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The Molecular Formula of a Hydrocarbon

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A liquid hydrocarbon is found to be 16.37% H by mass. A 1.158-g vaporized sample of the hydrocarbon has 385-mL volume at 71.0 °C and 749 mmHg. What is the molecular formula of the hydrocarbon?

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Solution Summary

Given the amount of carbon present in an unknown liquid hydrocarbon, and the some ideal gas property of the unknown liquid, the molecular formula is calculated step-by-step by first calculating the emperical formula, followed by using the ideal gas equation.

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In order to calculate the molecular formula we need to know the empirical formula and the molecular mass of the sample. In the problem, we have enough information to determine these quantities.
Since sample is a hydrocarbon, it's made up of carbon (C) and hydrogen (H) only. The problem states that 16.37% of the sample is H, therefore the percentage of carbon (%C) will be:
%C 100 -16.37 = 83.63%
Assuming we had 100-g of the sample, the mass of carbon will be 83.63-g and hydrogen 16.37-g.
Next calculating the moles of C and H for a in a 100-g sample gives using the general formula for calculating moles giving the mass.
Number of moles = given mass in g / atomic mass (from any periodic table)
Number of moles of H = 16.37 g/1.008 gmol-1 = 16.24 moles
Number of moles of C = 83.63 g/12.01 gmol-1 = 6.963 ...

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