A hydrocarbon (alkane or cycloalkane) is found by combustion analysis to contain 87.17% Carbon and 12.83% Hydrogen by mass. Determine the smallest possible molecular formula.
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Take a hypothetical 100 gram sample:
(87.17 g C) / (12.0108 g/mol) = 7.25763 mol C
(12.83 g H) / (1.0079 g/mol) = 12.7294 mol H
Divide by the smaller number of moles:
7.25763 C / 7.25763 = 1.00000
12.7294 H / 7.25763 = 1.75393
In order to make these ratios close to integers, multiply by 4, then round to the nearest whole number to find the empirical formula:
C4H7
(87.17 g C) / (12.0108 g/mol) = 7.25763 mol C
(12.83 g H) / (1.0079 g/mol) = 12.7294 mol H
Divide by the smaller number of moles:
7.25763 C / 7.25763 = 1.00000
12.7294 H / 7.25763 = 1.75393
In order to make these ratios close to integers, multiply by 4, then round to the nearest whole number to find the empirical formula:
C4H7
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Assume 100 g now (87.17g C)/(12 g/mole) = 7.26 moles C and (12.83 g H)/(1 g/mole) = 12.83 moles H, so the ratio of H to C is 12.83/7.26 or 1.76 to 1 and the molecular formula (or the empirical formula) must match it. To get to whole numbers, looks like we have to multiply each of these by the factor 4 to get H7C4 or C4H7 which would be the empirical formula and the smallest possible molecular formula.