Question

The molecular formula weight by empirical formula weight of a compound is \(3 .\) The empirical formula is \(\mathrm{CH}_{2}\). The vapour density of the compound is: (a) 21 (b) \(11.5\) (c) 33 (d) 43

Short answer

The correct vapour density is 21 (option a).

Step-by-step solution

Identify Known Information

We know the molecular formula weight is 3 times the empirical formula weight. The empirical formula given is \( \mathrm{CH}_{2} \).

Calculate Empirical Formula Weight

The weight of each element in the empirical formula \( \mathrm{CH}_{2} \) is carbon (C) = 12 and hydrogen (H) = 1. The empirical formula weight is \( 12 + 2 \times 1 = 14 \).

Determine Molecular Formula Weight

Since the molecular formula weight is 3 times the empirical formula weight, it is \( 3 \times 14 = 42 \).

Calculate Vapour Density

The vapour density is half of the molecular weight. Therefore, vapour density is \( \frac{42}{2} = 21 \).

Select the Correct Answer

Compare the calculated vapour density with the given options: (a) 21, (b) 11.5, (c) 33, (d) 43. The correct answer is (a) 21.

Key concepts

Molecular Formula

A molecular formula gives you the exact number of atoms of each element present in a molecule of a compound. It provides a more detailed expression of the composition than the empirical formula, which only depicts the simplest ratio of elements in the compound. For instance, if we know the empirical formula is \( \mathrm{CH}_{2} \), and the molecular formula is three times the empirical formula, the molecular formula becomes \( \mathrm{C}_{3}\mathrm{H}_{6} \).
It's important to understand that while the empirical formula provides a general ratio, the molecular formula shows the actual number of atoms in the molecule, giving us a full picture of the molecule's structure and behavior.

Vapour Density

Vapour density is a property used to describe gases and is defined as half the molecular weight (or molar mass) of the compound. This concept is critical when you're dealing with gases and is especially helpful for determining the molecular weight when compared to a reference gas, typically hydrogen.
The formula for vapour density can be defined as:

• Vapour Density = \( \frac{\text{Molecular Weight}}{2} \).

For example, if the molecular weight of a compound is determined to be 42, then:

• The vapour density is \( \frac{42}{2} = 21 \).

This information can be used to aid in identifying and characterizing gases during chemical analysis.

Chemical Compounds Analysis

Chemical compounds analysis involves determining the composition, structure, and properties of a chemical substance. This process helps in understanding how compounds react and interact with each other. There are several methods to analyze chemical compounds, including:

• Empirical Formula Determination: Defines the simplest ratio of atoms in a compound.
• Molecular Formula Identification: Reveals the precise number of each type of atom presenting in the compound.
• Spectral Analysis: Techniques like mass spectrometry or infrared spectroscopy help in identifying the molecular structure.

By conducting these analyses, chemists can gain insights into the functionalities and potential applications of a compound, such as their behavior under different conditions and reactions.