Gases

Gases are the simplest state of matter, characterized by complete freedom of molecular motion and high compressibility. To master this chapter for your BISE board exams, you must thoroughly understand the foundational gas laws that describe the quantitative relationships between pressure ($P$), volume ($V$), temperature ($T$), and the number of moles ($n$). These include Boyle’s Law (inverse relationship between pressure and volume at constant $T$), Charles's Law (direct relationship between volume and absolute temperature at constant $P$), Avogadro’s Law (volume is directly proportional to moles at constant $T$ and $P$), and Gay-Lussac's Law. Combining these yields the General Gas Equation ($PV = nRT$), where $R$ is the universal gas constant. Expect numerical problems based on these laws, particularly requiring conversions of temperature to the Kelvin scale and pressure to atmospheres (atm) or torrs.

A critical conceptual distinction in board exams is between Ideal Gases and Real Gases. An ideal gas perfectly obeys the gas laws and kinetic molecular theory under all conditions, meaning there are no intermolecular forces and molecules possess zero volume. However, real gases (like $\text{O}_2$, $\text{CO}_2$, and $\text{NH}_3$) deviate from ideal behavior at low temperatures and high pressures because intermolecular attractions become significant and the volume of the gas molecules is no longer negligible compared to the container. To account for this, Johannes van der Waals modified the ideal gas equation, introducing correction factors for pressure (intermolecular forces) and volume (finite molecular size) to derive the van der Waals Equation.

You must also prepare the physical principles governing gas behavior, starting with Dalton’s Law of Partial Pressures, which states that the total pressure of a mixture of non-reacting gases is the sum of their individual partial pressures. A classic board exam numerical involves calculating the pressure of a gas collected over water, which requires subtracting the vapor pressure of water at that specific temperature. Furthermore, study Graham's Law of Effusion and Diffusion, which relates the rate of gas escape or mixing inversely to the square root of its molar mass ($r \propto 1/\sqrt{M}$). Finally, the Kinetic Molecular Theory of Gases (KMT) is a favorite short- and long-question topic; review its core postulates—such as gas molecules being in continuous random motion and collisions being perfectly elastic—along with how KMT theoretically derives Boyle's and Charles's laws and explains Absolute Zero ($0\text{ K}$ or $-273.15^\circ\text{C}$).