Final answer:
The molecular formula of nicotine is determined by converting its percentage composition to an empirical formula, calculating the empirical formula mass, and then multiplying by the number of empirical units in the molecular formula, resulting in C₁0H₁4N₂. Option A
Step-by-step explanation:
To determine the molecular formula for nicotine, we need to first calculate the empirical formula of nicotine based on its percentage composition by mass, and then compare the empirical formula mass to the molar mass to find how many empirical units are in the molecular formula.
We are given that the molar mass of nicotine is approximately 162.3 g/mol. From the percentage composition, we can assume we have 100 g of nicotine, which would contain 74.02 g of carbon (C), 8.710 g of hydrogen (H), and 17.27 g of nitrogen (N). To find the moles of each element, we divide by their atomic masses (C: 12.01 g/mol, H: 1.008 g/mol, N: 14.01 g/mol):
C: 74.02 g / 12.01 g/mol ≈ 6.16 mol
H: 8.710 g / 1.008 g/mol ≈ 8.64 mol
N: 17.27 g / 14.01 g/mol ≈ 1.23 mol
Next, we calculate the molar ratios of these elements by dividing by the smallest number of moles, those of nitrogen in this case:
C:N ratio = 6.16 / 1.23 ≈ 5
H:N ratio = 8.64 / 1.23 ≈ 7
N:N ratio = 1.23 / 1.23 = 1
The empirical formula is then C5H7N. The empirical formula mass for this compound is 81.13 g/mol.
Since the molar mass for nicotine is given as 162.3 g/mol and the empirical formula mass is 81.13 g/mol, we can determine that each nicotine molecule contains two formula units (162.3 g/mol / 81.13 g/mol = 2). Hence, to find the molecular formula, we multiply each subscript of the empirical formula by two:
(C5H7N)2 = C10H14N2
Therefore, the molecular formula of nicotine is C10H14N2, which corresponds to option A).