of atom. Educational objective: Compounds may be described by their empirical, molecular, and structural formulae. Empirical formulae describe only the relative ratios of each type of atom, molecular formulae describe the actual numbers of each type of atom, and structural formulae describe the spatial arrangement of the atoms.

An 84-Mg Sample of a Compound Is Found to Contain