Problem 14 - A Complete Resource Book in Chemistry for JEE Main

Question

In a hydrocarbon, mass ratio of hydrogen and carbon is \(1: 3\), the empirical formula of hydrocarbon is (a) \(\mathrm{CH}_{2}\) (b) \(\mathrm{CH}_{4}\) (c) \(\mathrm{CH}_{3}^{2}\) (d) \(\mathrm{CH}\)

Step-by-Step Solution

Answer

The empirical formula of the hydrocarbon is \(\mathrm{CH}_4\).

Step 1: Understanding the Mass Ratio

The problem states that the mass ratio of hydrogen to carbon in the hydrocarbon is 1:3. This means for every 1 mass unit of hydrogen, there are 3 mass units of carbon.

Step 2: Determine Moles from Mass Ratios

To find the empirical formula, convert the mass ratio into a mole ratio. The atomic mass of hydrogen (H) is approximately 1 g/mol, and the atomic mass of carbon (C) is approximately 12 g/mol. This transforms the mass ratio to a mole ratio: - Convert 1 mass unit of hydrogen to moles: \[ \frac{1}{1} = 1 \text{ mole of hydrogen} \]- Convert 3 mass units of carbon to moles: \[ \frac{3}{12} = 0.25 \text{ moles of carbon} \] Thus, the mole ratio is 1 mole of hydrogen to 0.25 moles of carbon.

Step 3: Simplifying the Ratio to Find Empirical Formula

To find the simplest whole number ratio, divide each number of moles by the smallest value obtained.For hydrogen, the smallest value is 0.25 moles of carbon, therefore for hydrogen: \[\frac{1}{0.25} = 4\]For carbon, it remains:\[\frac{0.25}{0.25} = 1\]Therefore, the simplest whole number ratio is 4 hydrogens to 1 carbon.

Step 4: Writing the Empirical Formula

Based on the simplified ratio, the empirical formula is represented as the number of hydrogen atoms per one carbon atom: - 4 hydrogens - 1 carbonThis results in the empirical formula: \(\mathrm{CH}_4\).

Key Concepts

Hydrocarbons

Hydrocarbons are fundamental organic compounds consisting solely of hydrogen and carbon atoms. They are the simplest type of organic molecules, forming the backbone of organic chemistry. Understanding the structure and properties of hydrocarbons is crucial for studying both chemistry and various industrial applications.
Hydrocarbons can be divided into several categories, including:

• Alkanes: Saturated hydrocarbons with single bonds, with the general formula of \( \text{C}_n\text{H}_{2n+2} \).
• Alkenes: Unsaturated hydrocarbons with at least one double bond, shown as \( \text{C}_n\text{H}_{2n} \).
• Alkynes: Unsaturated hydrocarbons that contain at least one triple bond, represented as \( \text{C}_n\text{H}_{2n-2} \).

Hydrocarbons are found in many natural sources, such as crude oil and natural gas, and serve as fuels and raw materials for various chemical industries. Their importance extends from being energy sources to the synthesis of plastics and pharmaceuticals.
Studying the empirical formula, as in the exercise, involves determining the simplest ratio of the elements present, giving insight into the fundamental composition of these important compounds.

Mole Ratio

The mole ratio is a critical concept in chemistry as it allows chemists to understand the proportions of different elements or compounds involved in a chemical reaction. It is the ratio between the amounts of moles of any two compounds involved in a reaction or a particular compound's composition.
When calculating a mole ratio, the process generally involves the following:

• Identifying the elements or compounds for which the mole ratio is required.
• Converting mass to moles using atomic or molecular weights, given in g/mol. This utilizes the atomic masses of elements such as hydrogen (1 g/mol) and carbon (12 g/mol).
• Determining the ratio by dividing the number of moles of each substance by the smallest number of moles present.

In the exercise, the mass ratio of hydrogen to carbon was converted into a mole ratio to discover the empirical formula of a hydrocarbon. Proper understanding and calculation of mole ratios are essential for empirical and molecular formula determinations as well as for stoichiometric calculations in reactions.

Empirical Formula Calculation

Calculating an empirical formula involves several steps aimed at finding the simplest whole-number ratio of elements in a compound. It offers an efficient way of understanding the proportion of elements in a hydrocarbon, which is essential in both academic and practical applications of chemistry.
To determine an empirical formula, follow these steps:

• Start with the mass ratio of the elements involved, as provided in the problem.
• Convert these masses to moles using the atomic masses of each element.
• Simplify the mole values to the smallest whole numbers by dividing all values by the smallest value observed.
• Write out the ratios as subscripts in a chemical formula.

For instance, in the exercise given, the empirical formula calculation concluded with \(\text{CH}_4\), meaning that for every carbon atom in the specific hydrocarbon, there are four hydrogen atoms. Empirical formulas do not provide information about the actual numbers of atoms or molecule structure beyond the simplest numerical ratio, yet they are a foundational step in chemical analysis and synthesis.