Problem 90 - A Complete Resource Book in Chemistry for JEE Main

Question

On combustion, \(0.2 \mathrm{~g}\) of an organic compound containing carbon, hydrogen and oxygen yields \(0.147 \mathrm{~g}\) carbon dioxide and \(0.12 \mathrm{~g}\) water. The percentage of carbon, hydrogen and oxygen respectively in the compound is (a) \(22.5,8.7\) and \(68.8\) (b) \(20,6.7\) and \(73.3\) (c) \(18.2,9.5\) and \(72.3\) (d) \(28.9,12.8\) and \(58.8\)

Step-by-Step Solution

Answer

(b) 20, 6.7, and 73.3

Step 1: Calculate the Mass of Carbon in CO2

First, determine the mass of carbon in the given carbon dioxide ( 0.147 \, \text{g}). Use the fact that carbon dioxide is composed of carbon ( \text{C}) and oxygen ( \text{O}_2), with vast majority of its weight coming from the oxygen atoms. The molar mass of carbon dioxide ( \text{CO}_2) is 44 \, \text{g/mol}, and the molar mass of carbon ( C) alone is 12 \, \text{g/mol).Mass of carbon:\[\frac{12 \, \text{g/mol}}{44 \, \text{g/mol}} \times 0.147 \, \text{g} = 0.04 \, \text{g}\]

Step 2: Calculate the Mass of Hydrogen in H2O

Next, determine the mass of hydrogen in the given volume of water ( 0.12 \, \text{g}). Water ( \text{H}_2\text{O}) consists of two hydrogen atoms and one oxygen atom.The molar mass of water is 18 \, \text{g/mol}, and the molar mass of hydrogen is 1 \, \text{g/mol}. Since there are two hydrogen atoms per molecule of water, their combined molar mass is 2 \, \text{g/mol}.Mass of hydrogen:\[\frac{2 \, \text{g/mol}}{18 \, \text{g/mol}} \times 0.12 \, \text{g} = 0.0133 \, \text{g}\]

Step 3: Calculate the Mass of Oxygen in the Compound

The original compound has a total mass of 0.2 g. By subtracting the masses of carbon and hydrogen from this total, you can find the mass of oxygen in the compound.Mass of oxygen:\[0.2 \, \text{g} - 0.04 \, \text{g} - 0.0133 \, \text{g} = 0.1467 \, \text{g}\]

Step 4: Calculate the Percentage of Carbon, Hydrogen, and Oxygen

Use the masses calculated in the previous steps to determine the percentages of carbon, hydrogen, and oxygen in the compound relative to the total mass (0.2 g).Percentage of carbon:\[\frac{0.04 \, \text{g}}{0.2 \, \text{g}} \times 100 = 20\%\]Percentage of hydrogen:\[\frac{0.0133 \, \text{g}}{0.2 \, \text{g}} \times 100 = 6.65\%\]Percentage of oxygen:\[\frac{0.1467 \, \text{g}}{0.2 \, \text{g}} \times 100 = 73.35\%\]

Step 5: Identify the Correct Answer Option

Compare the calculated percentages of carbon, hydrogen, and oxygen with the given options: - Option (a): 22.5, 8.7, 68.8 - Option (b): 20, 6.7, 73.3 - Option (c): 18.2, 9.5, 72.3 - Option (d): 28.9, 12.8, 58.8 The percentages calculated are approximately 20, 6.7, and 73.3, which correspond most closely with option (b).

Key Concepts

Combustion Analysis

Combustion analysis is a crucial technique in organic chemistry, especially for determining the composition of elements in a compound.
During this process, a known mass of an organic compound undergoes combustion. This means it is burned completely, usually in the presence of excess oxygen, to produce carbon dioxide (\(CO_2\)) and water (\(H_2O\)). When a substance containing carbon and hydrogen combusts, the carbon present in the compound converts entirely into carbon dioxide, while the hydrogen converts into water. This transformation facilitates the measurement of each element's contribution by mass.
The essence of combustion analysis is that by quantifying the resulting \(CO_2\) and \(H_2O\), you can infer the amounts of carbon and hydrogen in the original compound. It’s a systematic way to deduce essential details about organic compounds, especially in a laboratory setting where precise measurements guide the identification of unknown substances.

Mass Percentage Calculation

Once you've quantified the masses of carbon and hydrogen from the combustion products, you're tasked with calculating the mass percentages.
Mass percentage calculation involves determining the proportion of each element's mass relative to the total mass of the compound under analysis.
To do this, find the mass of each element and divide it by the total mass of the original compound, then multiply by 100 to convert it into a percentage. Here’s how this works with a quick formula:- - Calculate the percentage: \(\frac{\text{mass of element}}{\text{total mass}} \times 100\).Applying this to our specific example, - - Carbon percentage: \(\frac{0.04 \, \text{g}}{0.2 \, \text{g}} \times 100 = 20\%\) - Hydrogen percentage: \(\frac{0.0133 \, \text{g}}{0.2 \, \text{g}} \times 100 = 6.65\%\) - Oxygen percentage: The remainder of the mass, as no direct oxygen data is attainable in a combustion process - \(\frac{0.1467 \, \text{g}}{0.2 \, \text{g}} \times 100 = 73.35\%\)This systematic approach enables us to express a compound's composition in percentages, crucial for comparing and contrasting different substances.

Organic Chemistry Problem-Solving

Organic chemistry problem-solving frequently involves exercises like our combustion analysis example. It blends theoretical knowledge with practical calculations, teaching you to derive meaningful insights from experimental data.
At its core, problem-solving in organic chemistry is about understanding reactions and their outcomes. Combustion is just one of many reactions, but its straightforward nature provides a great groundwork for learning. In our example, tackling the problem solution involved:

• Identifying the compound constituents based on combustion results
• Breaking down the reaction products to backtrack the original elements' compositions
• Using mathematical formulas to assess mass percentages and solve for the unknowns

Approaching each step logically helps reveal how elements react and relate in broader organic processes.
Developing these skills is foundational for any aspiring chemist, aiding in the comprehension and prediction of more complex organic phenomena.