Problem 31 - A Complete Resource Book in Chemistry for JEE Main

Question

At STP the density of a gas (mol. wt \(=45\) ) in \(\mathrm{g} / \mathrm{L}\) is (a) \(11.2\) (b) 1000 (c) 2 (d) 224

Step-by-Step Solution

Answer

The density of the gas at STP is approximately 2 g/L (option c).

Step 1: Understand the Standard Conditions

STP stands for Standard Temperature and Pressure, which means the temperature is 273 K and the pressure is 1 atm. At these conditions, 1 mole of an ideal gas occupies a volume of 22.4 L.

Step 2: Identify the Formula for Density

The density (\(d\)) of a gas is expressed as the mass of the gas per unit volume. The formula for density is \(d = \frac{m}{V}\), where \(m\) is the mass (in grams) and \(V\) is the volume (in liters).

Step 3: Apply the Ideal Gas Law Concept

Use the concept that at STP, 1 mole of gas occupies 22.4 L. Therefore, for a gas with molecular weight (mol. wt) of 45 g/mol, the mass of 45 g will occupy 22.4 L.

Step 4: Calculate the Density

Using the formula for density and the ideal gas volume:\[d = \frac{m}{V} = \frac{45}{22.4} \approx 2.01 \, \text{g/L}\]So, we can approximate this value to 2 g/L based on the given options.

Key Concepts

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure, abbreviated as STP, refers to a set of conditions for measuring gases, which is widely accepted in scientific calculations and experiments. STP conditions are standardized to ease comparison between different gases and various experiments. Typically, STP conditions are defined as a temperature of 273 Kelvin (0 degrees Celsius) and a pressure of 1 atmosphere (atm).

• At STP, 1 mole of an ideal gas occupies a volume of 22.4 liters.
• Understanding STP is crucial for accurate gas calculations in chemistry.

The concept of STP allows scientists to predict and calculate behaviors of gases under these specific conditions, making it essential for solving problems related to gas density and volume.

Ideal Gas Law

The Ideal Gas Law is a fundamental principle often used to relate the properties of gases. It combines several different laws into one equation, helping to understand and calculate the behavior of gases. The equation is expressed as:\[ PV = nRT \]Where:

• \(P\) is the pressure in atmospheres (atm)
• \(V\) is the volume in liters (L)
• \(n\) is the number of moles of gas
• \(R\) is the ideal gas constant, which is 0.0821 L·atm/mol·K
• \(T\) is the temperature in Kelvin (K)

The Ideal Gas Law provides a way to calculate one of the variables if the others are known. In the context of the problem, it aids in finding the volume that a gas occupies and thus calculating its density at STP conditions.

Molecular Weight

Molecular Weight, sometimes referred to as molar mass, is an important concept when calculating the amount of a substance in a chemical equation or physical process. It represents the mass of one mole of a given substance, typically expressed in grams per mole (g/mol).

• Knowing the molecular weight is essential to determine the mass of the gas that occupies a specific volume, like at STP.
• The molecular weight is calculated as the sum of the atomic weights of all atoms in a molecule.

In many gas-related calculations, such as determining density, the molecular weight helps to establish the relationship between the mass of the substance and the volume it occupies, crucial for using the formula \(d = \frac{m}{V}\) to find the density of gases under specific conditions.