Problem 14 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

An organic compound is estimated through Dumas method and was found to evolve 6 moles of \(\mathrm{CO}_{2}, 4\) moles of \(\mathrm{H}_{2} \mathrm{O}\) and 1 mole of nitrogen gas. The formula of the compound is: (a) \(\mathrm{C}_{12} \mathrm{H}_{8} \mathrm{~N}\) (b) \(\mathrm{C}_{12} \mathrm{H}_{8} \mathrm{~N}_{2}\) (c) \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{~N}_{2}\) (d) \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{~N}\)

Step-by-Step Solution

Answer

The compound is C6H8N2, option (c).

Step 1: Determine Carbon Atoms

Each mole of CO2 contains one carbon atom. Since 6 moles of CO2 are evolved, there are 6 carbon atoms in the compound. Thus, the compound contains C6.

Step 2: Determine Hydrogen Atoms

Each mole of H2O contains 2 hydrogen atoms. Since 4 moles of H2O are evolved, there are 8 hydrogen atoms in the compound. Thus, the compound contains H8.

Step 3: Determine Nitrogen Atoms

Each mole of nitrogen gas, N2, indicates 2 nitrogen atoms in the compound. As 1 mole of nitrogen gas is evolved, the compound contains 2 nitrogen atoms.

Step 4: Assemble the Compound Formula

Using the information from steps 1, 2, and 3, the formula of the compound is C6H8N2.

Key Concepts

Dumas Method

The Dumas Method is a classic technique used to determine the chemical formula of organic compounds. It involves burning a known amount of a substance and analyzing the combustion products.
This helps to figure out the empirical formula by measuring elements like carbon, hydrogen, and nitrogen present.
During combustion, carbon translates into carbon dioxide and hydrogen into water. Nitrogen, on the other hand, is often liberated as nitrogen gas.

• Using this method, it is easier to analyze elements in a compound.
• It provides precise measurements of moles of gases produced.

Given these data, the molecular formula can be pieced together systematically by counting the atoms from combustion products.

Molecular Formula

The molecular formula represents the exact number of each type of atom in a single molecule of a compound. It is more specific than an empirical formula, which only indicates the simplest ratio of the components.
The process requires accurately determining the types and numbers of atoms involved, often relying on results from methods like the Dumas Method.
In the provided exercise, each mole of evolved \(\mathrm{CO}_{2}\) gave insights into the number of carbon atoms, while \(\mathrm{H}_{2} \\mathrm{O}\) served to determine hydrogen.

• Molecular formulas help in understanding the actual weight and composition.
• They are crucial for identifying different compounds with similar general compositions but different molecule structures.

Thus, by assembling information from combustion products, the molecular formula like \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{~N}_{2}\) can be derived.

Combustion Analysis

Combustion Analysis is a method used to understand the composition of a compound by burning it completely in the presence of oxygen. This analytical technique is used especially for organic compounds.
It involves measuring the amounts of \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \\mathrm{O}\) formed, which indicates the number of carbon and hydrogen atoms, respectively.

• This method is reliable for detecting even minimal quantities of elements.
• The results can be used to backtrack to the original composition of the compound.

Through combustion, particles are transformed into measurable gases. Understandably, each mole of carbon appears as a mole of \(\mathrm{CO}_{2}\). Similarly, each mole of hydrogen becomes half a mole of \(\mathrm{H}_{2} \\mathrm{O}\). Looking at these measurable products, a chemist can calculate the empirical formulas, step by step.

Stoichiometry

Stoichiometry focuses on measuring the quantitative relationships among substances as they undergo chemical reactions. It is a central concept in chemistry, allowing chemists to predict the amounts of products and reactants in any given reaction.
In exercises like the one you are tackling, stoichiometry helps to understand and calculate the exact proportions of elements involved based on measured emissions.
This includes keeping track of every atom involved in the reactions so that their proportions are accurately understood.

• It's key to balancing chemical equations by determining reactant and product ratios.
• Helps in real-world applications where creating precise chemical products is essential.

Thus, in the case of the Dumas Method, stoichiometry ensures that the amounts of \(\mathrm{CO}_{2}\), \(\mathrm{H}_{2} \\mathrm{O}\), and nitrogen provide insight into the molecular composition of the original compound.