Question

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

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

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 = \((0.9855 atm x 0.193 L) / (0.0821 atm.L/(mol.K) x 299.1K)\)

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.

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.

Key concepts

Molecular Mass Calculation

To calculate the molecular mass, we first need to determine the number of moles in the sample using the Ideal Gas Law. The Ideal Gas Law is formulated as: \[ PV = nRT \] Where:

• P represents pressure
• V represents volume
• n represents the number of moles
• R is the ideal gas constant
• T is temperature in Kelvin

By rearranging the formula, we find that:\[ n = \frac{PV}{RT} \] This step requires you to convert all the given values into the correct units. Pressure in atm, volume in liters, and temperature in Kelvin. Once you have the moles from this calculation, the molecular mass is simply found as:\[ \text{Molecular mass} = \frac{\text{mass (g)}}{\text{moles}} \] This demonstrates how mass, the amount of substance, and the overseen conditions define the molecular mass of a gaseous sample.

Hydrocarbons

Hydrocarbons are organic compounds that consist only of carbon and hydrogen atoms. These molecules are fundamental in chemistry and are categorized by the types of bonds between carbon atoms:

• Alkanes: Saturated hydrocarbons with single bonds (C-C). Example: Methane, Ethane.
• Alkenes: Unsaturated hydrocarbons with at least one double bond (C=C). Example: Ethylene, Propylene.
• Alkynes: Unsaturated hydrocarbons with at least one triple bond (C≡C). Example: Acetylene.

The properties and reactivity of hydrocarbons depend on their structure. They serve as a primary source of fuel and are major components in many polymers. By understanding the molecular mass of a hydrocarbon, we can deduce the possible combinations of carbon and hydrogen that match the calculated molecular weight and structural possibilities.

Condensed Structural Formula

The condensed structural formula is a way of representing organic molecules more compactly. Instead of drawing each individual bond, we write it in such a way that each group is listed along a carbon chain. For example, the condensed structural formula for butane, which is detailed as \(C_4H_{10}\), can be written as \(CH_3(CH_2)_2CH_3\).
The condensed formula highlights the sequence of bonding without explicitly showing every bond, emphasizing the carbon framework's connectivity. When determining a plausible condensed structural formula of a hydrocarbon, calculating its molecular mass first helps identify possible number of carbon and hydrogen atoms. Then, the scientific form of hydrocarbon based on its molecular mass is deduced into a condensed formula, reflecting its simple structure and possible branches.