Problem 211 - A Complete Resource Book in Chemistry for JEE Main

Question

A gaseous hydrocarbon given upon combustion \(0.72 \mathrm{~g}\) of water and \(3.08 \mathrm{~g}\) of \(\mathrm{CO}_{2}\). The empirical formula of the hydrocarbon is \([2013]\) (a) \(\mathrm{C}_{6} \mathrm{H}_{5}\) (b) \(\mathrm{C}_{?} \mathrm{H}_{8}\) (c) \(\mathrm{C}_{2} \mathrm{H}_{4}\) (d) \(\mathrm{C}_{3} \mathrm{H}_{4}\)

Step-by-Step Solution

Answer

The empirical formula of the hydrocarbon is \( \text{C}_{3} \text{H}_{4} \).

Step 1: Determine Moles of Water

Combustion of hydrocarbon results in formation of water. The number of moles of water is given by:\[ \text{Moles of } \text{H}_2\text{O} = \frac{0.72 \text{ g}}{18.015 \text{ g/mol}} \approx 0.04 \text{ moles} \]Where 18.015 g/mol is the molar mass of water.

Step 2: Calculate Moles of CO2

Combustion of hydrocarbon also results in carbon dioxide. Using the molar mass of CO2, calculate moles:\[ \text{Moles of } \text{CO}_2 = \frac{3.08 \text{ g}}{44.01 \text{ g/mol}} \approx 0.07 \text{ moles} \]Where 44.01 g/mol is the molar mass of CO2.

Step 3: Find Moles of Carbon

Each mole of CO2 contains one mole of carbon. Thus, the moles of carbon in the hydrocarbon are:\[ \text{Moles of Carbon} = 0.07 \text{ moles} \]

Step 4: Find Moles of Hydrogen

Each mole of water has two moles of hydrogen. Thus, the moles of hydrogen from water are:\[ \text{Moles of Hydrogen} = 2 \times 0.04 = 0.08 \text{ moles} \]

Step 5: Calculate the Empirical Formula

The empirical formula is from the ratio of moles of carbon to moles of hydrogen:1. Divide each by the smallest number (0.07). - Carbon: \( \frac{0.07}{0.07} = 1 \) - Hydrogen: \( \frac{0.08}{0.07} \approx 1.14 \)2. Multiply to get whole numbers, hence: - Carbon: 7 - Hydrogen: 8 Thus, the simplest formula is \( \text{C}_3\text{H}_4 \), option (d).

Key Concepts

Combustion Analysis

Combustion analysis is a method used to determine the empirical formula of a compound, particularly hydrocarbons, by analyzing the combustion products. When hydrocarbons combust, they typically produce carbon dioxide (CO₂) and water (H₂O). By measuring the amounts of these products, we can infer the composition of the original hydrocarbon.

The process begins by burning the hydrocarbon completely, ensuring that all the carbon is converted to CO₂ and all the hydrogen into H₂O. The key idea is to relate the mass of these products back to the number of moles of carbon and hydrogen in the original compound. With the moles, we can deduce the simplest whole-number mole ratio of elements, leading us to the empirical formula.

Detailed calculations involve determining the moles of each product using their known molar masses. Then, we calculate the moles of carbon present from CO₂ and hydrogen from H₂O, since each CO₂ molecule contains one carbon atom and each H₂O contains two hydrogen atoms. This information is crucial for determining the correct empirical formula.

Molar Mass

Molar mass is an essential concept in chemistry, particularly in calculations related to empirical formulas. It represents the mass of one mole of a chemical substance and is expressed in grams per mole (g/mol). Understanding molar mass allows us to convert between the mass of a substance and the amount in moles, which is essential for quantitative chemical analysis.

For example, in combustion analysis, knowing the molar masses of H₂O (18.015 g/mol) and CO₂ (44.01 g/mol) helps in determining the number of moles of each substance produced. This, in turn, reflects the relative number of moles of each element in the original hydrocarbon compound.

To perform these calculations, we divide the given mass by the molar mass. This gives us the number of moles, which is a stepping stone towards finding the empirical formula. This approach makes it easier to understand how much of each element contributes to the total mass and to ensure accurate stoichiometric calculations.

Hydrocarbons

Hydrocarbons are organic compounds consisting entirely of carbon and hydrogen atoms. They form the basis of a vast family of natural substances and serve as the primary constituents of fossil fuels. In the context of combustion analysis, hydrocarbons are often the substance of interest because their complete combustion yields water and carbon dioxide.

Gasoline, methane, and ethylene are some common examples of hydrocarbons. Their diversity arises from the varied arrangements and bonding of carbon atoms, allowing for countless structural varieties, each with unique chemical properties.

In a typical combustion analysis of a hydrocarbon, the process helps us determine the simplest ratio of carbon to hydrogen, which defines the compound's empirical formula. For example, if a hydrocarbon combusts to produce a certain amount of CO₂ and H₂O, we can determine that it corresponds to a particular empirical formula like C₃H₄, as highlighted in our original problem. Understanding the properties and behavior of hydrocarbons is essential for fields ranging from environmental science to industrial chemistry.