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) \(\mathrm{CH}_{3}\) (d) \(\mathrm{CH}\)

Step-by-Step Solution

Answer

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

Step 1: Understand 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 gram of hydrogen, there are 3 grams of carbon.

Step 2: Determine Moles from Mass

To find the empirical formula, we need to use moles instead of mass. The molar mass of hydrogen (H) is approximately 1 g/mol, and that of carbon (C) is approximately 12 g/mol. Convert the mass ratio into a mole ratio: \( \frac{1}{1} : \frac{3}{12} \).

Step 3: Simplify the Mole Ratio

Calculate the moles of each element: For hydrogen, it is \( 1 \text{ mole} \); for carbon, it is \( 0.25 \text{ moles} \). Divide both mole quantities by the smallest number of moles (0.25 in this case) to get whole numbers: \( \frac{1}{0.25} : \frac{0.25}{0.25} = 4 : 1 \).

Step 4: Write the Empirical Formula

The simplified mole ratio is 4 moles of hydrogen to 1 mole of carbon. Therefore, the empirical formula is \( \mathrm{CH}_4 \).

Key Concepts

Hydrocarbon Chemistry

To understand hydrocarbon chemistry, it's essential to know what hydrocarbons are. Hydrocarbons are organic compounds composed entirely of hydrogen and carbon atoms. They serve as the foundation of organic chemistry and are the primary components of many fuels and solvents. These compounds can be classified into various types based on the types of bonds connecting the atoms. For example:

• Alkanes: Hydrocarbons with single bonds, such as methane (\( \mathrm{CH}_{4} \)), propane, etc.
• Alkenes: Hydrocarbons with at least one double bond, such as ethene.
• Alkynes: Hydrocarbons with at least one triple bond, such as acetylene.

Understanding the specific arrangement and bonding of these atoms helps us predict the chemical behavior of hydrocarbons. The empirical formulation of a hydrocarbon, like \( \mathrm{CH}_{4} \), provides insight into the simplest ratio of hydrogen to carbon atoms present.

Mass Ratio

The mass ratio is a crucial aspect of chemistry as it relates to the proportion of each element in a compound by mass. In the context of the problem, we have a mass ratio of hydrogen to carbon as \(1:3\). This ratio signifies that, for every 1 gram of hydrogen, there are 3 grams of carbon. This ratio serves as a stepping stone to determine the mole ratio, an important calculation for finding empirical formulas. To convert this mass ratio into a more usable form, we need to understand the molar masses of the elements involved:

• The molar mass of hydrogen is approximately 1 g/mol.
• The molar mass of carbon is approximately 12 g/mol.

Thus, by understanding these mass ratios, we can determine the number of moles of each element, which is a critical step in finding the empirical formula.

Mole Concept

The mole concept is fundamental to chemistry. It allows us to quantify the amount of a substance in a way that's more meaningful than simply counting units one by one. A "mole" represents \(6.022 \times 10^{23}\) particles, known as Avogadro's number. This large number helps chemists convert mass ratios into equations using moles, making calculations easier. In the hydrocarbon problem, We start with a given mass ratio: hydrogen to carbon is \(1:3\). By converting these masses to moles using the respective molar masses of hydrogen and carbon, we simplify the equation into a form like \(n : 1\), where \(n\) represents the mole ratio of hydrogen to carbon. To simplify, divide by the smallest number of moles. This step is crucial in obtaining whole numbers needed for an empirical formula. Using the mole concept, we move from a simple ratio to a formula, in this case, \( \mathrm{CH}_4 \), depicting the simplest whole number ratio of atoms in the compound.