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
CH4.

Step 1: Understand the Mass Ratio

We know the mass ratio of hydrogen to carbon in the hydrocarbon is given as 1:3. This means for every 1 part by mass of hydrogen, there are 3 parts by mass of carbon.

Step 2: Relate Mass to Moles

Convert the mass ratio to mole ratio. The molar mass of hydrogen (
H) is about 1 g/mol, and the molar mass of carbon (
C) is about 12 g/mol. Using the formula for moles: \[ \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} \]For hydrogen: \[ \frac{1}{1} = 1 \text{ mole of } H \]For carbon: \[ \frac{3}{12} = 0.25 \text{ moles of } C \]

Step 3: Determine the Empirical Formula

To determine the empirical formula, compare the mole ratio. We have 1 mole of
H for every 0.25 moles of
C. Divide each by the smaller amount, which is 0.25:\[ \text{Hydrogen:} \quad \frac{1}{0.25} = 4 \]\[ \text{Carbon:} \quad \frac{0.25}{0.25} = 1 \]This gives the empirical formula as
CH4.

Key Concepts

Understanding Mass Ratio

In chemistry, a mass ratio is a comparison of the mass of one element to the mass of another in a compound. It provides vital information indicating how elements combine in specific proportions by weight. For example, if a hydrocarbon has a mass ratio of hydrogen to carbon of \(1:3\), this implies that for every single gram of hydrogen, there are 3 grams of carbon present.

This concept is foundational when figuring out the empirical formula of a compound, which is the simplest whole-number ratio of atoms of each element in a compound.

Importance of Mole Ratio

Mole ratio is an essential concept in determining the empirical formula. It describes the proportion of moles of one substance to the moles of another. To convert a mass ratio into a mole ratio, you must use the molar mass of each element involved.

In our hydrocarbon example, convert the mass ratio \(1:3\) into moles. Since the molar mass of hydrogen is \(1\,\text{g/mol}\), and for carbon \(12\,\text{g/mol}\), we'll calculate the moles:

• Hydrogen: \(\frac{1}{1} = 1 \text{ mole}\)
• Carbon: \(\frac{3}{12} = 0.25 \text{ moles}\)

Converting these values helps you find the simplest mole ratio, crucial for deriving the empirical formula.

Identifying Hydrocarbons

A hydrocarbon is a compound made up entirely of hydrogen and carbon atoms. These compounds are the basic structure of many organic substances and can take various forms.

They can be categorized as:

• Alkanes: Saturated hydrocarbons with single bonds (e.g., methane \(\text{CH}_4\))
• Alkenes: Unsaturated hydrocarbons with double bonds
• Alkynes: Unsaturated hydrocarbons with triple bonds

Different hydrocarbons may have different empirical formulas, influenced by how the hydrogen and carbon atoms combine, as highlighted in our problem where the empirical formula result was methane \(\text{CH}_4\).

Exploring Molar Mass

Molar mass is pivotal in the conversion of mass to moles. It tells you the mass of one mole of a substance, measured in g/mol. To compute moles, divide the mass of the substance by its molar mass.

For hydrogen, the molar mass is \(1 \, \text{g/mol}\), and for carbon, it is \(12 \, \text{g/mol}\). This disparity is crucial, as it affects how you convert a given mass ratio into a mole ratio, preparing you to determine the simplest empirical formula. It's pivotal in analyzing our example, demonstrating how the significant differences in molar masses lead to different numbers of moles for hydrogen and carbon from a given mass.

Always remember, understanding molar mass is essential for scaling chemical reactions, conceptualizing formulas, and executing laboratory practices efficiently.