States Of Matter – JEE Main ChemistryPractice Questions & PYQs

According to the Maxwell-Boltzmann distribution, raising the temperature imparts higher kinetic energy to gas molecules, which shifts the most probable speed toward a higher value. Because the total number of molecules remains constant, the area under the distribution curve must also be conserved, forcing the curve to broaden and flatten as the velocity range expands. This flattening effect ensures that as the distribution peak moves to the right, its height decreases, meaning that a smaller fraction of the total population occupies the most probable speed state compared to the lower temperature.

The kinetic theory of gases dictates that the average kinetic energy of an ideal gas atom is directly proportional to its absolute temperature, which must be measured in Kelvin. Converting the temperatures from 20°C to 40°C requires adding 273 to each, resulting in absolute values of 293 Kelvin and 313 Kelvin. Because the average kinetic energy follows the relationship $\text{K.E.} = \frac{3}{2}kT$, where $k$ is the Boltzmann constant, the constant factors cancel out when finding the ratio of the final energy to the initial energy. This leaves the calculation simply as the ratio of the two absolute temperatures, expressed as $\frac{\text{K.E.}_2}{\text{K.E.}_1} = \frac{313}{293}$.

The Van der Waals equation $(P + \frac{an^2}{V^2})(V - nb) = nRT$ modifies the ideal gas law to accommodate the reality that gas particles possess finite dimensions. Within this framework, the constant $b$ acts as a volume correction factor that effectively subtracts the physical space taken up by the molecules themselves from the total volume of the container. This adjustment recognizes that, unlike ideal gas particles which are treated as point masses, real gas molecules occupy a specific amount of space, thereby reducing the actual volume available for free movement.

The behavior of molecules in an ideal gas is fundamentally governed by Newton's first law of motion, which dictates that an object in motion will maintain a constant velocity and trajectory unless influenced by an external force. Because gas particles experience no significant interactions with one another between impacts, they maintain a direct, linear path during the interval between any two successive collisions. These short straight-line trajectories are only interrupted by the impulsive forces of collisions, which result in the cumulative effect of random, chaotic motion throughout the gas.

The universal gas constant, $R$, acts as the proportionality factor in the ideal gas equation $PV = nRT$, meaning its numerical value depends entirely on the units selected for pressure, volume, and energy. In the SI system, where energy is measured in Joules, the constant is 8.314 Joules per mole per Kelvin. While other equivalent values include 0.0821 litre-atmospheres per mole per Kelvin, 1.987 calories per mole per Kelvin, and $8.314 \times 10^{7}$ ergs per mole per Kelvin, the provided value of 8.3 accurately matches the standard energy constant measured in Joules.

The ideal gas law, $PV = nRT$, defines the relationship between pressure $P$, volume $V$, amount of substance $n$, gas constant $R$, and temperature $T$. Since the number of moles per litre represents the concentration $\frac{n}{V}$, we can isolate this variable by rearranging the ideal gas equation. By dividing both sides of the equation by $V$ and then by the product $RT$, we find that the molar concentration is expressed as:

$\frac{n}{V} = \frac{P}{RT}$

The kinetic theory of gases establishes a microscopic foundation that describes gas behavior through molecular collisions and kinetic energy, leading to the fundamental relation $PV = \frac{1}{3} N m v_{rms}^2$. Because this overarching theory links molecular properties to macroscopic observables, it serves as the mathematical basis from which empirical relationships like Boyle's law, Charles's law, and Avogadro's law are all derived. Consequently, this comprehensive model acts as a unifying framework that confirms the validity of each of these gas laws simultaneously.