Problem 189 - A Complete Resource Book in Chemistry for JEE Main

Question

An organic compound (A) contains only \(\mathrm{C}, \mathrm{H}\) and \(\mathrm{O}\) atoms. On reaction with excess of \(\mathrm{CH}_{3} \mathrm{MgI}\), (A) gives a gas (X) whose volume under STP conditions was found to be \(67.2\) litre. The maximum number of hydroxyl groups in the compound (A) are

Step-by-Step Solution

Answer

Compound (A) has 3 hydroxyl groups.

Step 1: Understanding the Mole

1 mole of any gas at Standard Temperature and Pressure (STP) occupies 22.4 liters. Given that gas (X) has a volume of 67.2 liters at STP, we can calculate the number of moles of gas (X).

Step 2: Calculate the Number of Moles of Gas X

Using the formula: \[ \text{Number of moles} = \frac{\text{Gas volume at STP}}{22.4} \]Substitute the given volume of gas (X):\[ \text{Number of moles of } X = \frac{67.2}{22.4} = 3 \]Thus, 3 moles of gas (X) were formed.

Step 3: Identify the Gas X

Since the gas (X) is generated by the reaction of compound (A) with excess \( \text{CH}_3\text{MgI} \), it is likely \( \text{CH}_4 \), a common gaseous product when alcohols or carbonyl compounds react with Grignard reagents. 3 moles of \( \text{CH}_4 \) indicate that 3 moles of 'A' contained 3 moles of units capable of generating \( \text{CH}_4 \).

Step 4: Determine the Number of Hydroxyl Groups

Each hydroxyl group (\( \text{OH} \)) in compound (A) reacts with \( \text{CH}_3\text{MgI} \) to liberate \( \text{CH}_4 \). Hence, if 3 moles of \( \text{CH}_4 \) are formed, compound (A) must have 3 hydroxyl groups.

Key Concepts

Grignard Reagent Reaction

Grignard reagents are fascinating compounds in organic chemistry. They are typically represented as \( \text{RMgX} \), where \( \text{R} \) is an organic group like an alkyl or aryl, and \( \text{X} \) is a halide. These reagents are powerful because they can add to a carbonyl group, among other things. In our exercise, the organic compound \( (A) \) reacts with an excess of \( \text{CH}_3\text{MgI} \), a common Grignard reagent.

When alcohols or compounds containing hydroxyl groups react with Grignard reagents, they can release methane gas \( (\text{CH}_4) \). This is because the Grignard reagent effectively replaces the hydroxyl \((\text{OH})\) hydrogen with a methyl \((\text{CH}_3)\) group, resulting in the release of methane. This is an important reaction as it provides insights into the structure of the unknown compounds.

To summarize:

• Grignard reagents add to carbonyls and other organic compounds.
• In the presence of \( \text{OH} \) groups, these reactions can produce methane.
• Information about the gas produced can help determine the functional groups present in the original compound.

Methane Formation

In the specific reaction detailed in the exercise, methane \( (\text{CH}_4) \) plays a key role. Methane is a simple hydrocarbon and it is usually generated during Grignard reactions if hydroxyl group-containing compounds are present. Let’s take a closer look at how this happens.

Each hydroxyl \((\text{OH})\) group in compound \((A)\) reacts with a methyl magnesium iodide \((\text{CH}_3\text{MgI})\) to produce \(\text{CH}_4\). This hydrogen from the \(\text{OH}\) group bonds with \(\text{CH}_3\) from the Grignard reagent to form methane, while the rest of the Grignard reagent bonds with the remaining part of the molecule.

What does this tell us? If you generate 3 moles of methane, it means that there were originally 3 hydroxyl groups in compound \((A)\). It is a one-to-one relationship. The yield of methane can act as a direct indicator of how many hydroxyl groups are present.

• Each \(\text{OH}\) group releases a \(\text{CH}_4\) molecule.
• Seeing more methane indicates more \(\text{OH}\) groups were present.

STP Condition Calculations

Standard Temperature and Pressure (STP) is a crucial set of conditions used in chemical calculations. STP is where the temperature is defined as 0°C (273.15 K) and pressure as 1 atmosphere (atm). Under these conditions, one mole of any ideal gas occupies 22.4 liters.

In the exercise, gas \((X)\) measured 67.2 liters at STP. Using the knowledge that 22.4 liters equals one mole, we can determine how many moles of methane \((\text{CH}_4)\) were produced. This is done using the formula:\[ \text{Number of moles of } X = \frac{\text{Gas volume at STP}}{22.4} \]Substituting \(67.2\) liters gives us 3 moles of methane, pointing to the presence of 3 hydroxyl groups in compound \((A)\).

• STP conditions simplify gas volume calculations.
• Using STP, we connect gas volume directly to the reactions happening at the molecular level.