Problem 25 - A Complete Resource Book in Chemistry for JEE Main

Question

The density of air is \(0.001293 \mathrm{~g} / \mathrm{cc}\) at STP. Its vapour density is (a) \(0.001293\) (b) \(8.2786\) (c) \(14.48\) (d) \(6.2706\)

Step-by-Step Solution

Answer

The vapor density of air is 14.48 (option c).

Step 1: Understanding the Problem

We need to find the vapor density of air based on its given density at Standard Temperature and Pressure (STP). The vapor density is calculated using the formula: \[ \text{Vapor Density} = \frac{\text{Molar mass of gas}}{2} \] since the density at STP is known, we will use it to find the molar mass first.

Step 2: Finding the Molar Mass

The density of a gas at STP can be used to find its molar mass using the equation: \[ \text{Molar Mass} = \text{Density} \times 22.414 \] where 22.414 L/mol is the molar volume at STP in liters. The given density of air is 0.001293 g/cc, which is equivalent to 1.293 g/L. Thus, \[ \text{Molar Mass} = 1.293 \text{ g/L} \times 22.414 \text{ L/mol} \approx 28.99 \text{ g/mol} \].

Step 3: Calculating the Vapor Density

Once the molar mass of air is known, we can calculate the vapor density. Use the formula: \[ \text{Vapor Density} = \frac{\text{Molar Mass}}{2} = \frac{28.99}{2} \approx 14.495 \].

Step 4: Selecting the Correct Option

Among the given choices, the one closest to our calculated vapor density of 14.495 is 14.48. Therefore, the correct option is (c) 14.48.

Key Concepts

Molar Mass

Molar mass is a fundamental concept in chemistry, crucial for converting between the mass of a substance and the amount in moles. Molar mass is defined as the mass of one mole of a substance, usually expressed in grams per mole (g/mol).
Understanding molar mass allows you to link macroscopic measurements of matter to their molecular composition.

To calculate the molar mass of a compound, sum up the atomic masses of each element in its chemical formula.

• For example, in CO extsubscript{2}, you add the atomic mass of one carbon atom (about 12 g/mol) to that of two oxygen atoms (about 16 g/mol each), resulting in a molar mass of approximately 44 g/mol.
  

In the context of gases at Standard Temperature and Pressure (STP), molar mass can also be determined through the gas's density. This relates to the equation: \[ \text{Molar Mass} = \text{Density} \times 22.414 \]\ In this equation, 22.414 is the molar volume of a gas at STP in liters.

For example, the density of air is given in the problem as 1.293 g/L at STP, leading to a molar mass of about 28.99 g/mol. This molar mass can then be applied to further calculations, such as the determination of vapor density.

STP Conditions

Standard Temperature and Pressure (STP) is a set of pre-defined conditions used in scientific calculations to allow for consistent and reproducible results. STP is often defined as a temperature of 0°C (273.15 K) and a pressure of 1 atm. Under these conditions:

• The molar volume of an ideal gas is 22.414 liters per mole.
  
• Gas behavior follows the ideal gas law more closely, simplifying calculations.
  
• STP provides a common point of reference in experiments and theoretical calculations.
  

Using STP is particularly useful in experiments involving gases, allowing chemists to predict and calculate volumes, pressures, and the molar mass of gases with precision.
Having a standard baseline reduces uncertainties that could occur due to variable temperatures and pressures in different laboratory settings.

By working with gases at STP, chemists can more easily convert between measured volumes and number of moles, facilitating accurate conversions to molar mass and other properties, such as vapor density.
Utilizing the concept of STP conditions, in this case, aids in finding the vapor density as the known density at STP can directly help us find the molar mass of air.

Density of Air

Density is an important property that describes how much mass is present in a given volume. For air, a typical density value at STP is 0.001293 g/cc, which translates to 1.293 g/L.
Knowing the density of a gas at STP is extremely helpful when calculating other properties such as molar mass and vapor density.

Understanding air density:

• Density is crucial for many applications, including meteorology, aviation, and engineering.
  
• Changes in air density can affect how objects move and perform within the atmosphere.
  
• Density also determines how much air is present in a given space, impacting the buoyant force of objects in it.
  

In the context of chemistry, density allows chemists to convert between the physical bulk measurement of volume and a chemical measure of quantity, like moles or molecules, via its relationship to the molar mass.
This relationship is exemplified in the conversion used here: \[ \text{Molar Mass} = \text{Density} \times 22.414 \] Calculating vapor density, which is defined as half the molar mass of a gas, relies on understanding and determining the density of that gas.
For air, this means that its given density allows us to find its molar mass and subsequently use that to evaluate its vapor density as part of the exercise provided.