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Chapter 10: Problem 104

A \(0.325 \mathrm{g}\) sample of a gaseous hydrocarbon occupies a volume of \(193 \mathrm{mL}\) at \(749 \mathrm{mmHg}\) and \(26.1^{\circ} \mathrm{C}\). Determine the molecular mass, and write a plausible condensed structural formula for this hydrocarbon.

Short Answer

Expert verified
First, calculate the number of moles of the gaseous hydrocarbon using the ideal gas law formula. Then, find the molecular mass by dividing the given mass by the number of moles. The structure of the hydrocarbon can be deduced by checking which structures could have a molecular weight corresponding to the calculated one.

Step by step solution

01

Determining Moles using the Ideal Gas Law

Using the ideal gas law formula \(PV = nRT\), we rearrange to find n (the number of moles) = \(PV/RT\). First, we have to make sure that all variables are in the correct units. Pressure should be in atm, so convert 749 mmHg to atm by dividing by 760: \(749 mmHg / 760 = 0.9855 atm\). Volume should be in L, so convert 193 mL to L by dividing by 1000: \(193 mL / 1000 = 0.193 L\). Temperature should be in Kelvin, so convert 26.1°C to K by adding 273: \(26.1 + 273 = 299.1 K\). Therefore, n = \((0.9855 atm x 0.193 L) / (0.0821 atm.L/(mol.K) x 299.1K)\)
02

Calculating Molecular Mass

Molecular mass is calculated as \(mass (g) / moles\). We calculated the number of moles in Step 1, and the mass of the sample is given as 0.325 g. Therefore, Molecular mass = \(0.325 g / moles\) acquired from step 1.
03

Finding the Condensed Structure

Hydrocarbons are composed solely of carbon and hydrogen, and their molecular masses are multiples of the combined atomic masses of carbon (approximately 12 amu) and hydrogen (approximately 1 amu). If the calculated molecular weight aligns with those requirements, it will provide a clue for the number of carbon and hydrogen atoms, hence identifying the hydrocarbon structure.

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