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 (Option a).

Step 1: Understand the Problem

We are given a mass of a compound (116 mg) that displaces 44.8 mL of air at standard temperature and pressure (STP) when vaporized. We need to find the molecular mass of this compound using the ideal gas equation.

Step 2: Convert Measurements

Convert the mass of the compound from milligrams to grams for analysis in standard units:\[116 \text{ mg} = 0.116 \text{ g}\]

Step 3: Volume Conversion at STP

Recognize that 1 mole of any gas occupies 22.4 L or 22400 mL at STP. This means:\[V_{m} = 22400 \text{ mL/mol}\]This is the volume one mole of a gas occupies under STP.

Step 4: Calculate Moles of the Compound

Using the displaced volume of 44.8 mL, convert it into moles of gas displaced:\[\text{Moles of compound} = \frac{44.8 \text{ mL}}{22400 \text{ mL/mol}} = 0.002 \text{ mol}\]

Step 5: Compute Molecular Mass

Now, calculate the molecular mass (M) using the formula:\[M = \frac{\text{mass in grams}}{\text{moles}}\]Substituting the values, we have:\[M = \frac{0.116 \text{ g}}{0.002 \text{ mol}} = 58 \text{ g/mol}\]

Step 6: Final Answer

Comparing with the options provided, the molecular mass of the compound is 58 g/mol.

Key Concepts

Ideal Gas Equation

The Ideal Gas Equation is a fundamental concept in chemistry and physics that relates the pressure, volume, and temperature of a gas with its number of moles. It is represented by the formula:\[PV = nRT\]Where:

• \( P \) is the pressure of the gas in atmospheres.
• \( V \) is the volume of the gas in liters.
• \( n \) is the number of moles of the gas.
• \( R \) is the ideal gas constant, equal to \( 0.0821 \, \text{L.atm/mol.K} \).
• \( T \) is the temperature in Kelvin.

This equation helps us calculate one of these properties if the other three are known. It is based on the concept of an "ideal gas," which is a theoretical gas composed of many randomly moving point particles that interact only upon collisions. This equation is crucial for understanding gas behaviors under various conditions, especially STP (Standard Temperature and Pressure), making it indispensable for calculating molecular masses and moles as seen in various practical applications.

Victor Meyer's Apparatus

Victor Meyer's apparatus is a classical tool used to determine the molecular mass of a volatile substance. The method involves heating a known mass of the substance until it vaporizes and displaces a measured volume of air in a closed space. This setup allows chemists to calculate the volume occupied by a known mass of vaporized gas, which directly relates to the number of moles of the gas. The key advantages of using Victor Meyer's apparatus are its simplicity and precision. It relies on basic principles such as the ideal gas law and provides accurate results when the sample is completely vaporized. This approach is particularly effective for substances that are gaseous under experimental conditions or can be easily vaporized, making it suitable for calculating molecular weights and understanding gas behaviors in different contexts.

Standard Temperature and Pressure

Standard Temperature and Pressure (STP) is a reference point used in chemistry to provide standard conditions for measuring gases. At STP, the conditions are defined as:

• Temperature: \( 0^\circ \text{C} \) or \( 273.15 \text{ K} \).
• Pressure: \( 1 \text{ atm} \) (atmosphere).

Under these conditions, one mole of any ideal gas occupies a volume of 22.4 liters or 22400 milliliters. STP allows scientists to predict how gases will behave and compare them under consistent conditions. It is crucial for calculations involving the ideal gas equation, as it links moles, volume, and molecular mass directly. In practice, when scientists measure the volume of a gas at STP and know the mass of the sample, they can easily calculate the molecular mass by determining the number of moles displaced, facilitating further chemical and physical analysis.

Moles Calculation

Calculating moles is an essential process in chemistry, as it relates mass and volume to the number of moles of a substance. The mole is a base unit in the International System of Units (SI) that measures the amount of substance. This calculation typically involves the following process:To calculate moles:

• Determine the mass of the substance in grams.
• Find out the molecular mass of the compound (usually given or calculated).

To convert volume of a gas at STP into moles:

• Use the formula \( \text{moles} = \frac{\text{Volume (mL)}}{22400} \), since one mole of gas at STP occupies 22.4 liters or 22400 milliliters.

By using the formula \( M = \frac{\text{mass}}{\text{moles}} \), you can find the molecular mass, given the mass and the number of moles. This method allows chemists to transition between volume, moles, and mass seamlessly and is vital for solving problems involving gas behaviors, especially using devices like Victor Meyer's apparatus.