Question

A gaseous hydrocarbon has \(85 \%\) carbon and vapour density of 28 . The possible formula of the hydrocarbon will be: (a) \(\mathrm{C}_{4} \mathrm{H}_{8}\) (b) \(\mathrm{C}_{2} \mathrm{H}_{4}\) (c) \(\mathrm{C}_{2} \mathrm{H}_{2}\) (d) \(\mathrm{C}_{3} \mathrm{H}_{6}\)

Short answer

The formula of the hydrocarbon is \( \text{C}_4\text{H}_8 \).

Step-by-step solution

Understanding the Vapour Density

The vapour density of a compound is given and is equal to half of its molar mass. So, if the vapour density is 28, then the molar mass of the hydrocarbon is calculated by multiplying the vapour density by 2. This gives us the molar mass: \\[\text{Molar mass} = 28 \times 2 = 56 \text{ g/mol} \]

Calculating the Mass of Carbon

Since the hydrocarbon has 85% carbon, the mass of carbon present per mole of hydrocarbon can be calculated as follows: \[\text{Mass of carbon} = \frac{85}{100} \times 56 \text{ g/mol} = 47.6 \text{ g/mol}\]

Calculating Moles of Carbon

We know that the atomic mass of carbon is approximately 12. Therefore, the number of moles of carbon in the hydrocarbon is: \[\text{Moles of carbon} = \frac{47.6}{12}\] By calculating, we find \[\frac{47.6}{12} \approx 3.97 \] This hints that there are about 4 carbon atoms.

Determining the Number of Hydrogens

Knowing that there are 4 carbon atoms, determine the number of hydrogen atoms by using the remaining mass after accounting for carbon. The leftover mass for hydrogen per mole is: \[\text{Mass of hydrogen} = 56 - 47.6 = 8.4 \text{ g/mol} \] As the atomic mass of hydrogen is about 1, the number of hydrogen atoms is: \[\frac{8.4}{1} = 8.4\] Thus, approximately 8 hydrogen atoms.

Matching the Molecular Formula

Combining the calculated numbers of carbon and hydrogen atoms yields a molecular formula. With about 4 carbon atoms and 8 hydrogen atoms, we get \(\text{C}_4\text{H}_8\). This corresponds to option (a) \(\text{C}_4\text{H}_8\).

Key concepts

Molecular Formula

The molecular formula of a compound provides the exact number of each type of atom within a molecule. In the case of hydrocarbons, this includes only carbon and hydrogen atoms. To determine the molecular formula, you need to know not only the number of atoms present, but also their types. This means identifying how many carbon and hydrogen atoms are in a molecule. Molecular formulas are important because they allow chemists to understand the composition and structure of a compound by providing the precise ratios of different atoms. They are a crucial tool in chemistry for identifying and comparing different substances.

Hydrocarbon

Hydrocarbons are compounds made entirely of carbon and hydrogen atoms. They are the fundamental building block of organic chemistry and are found in many everyday substances, like gasoline and natural rubber. Hydrocarbons can be classified into different types based on the arrangement of their carbon atoms:

• Alkanes: Saturated hydrocarbons with single bonds. Example: Methane, CH₄.
• Alkenes: Unsaturated hydrocarbons with at least one double bond. Example: Ethylene, C₂H₄.
• Alkynes: Unsaturated hydrocarbons with at least one triple bond. Example: Acetylene, C₂H₂.

Knowing the type of hydrocarbon is important since it affects the physical and chemical properties of the compound.

Molar Mass Calculation

Molar mass is the weight of one mole of a substance, expressed in grams per mole. It is a critical value for determining the molecular formula of a compound since it provides insight into the amount of each element present in the molecule. To calculate molar mass, you can use the known atomic masses of the elements involved. For hydrocarbons, add the atomic mass of carbon (roughly 12 g/mol) and hydrogen (about 1 g/mol) according to how many of each atom are in the molecule. In the exercise above, the vapour density was used to determine the molar mass. Vapour density is half the molar mass, which when doubled, gives the complete molar composition of the compound.

Carbon Content in Compounds

Determining the carbon content in compounds is essential for characterizing hydrocarbons. This is usually expressed as a percentage, indicating the proportion of the compound’s mass made up by carbon. Through calculation, the carbon content can tell you how many moles of carbon are present in a mole of the compound. By dividing the mass of carbon by the atomic mass of carbon, you establish the moles present. In the provided exercise, the carbon content was given as 85%, and knowing this allowed us to compute how many carbon atoms may exist in the molecule by utilizing the compound’s molar mass.