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The empirical formula of a compound gives the simplest whole-number ratio of atoms of each element in the compound. In the case of hydrocarbons, the empirical formula represents the basic building block of the compound, consisting only of carbon and hydrogen atoms. To determine this ratio, we need to know the number of moles of each element present. This can be obtained from their respective masses and molar masses.
In our hydrocarbon sample, the procedure starts with understanding the proportion of hydrogen (17.3% by mass). Thus, 82.7% is carbon by mass. From this, we calculate the moles of each element, assuming a total mass of the sample (e.g., 100g for ease of calculation). The moles of hydrogen are derived from the number of hydrogen atoms divided by Avogadro's number. For carbon, it involves subtracting the hydrogen mass from the total mass and using carbon's molar mass (12 g/mol) to find carbon moles.
This ratio is crucial as it forms the basis for the empirical formula. The step-wise comparison of moles of hydrogen and carbon gives the simplest ratio, thereby determining the empirical formula CmHn for the hydrocarbon in question.

Calculating the molar mass of a hydrocarbon involves using the found empirical formula. This is done by multiplying the number of carbons and hydrogens in the empirical formula by their respective molar masses (12 g/mol for carbon and 1 g/mol for hydrogen).
The empirical formula gives a theoretical molar mass, which can assist as a benchmark when comparing with the actual molar mass range—as indicated in the problem (55-65 g/mol). This comparison helps refine our understanding of the compound's composition, whether the empirical formula represents the true formula or a simplified version.
To see if the empirical formula matches the molar mass range given, we multiply the discrete atomic masses by the integers in the derived empirical formula. Any discrepancies between the calculated and given molar mass might suggest a need to scale the empirical formula by an integer factor (e.g., doubling the empirical formula if its molar mass is half of the actual observed range). This way, the empirical formulary is validated or revised to match the observed compound.

Atomic composition analysis helps in verifying the identities and quantities of each element present in a compound. For hydrocarbons, this analysis focuses on understanding how much hydrogen and carbon is present through their moles.
The first step in this process is quantifying hydrogen atoms in moles using Avogadro's number. This number reveals the relative amount of hydrogen compared to carbon, allowing for calculations of composition and supporting the development of the empirical formula.
A strategic element here is assuming a convenient total mass for calculations—often 100 grams—to simplify percentage conversion to mass calculation. This aids in aligning the percentage of each element contribution to total atomic masses, with weight percent figures turning directly into grams. From here, it divides for moles using known atomic masses, authenticating empirical ratios directly through quantifiable scientific measures, translating this analysis into actionable data needed for further formula and mass precision.