Problem 154 - A Complete Resource Book in Chemistry for JEE Main

Question

\(0.2063 \mathrm{~g}\) of an organic compound (molar mass 168 ) was heated with sufficient amount of HI and the resulting solution was treated with alcoholic \(\mathrm{AgNO}_{3}\) solution. This led to precipitation of \(0.8658 \mathrm{~g}\) of \(\mathrm{AgI}\). The number of methoxy groups in one molecule of the organic compound is /are (Given : Atomic mass of \(\mathrm{Ag}=108, \mathrm{I}=127)\) (a) 2 (b) 3 (c) 1 (d) 4

Step-by-Step Solution

Answer

(b) 3

Step 1: Determine the Moles of AgI Precipitated

First, calculate the moles of AgI precipitated using its given mass and molar mass. The molar mass of \( \text{AgI} \) is \( 108 + 127 = 235 \, \text{g/mol} \). So, the moles of \( \text{AgI} \) are \( \frac{0.8658 \, \text{g}}{235 \, \text{g/mol}} \approx 0.003683 \, \text{mol} \).

Step 2: Relate Moles of AgI to Methoxy Groups

In the reaction, each methoxy group in the organic compound forms one molecule of \( \text{AgI} \). Therefore, the moles of methoxy groups present are equal to the moles of \( \text{AgI} \) formed, which is \( 0.003683 \, \text{mol} \).

Step 3: Determine Moles of Organic Compound

Calculate the moles of the organic compound using its given mass and molar mass. The moles of organic compound are \( \frac{0.2063 \, \text{g}}{168 \, \text{g/mol}} \approx 0.001228 \, \text{mol} \).

Step 4: Calculate Methoxy Groups per Molecule

Find the number of methoxy groups in one molecule of the organic compound by dividing the moles of methoxy groups by the moles of the organic compound: \( \frac{0.003683 \, \text{mol}}{0.001228 \, \text{mol}} \approx 3 \). Thus, there are 3 methoxy groups per molecule of the organic compound.

Key Concepts

Organic Chemistry

Organic chemistry is a fascinating branch of chemistry focusing on the structure, properties, composition, reactions, and synthesis of carbon-containing compounds. These compounds can range from the simplest hydrocarbons to complex molecules like proteins, DNA, and polymers. In this context, understanding organic chemistry is crucial for analyzing reactions involving organic compounds.

Organic compounds often include elements such as hydrogen, nitrogen, oxygen, halogens, phosphorus, silicon, and sulfur. The presence of these elements, along with carbon, forms various functional groups such as alcohols, amines, acids, and in this case, methoxy groups.

A methoxy group is an example of a functional group, derived from methanol and composed of a methyl group (CH₃) bonded to an oxygen atom, denoted as –OCH₃. These groups play a significant role in determining the properties and reactions of the organic molecule. Identifying the number and position of methoxy groups is often critical in organic chemistry for deducing how a molecule behaves chemically.

Stoichiometry

Stoichiometry is the aspect of chemistry that involves calculating the quantities of reactants and products in chemical reactions. It is based on the conservation of mass and the concept that matter can neither be created nor destroyed.

In stoichiometry, balanced chemical equations are paramount. They show the ratio of molecules involved in a reaction and allow us to calculate the unknown quantities of reactants or products. For instance, if we know the amount of one reactant, we can determine how much product will be formed.

In solving the exercise, we used stoichiometry to determine the moles of silver iodide (AgI) produced, which is directly related to the number of methoxy groups in the organic compound. Since each methoxy group reacts to form one molecule of AgI, the stoichiometric relationship reveals the number of methoxy functional groups present in the original molecule.

Molecular Structure Determination

Determining the molecular structure of a compound involves identifying the types and numbers of atoms connected in its molecules, and often, the spatial arrangement of these atoms.

This process is critical in chemistry as it allows chemists to understand a molecule's properties, reactivity, and interactions with other molecules. The molecular structure can be determined using experimental techniques such as nuclear magnetic resonance (NMR), infrared spectroscopy (IR), and mass spectrometry (MS), in addition to chemical reactions like the one discussed.

In our exercise, we determined the number of methoxy groups (–OCH₃) in the organic compound through a chemical reaction with HI and subsequent formation of AgI. This reaction offered insight into the molecular structure by correlating the amount of AgI precipitated with the number of methoxy groups in the compound. This correlation allows for a precise understanding of the molecular composition and the role of functional groups in the molecules' structure and reactivity.