At 1 atm and \(273 \mathrm{~K}\) the density of gas, whose molecular weight is 45 , is: (a) \(44.8 \mathrm{~g} / \mathrm{L}\) (b) \(11.4 \mathrm{~g} / \mathrm{L}\) (c) \(2 \mathrm{~g} / \mathrm{L}\) (d) \(3 \mathrm{~g} / \mathrm{L}\)

The Ideal Gas Law is the cornerstone of gas calculations, including those involving gas density. It's an equation of state that relates pressure (\( P \)), volume (\( V \)), temperature (\( T \)), and number of moles (\( n \)) for an ideal gas. Represented as \( PV = nRT \), where \( R \) is the gas constant, this law assumes that gas particles do not interact and that the volume occupied by gas molecules is negligible.

When working with the Ideal Gas Law, remember it's crucial for all units to be consistent. In the context of density calculations, if pressure is in atmospheres (atm) and volume is in liters (L), the value of \( R \) should be \( 0.0821 \text{L atm K}^{-1} \text{mol}^{-1} \). Knowing how to manipulate this formula is essential for solving a wide array of problems in chemistry, including finding the density of a gas under given conditions.

Molecular weight, also known as molecular mass, is the sum of the atomic masses of all the atoms in a molecule. It's measured in atomic mass units (amu) or grams per mole (g/mol). In the context of gas calculations, molecular weight allows us to relate moles to mass, which is particularly handy when using the Ideal Gas Law.

Molecular weight is critical to computing the number of moles from a given mass or vice versa. For instance, if we know the molecular weight of a substance and we have a certain mass of it, we can easily calculate the number of moles by dividing the mass by the molecular weight. This step paves the way for a plethora of calculations involving the moles of a substance, including those needed for density calculations.

Understanding gas density is essential when working with gases in various chemical applications. Gas density is the mass of the gas per unit volume and is usually expressed in grams per liter (g/L). Unlike liquids and solids, the density of a gas is greatly affected by pressure and temperature, hence it's often calculated using the Ideal Gas Law.

To find the density of a gas, the Ideal Gas Law is rearranged to express moles per volume (\( n/V \)), which equates to density (\( \rho \times \text{molecular weight} \times R \times T \times P \times 1 \tau\1 \times 82.1 \times 73 \times 45 \times 02.1 \times 73\text{g/L}\)). Thus, gas density allows chemists to predict how a gas will behave under changing pressure and temperature conditions, especially in stoichiometry and reaction calculations.

The Joint Entrance Examination (JEE) is a highly competitive test for aspiring engineers in India. Physical Chemistry forms a significant portion of the JEE Chemistry syllabus, where a thorough understanding of concepts like the Ideal Gas Law, molecular weights, and gas densities is tested. Problems related to these concepts are common and often integrate theoretical knowledge with practical problem-solving skills.

Effective preparation for JEE Physical Chemistry problems includes practicing a variety of problems, understanding the underlying principles, and being able to apply concepts in new and unfamiliar situations. Familiarity with formulas and their manipulations, like those used in density calculations, is incredibly important. Students should concentrate on understanding each step involved in the solution to deepen their conceptual knowledge and enhance their ability to tackle any question in the exam efficiently.