Problem 71 - A Complete Resource Book in Chemistry for JEE Main

Question

\(0.30 \mathrm{~g}\) of a volatile liquid displaces \(90.0 \mathrm{~cm}^{3}\) of air at STP in the Victor Meyer's method. The molecular mass of the liquid is (a) \(54.44 \mathrm{~g}\) (b) \(34.64 \mathrm{~g}\) (c) \(64.76 \mathrm{~g}\) (d) \(74.66 \mathrm{~g}\)

Step-by-Step Solution

Answer

The molecular mass of the liquid is 74.66 g.

Step 1: Understand the Victor Meyer's method

Victor Meyer's method involves the displacement of air by vapor to determine vapor density, which can be used to calculate the molecular mass of a volatile liquid. The volume of air displaced equals the volume of vapor at STP.

Step 2: Apply the ideal gas law at STP

At STP (standard temperature and pressure), 1 mole of any ideal gas occupies 22,400 cm³. Use this fact to determine the number of moles of the vapor. The formula is: \( n = \frac{V}{22,400} \), where \( V \) is the volume displaced (90.0 cm³).

Step 3: Calculate moles of the vapor

Substitute the volume into the formula from Step 2: \( n = \frac{90.0}{22,400} \approx 0.0040179 \) moles. This is the amount of vaporized liquid that corresponds to the displaced air.

Step 4: Determine the molecular mass of the liquid

Molecular mass (M) can be found using the mass of the liquid sample (0.30 g) and the moles (n) calculated: \( M = \frac{m}{n} \). Substitute the values: \( M = \frac{0.30}{0.0040179} \approx 74.66 \) g/mol.

Step 5: Match with the given options

Compare the calculated molecular mass (74.66 g/mol) with the given options: (a) 54.44 g, (b) 34.64 g, (c) 64.76 g, (d) 74.66 g. The correct answer is option (d) 74.66 g.

Key Concepts

Vapor Density

Vapor density is a crucial concept used in determining the molecular mass of a volatile liquid. It refers to the mass of a certain volume of a gas compared to the mass of an equal volume of hydrogen under the same conditions. Essentially, it helps in identifying how heavy a gas is relative to hydrogen. This concept is particularly important in Victor Meyer's method.

• The vapor density of a substance can be experimentally determined through the displacement method, where the volume of the displaced air by the vapor is measured.
• The molecular weight is then calculated as twice the vapor density, considering that hydrogen is the lightest known gas with a standard molecular weight of 2 g/mol.

Understanding vapor density helps bridge the gap between experimental measurements and theoretical calculations of molecular weights, especially in textbooks and laboratory settings.

Molecular Mass Calculation

Molecular mass calculation is achieved by using the connection between vapor density and the number of moles. Once the vapor density and the volume of gas displaced are known, you can determine the molecular mass.

• Start with the formula: \( M = \frac{m}{n} \), where \( m \) represents mass, and \( n \) the number of moles.
• The molecular mass constitutes the weight of one mole of the substance.
• This is how we deduced, in the step-by-step solution, that the molecular mass of the liquid vapor was determined to be around 74.66 g/mol after substituting values into equations.

This calculation underpins many experimental determinations in chemistry, offering insights into the properties of the substance studied.

Ideal Gas Law

The ideal gas law is a fundamental principle that relates the pressure, volume, and temperature of an ideal gas with its number of moles, and it's given by the equation: \( PV = nRT \).
This law assumes that the gas particles are in constant motion and do not interact with each other. It provides a great approximation for the behavior of gases under normal conditions.

• At Standard Temperature and Pressure (STP), this law simplifies the determination of volumes of gases—a mole of any ideal gas occupies 22,400 cm³.
• The ideal gas law is applied in Victor Meyer's method by using the molar volume at STP to calculate the number of moles, connecting physical measurements to molecular data efficiently.

This concept is essential for using theoretical predictions to interpret real-world laboratory data.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) offer a benchmark for comparing gas volumes in different experimental setups. Defined at 0°C (273.15 K) and 1 atm pressure, STP is crucial for using the ideal gas law efficiently.

• Under these conditions, one mole of any ideal gas occupies 22,400 cm³. This provides a standard reference for comparing gas behavior.
• STP serves as a transition point where theoretical concepts meet laboratory experiments, ensuring consistent comparisons.

In the context of Victor Meyer's method, understanding STP allows you to convert measured volumes of displaced gas into mole calculations without the complexity of varied environmental conditions.