Problem 21 - A Complete Resource Book in Chemistry for JEE Main

Question

'n' moles of an ideal gas at temperature \(\mathrm{T}\) (in Kelvin) occupy ' \(\mathrm{V}\) ' litres of volume, exerting a pressure of 'P' atomospheres. What is its concentration (in \(\left.\mathrm{mol} \mathrm{L}^{-1}\right)\) ? \((\mathrm{R}=\) gas constant \()\) (a) \(\mathrm{P} / \mathrm{RT}\) (b) \(\mathrm{PT} / \mathrm{R}\) (c) \(\mathrm{RT} / \mathrm{P}\) (d) \(\mathrm{R} / \mathrm{PT}\)

Step-by-Step Solution

Answer

The concentration of the gas is \( \frac{P}{RT} \) (Option a).

Step 1: Recall the Ideal Gas Law

The ideal gas law is expressed as \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.

Step 2: Define Concentration

Concentration \( C \) of a gas is defined as the number of moles per unit volume, expressed in \( \mathrm{mol} \; \mathrm{L}^{-1} \). Mathematically, \( C = \frac{n}{V} \).

Step 3: Rearrange Ideal Gas Law to Find n/V

From the ideal gas law \( PV = nRT \), you can express \( n \) as \( n = \frac{PV}{RT} \). To find \( \frac{n}{V} \), divide both sides by \( V \), resulting in \( \frac{n}{V} = \frac{P}{RT} \).

Step 4: Match Expression to Options

The expression for concentration \( \frac{n}{V} = \frac{P}{RT} \) matches option (a), which is \( \frac{P}{RT} \).

Key Concepts

Gas Concentration

Gas concentration is a fundamental concept in chemistry that measures how much of a substance is in a given volume. For gases, concentration is expressed as molarity, which is the number of moles of gas present per liter of volume. This is represented in units of \( \text{mol} \; \text{L}^{-1} \).
To determine the concentration \( C \) of an ideal gas, we use the formula \( C = \frac{n}{V} \), where \( n \) is the number of moles of the gas, and \( V \) is the volume.
The concept of gas concentration helps in understanding how particles interact within a given volume, influencing reaction rates and pressure. Recognizing how gas concentration changes under different conditions can help predict and control chemical processes, making this a crucial topic in preparatory courses like JEE Chemistry.

PV=nRT

The ideal gas law is a cornerstone of chemistry and physics, represented by the equation \( PV = nRT \). This equation connects the various properties of a gas: pressure \( P \), volume \( V \), number of moles \( n \), the gas constant \( R \), and temperature \( T \).
Each variable in the equation reflects a different aspect of a gas's behavior:

• **Pressure (P):** The force exerted by gas molecules per unit area.
• **Volume (V):** The space occupied by the gas.
• **Number of Moles (n):** Amount of substance, highlighting how many molecules are present.
• **Gas Constant (R):** A constant that makes the equation work quantitatively across different units, typically valued at 0.0821 L atm mol⁻¹ K⁻¹.
• **Temperature (T):** Measured in Kelvin, indicating the energy level of the gas particles.

Understanding \( PV = nRT \) helps in predicting how gases behave when conditions such as pressure or temperature change, which is vital in solving problems in exams like JEE.

Chemistry for JEE

Chemistry for JEE is designed to test students' understanding of core chemical principles and their ability to apply them to solve complex problems. The JEE (Joint Entrance Examination) is an important test for engineering aspirants in India and covers various topics in chemistry including physical chemistry, organic chemistry, and inorganic chemistry.
To excel in JEE Chemistry, students must grasp the application of concepts like the ideal gas law. Problems may ask you to derive a value using \( PV = nRT \), rearrange it, or predict how changing one parameter affects the others. This requires both conceptual understanding and practical problem-solving skills.
Gas laws, including the ideal gas law, form the basis for understanding how gases behave and interact. These laws also connect to larger themes in chemistry such as reaction kinetics and thermodynamics, making them fundamental in the learning process for every JEE aspirant.