Problem 49 - A Complete Resource Book in Chemistry for JEE Main

Question

\(116 \mathrm{mg}\) of a compound on vapourisation in a Victor Meyer's apparatus displaces \(44.8 \mathrm{~mL}\) of air measured at STP. The molecular mass of the compound is (a) \(58 \mathrm{~g}\) (b) \(48 \mathrm{~g}\) (c) \(116 \mathrm{~g}\) (d) \(44.8 \mathrm{~g}\)

Step-by-Step Solution

Answer

The molecular mass of the compound is 58 g/mol.

Step 1: Understand the Problem and Known Values

You are given that 116 mg of a compound displaces 44.8 mL of air at STP (Standard Temperature and Pressure) using Victor Meyer's apparatus. We need to find the molecular mass of the compound.

Step 2: Convert given values to standard units

Convert the mass of the compound from milligrams to grams:\[116 \text{ mg} = 0.116 \text{ g}\]The volume displaced is given as 44.8 mL, which equals 44.8 mL.

Step 3: Use the relation of volume at STP

At STP, 1 mole of any gas occupies 22400 mL (22.4 L). Therefore, the number of moles corresponding to 44.8 mL is calculated as:\[\text{Moles of gas} = \frac{44.8 \text{ mL}}{22400 \text{ mL/mol}} = 0.002 \text{ moles}\]

Step 4: Calculate the Molecular Mass

The molecular mass is the mass of the substance divided by the number of moles:\[\text{Molecular Mass} = \frac{0.116 \text{ g}}{0.002 \text{ moles}} = 58 \text{ g/mol}\]

Step 5: Choose the Correct Answer

Compare the calculated molecular mass with the given options. The calculated molecular mass is 58 g/mol, which matches option (a).

Key Concepts

Victor Meyer's Apparatus

Victor Meyer's apparatus is a classic laboratory device used for determining the molecular mass of volatile compounds.
The apparatus operates on the principle of volume displacement. When a known mass of a substance is vaporized inside the apparatus, it displaces an equal volume of air.
This allows scientists to determine the volume occupied by the vapor of the substance, and consequently, find out its molecular mass. Here's how it works:

• A small amount of the liquid or solid sample is placed in a bulb at the bottom of the apparatus.
• The entire setup is then heated, causing the sample to vaporize.
• As the sample turns into vapor, it pushes out an equivalent volume of air from the apparatus, which is measured.

By knowing how much air is displaced, you can find out how much space the vapor occupies.
Since the volume is directly related to the number of moles of gas at a given temperature and pressure, it leads to calculations of the molecular mass.
This method is particularly useful when other analytical techniques are not feasible or available.

Mole Concept

The mole concept is fundamental in chemistry and allows chemists to count atoms, molecules, and ions in a substance.
Understanding this concept is crucial for solving various chemical calculations, including molecular mass determination. Let's break it down:

• One mole of any substance contains exactly Avogadro's number of entities (atoms, molecules, ions, etc.), which is approximately \(6.022 \times 10^{23}\).
• This unit enables chemists to convert from atomic or molecular scales to macroscopic amounts.

For gases, the mole concept is especially straightforward because it ties directly to the volume a gas occupies under standard conditions.
At Standard Temperature and Pressure (STP), one mole of an ideal gas occupies exactly 22.4 liters.
This proportionality simplifies the task of calculating molecular masses when given a volume at STP. By knowing the volume displaced by the vapor, one can determine the number of moles of gas and consequently the molecular mass.

Standard Temperature and Pressure (STP)

STP refers to the conditions under which the behavior of gases is most often studied and related to theoretical frameworks.
At STP, the temperature is set at \(0^\circ\)C (273.15 K), and the pressure is 1 atmosphere (atm). These conditions are essential because:

• They provide a uniform benchmark for scientists to compare gas behaviors and calculate properties such as volume and density.
• Under STP, one mole of an ideal gas occupies 22.4 liters.

Using STP simplifies the calculations of various properties regarding volumes of gases.
For instance, if you know the volume of a gas at STP, you can quickly determine the number of moles it contains using the relation:
\[\text{Number of Moles} = \frac{\text{Volume of gas (in L)}}{22.4}\] STP allows for easy comparison and computation across different experiments and is crucial for consistent results in research and problem-solving.