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

The number of methoxy groups in one molecule of the compound is 3.

Step 1: Write the Reaction Equation

The organic compound containing methoxy groups reacts with HI to release methyl iodide, which then reacts with AgNO₃ to form the precipitate AgI.

Step 2: Calculate Moles of AgI Formed

Determine the moles of AgI produced. Use the formula \( \, \text{Moles of AgI} = \frac{\text{Mass of AgI}}{\text{Molar mass of AgI}} \).Given: \( \,\text{Mass of AgI} = 0.8658 \, \text{g} \), \( \,\text{Molar mass of AgI} = 108 + 127 = 235 \, \text{g/mol} \).\[ \text{Moles of AgI} = \frac{0.8658}{235} \approx 0.003684 \, \text{mol} \]

Step 3: Relate Moles of AgI to Moles of Methoxy Groups

In the reaction, each methoxy group results in one molecule of AgI. Hence, moles of AgI precipitated will equal the moles of methoxy groups in the sample. So, the number of methoxy groups = \( 0.003684 \, \text{mol} \).

Step 4: Calculate Moles of Organic Compound

Calculate the moles of the organic compound used. Given: \( \,\text{Mass of organic compound} = 0.2063 \, \text{g} \),\( \,\text{Molar mass} = 168 \, \text{g/mol} \).\[ \text{Moles of organic compound} = \frac{0.2063}{168} \approx 0.001228 \, \text{mol} \]

Step 5: Determine Number of Methoxy Groups per Molecule

Use the ratio of moles of methoxy groups to the moles of organic compound to find the number of methoxy groups per molecule.Number of methoxy groups per molecule = \( \frac{\text{Moles of methoxy groups}}{\text{Moles of organic compound}} = \frac{0.003684}{0.001228} \approx 3 \).

Key Concepts

Understanding Methoxy Groups

Methoxy groups are functional groups in organic chemistry composed of an oxygen atom bonded to a methyl group, represented as \(-OCH_3\). These groups are commonly found in organic molecules and can significantly influence their chemical behavior.

• They affect the molecule's solubility, primarily due to their polar nature, which increases polarity.
• The presence of methoxy groups often makes compounds more volatile and reactive in certain conditions.
• In chemical reactions, such as the one with hydrogen iodide (HI), methoxy groups can form methyl iodide (CH₃I), which is then quantifiable in reactions like the one performed in the solution process.

In our reaction, identifying methoxy groups was key, as they directly react with HI to form methyl iodide, which could then form the silver iodide (AgI) precipitate seen in the solution.

Molar Mass Calculation Simplified

Molar mass is a fundamental concept in chemistry, essential for converting between mass and moles, the standard unit in chemical calculations. To understand this exercise, recognizing the molar mass of substances like AgI and the organic compound is crucial.

• The molar mass of a compound is the sum of the atomic masses of all atoms in a molecule. For example, the molar mass of AgI is the sum of the molar masses of silver (Ag) and iodine (I), calculated as \(108 + 127 = 235\, \text{g/mol}\).


• By knowing the masses and molar masses involved, we can determine the moles, using the formula: \[ \text{Moles} = \frac{\text{mass}}{\text{molar mass}} \]
• In our problem, calculating the molar mass enabled us to find the number of methoxy groups in the compound, linking the mass of AgI precipitated directly to the number of methoxy groups.

Conducting Chemical Reaction Analysis

Chemical reaction analysis often involves understanding the processes at a molecular level. Breaking down interactions helps recognize the stoichiometry and yield of a reaction.

• Here, the organic compound reacts with HI. Each methoxy group forms methyl iodide, which then reacts with \(\text{AgNO}_3\) to produce \(\text{AgI}\), a solid precipitate.
• Tracking the precipitation of \(\text{AgI}\) provides a measure of the methoxy groups initially present, allowing us to deduce their number through careful stoichiometric calculations.


• This reaction-based analysis shows how the formation of a single measurable product, like \(\text{AgI}\), can inform us about the components of the original organic compound. This methodology is widely used in quantitative analysis in organic chemistry.

Understanding such chemical reactions and being able to unearthed details on functional groups results in comprehensive insights into the substance's chemical nature.