Problem 85 - A Complete Resource Book in Chemistry for JEE Main

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) \(\mathrm{C}_{2} \mathrm{H}_{3}\) (d) \(\mathrm{C}_{2} \mathrm{H}_{d}\)

Step-by-Step Solution

Answer

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

Step 1: Understand the question

We need to find the possible molecular formula of a hydrocarbon given that it consists of 85% carbon by weight and has a vapor density of 28.

Step 2: Calculate the molecular weight of the hydrocarbon

The vapor density is given as 28. The formula to find the molecular weight from vapor density is: \[ \text{Molecular Weight} = 2 \times \text{Vapor Density} \]. Thus, the molecular weight is \(2 \times 28 = 56\).

Step 3: Calculate carbon weight in the compound

Since carbon makes up 85% of the hydrocarbon by weight, the carbon weight in the compound is \(0.85 \times 56 = 47.6\) grams.

Step 4: Determine the number of carbon atoms

The atomic weight of carbon is roughly 12. The number of carbon atoms is \( \frac{47.6}{12} \approx 3.97 \), which we can approximate to 4 carbon atoms.

Step 5: Determine the number of hydrogen atoms

Using the molecular weight 56 and knowing the weight of carbon atoms (47.6 grams), the weight of hydrogen is \(56 - 47.6 = 8.4\) grams. The atomic weight of hydrogen is 1, so there are \( \frac{8.4}{1} = 8.4 \) hydrogen atoms.

Step 6: Identify the molecular formula

The close integer number for carbon atoms is 4 and for hydrogen atoms is 8. Hence, the molecular formula matching these numbers is \( \text{C}_4\text{H}_8 \).

Key Concepts

Vapor Density Calculation

Vapor density is an important concept when you want to understand the properties of gaseous substances, including hydrocarbons. Simply put, vapor density refers to the density of a vapor in comparison to a standard, which is often air or hydrogen. When you have the vapor density given, you can determine the molecular weight of a substance using a neat formula.

We have the formula:

• \[ \text{Molecular Weight} = 2 \times \text{Vapor Density} \]

So, if the vapor density of a hydrocarbon is 28, the molecular weight can be calculated as:

• \[ 56 = 2 \times 28 \]

This step is crucial as it simplifies the determination of the possible molecular formula. With a vapor density of 28, you quickly conclude the molecular weight is 56, setting the stage for subsequent calculations.

Percentage Composition in Hydrocarbons

Understanding the percentage composition of a hydrocarbon provides key insights into its molecular structure. For a hydrocarbon like the one in this exercise, knowing it contains 85% carbon means that a huge portion of its molecular weight is due to carbon atoms.

Here’s how you translate that percentage into a more graspable figure:

• The hydrocarbon’s molecular weight has been established as 56 grams.
• \[ 85\% \] of those 56 grams is due to carbon, therefore, the carbon weight is \( 0.85 \times 56 = 47.6 \) grams.

This calculation gives a clear picture of how much of the compound’s weight is derived specifically from carbon, making it easier to estimate the number of carbon atoms in the molecular structure.

Molecular Weight Derived from Vapor Density

Once you have the vapor density and have calculated the molecular weight, you can explore the specific arrangement of elements in the molecule. Here, knowing the molecular weight is 56 allows us to compute the actual number of hydrogen and carbon atoms. We deduced that carbon's contribution was 47.6 grams.

To find the number of carbon atoms:

• Use the atomic weight of carbon, approximately 12. So, \( \frac{47.6}{12} \approx 4 \) carbon atoms.

Next, to determine hydrogen's contribution:

• The remaining mass, \( 56 - 47.6 = 8.4 \) grams, is that of hydrogen.
• Given hydrogen's atomic weight is 1, you find \( \frac{8.4}{1} = 8.4 \) hydrogen atoms, which rounds to approximately 8.

These computations directly lead you to conclude that the empirical formula is \( \text{C}_4\text{H}_8 \), which aligns with the given conditions and theoretical calculations.