6 Most SAQ’s of States of Matter : Gases & Liquids Chapter in Inter 1st Year Chemistry (TS/AP)

4 Marks

SAQ-1 : Give the important postulates of kinetic molecular theory of gases.

Introduction

The Kinetic Molecular Theory (KMT) provides a foundational understanding of gas behavior. This theory offers a set of postulates that explain how gas molecules interact and behave under various conditions.

Key Postulates of the Kinetic Molecular Theory of Gases

1. Nature of Gases: Gases consist of a large number of tiny particles known as molecules.
2. Motion of Gas Molecules: Gas molecules are in constant, random motion, moving in all directions. These molecules move with high velocities.
3. Intermolecular Forces: Gas molecules do not attract or repel each other, implying no significant intermolecular forces.
4. Gravitational Influence: The movement of gas molecules is not significantly influenced by gravity.
5. Volume of Gas Molecules: The actual volume occupied by gas molecules is extremely small compared to the volume of their container.
6. Pressure of a Gas: The pressure exerted by a gas is due to the collisions of molecules with the container walls.
7. Nature of Molecular Collisions: Collisions between gas molecules are perfectly elastic, meaning they do not lose energy upon impact.
8. Relationship to Temperature: The average kinetic energy of gas molecules is directly proportional to the temperature of the gas.

Summary

The Kinetic Molecular Theory of Gases explains gas behavior by describing gases as collections of tiny, rapidly moving particles. The theory’s postulates cover the nature, motion, and interactions of gas molecules, as well as their relationship with temperature and pressure. Understanding these principles is crucial for comprehending how gases behave under different physical conditions.

---

SAQ-2 : Deduce (a) Boyle’s law (b) Charle’s law from kinetic gas equation.

Introduction

The kinetic gas equation provides a foundation for understanding the behavior of gases. This equation allows us to derive essential gas laws like Boyle’s Law and Charles’s Law, which describe how gases respond to changes in pressure, volume, and temperature.

Boyle’s Law

1. Starting from the Kinetic Gas Equation: The equation $$PV = \frac{1}{3} mn\bar{u}{ms}^2 = \frac{2}{3} \times \frac{1}{2} mn\bar{u}{rms}^2$$ relates pressure and volume to the kinetic energy of gas molecules.
2. Kinetic Energy and Temperature: The average kinetic energy (K.E) of gas molecules is directly proportional to the temperature (T), leading to K.E.∝T or K.E.=KT.
3. Proving Boyle’s Law: By keeping temperature (T) constant, the equation $$PV = \frac{2}{3} KT$$ implies that the product of pressure (P) and volume (V) remains constant, i.e., PV=constant. This relationship is known as Boyle’s Law.

Charles’s Law

1. Using the Derived Relation: From $$PV = \frac{2}{3} KT$$ rearranging gives $$\frac{V}{T} = \frac{2}{3} \times \frac{K}{P}$$
2. Proving Charles’s Law: When pressure (P) is constant, the ratio of volume (V) to temperature (T) remains constant, i.e., $$\frac{V}{T} = \text{constant}$$ This is Charles’s Law.

Summary

Boyle’s Law and Charles’s Law are fundamental in understanding gas behavior, showing how pressure, volume, and temperature are interconnected. These laws, derivable from the kinetic gas equation, illustrate the link between the motion of gas molecules and the gas’s macroscopic properties. For students, comprehending these derivations is crucial as it connects microscopic molecular behavior with observable, macroscopic gas properties.

---

SAQ-3 : Deduce Graham’s law from kinetic gas equation.

Introduction

Graham’s Law offers valuable insights into the relationship between the rate of diffusion of a gas and its molar mass. This relationship can be derived from the kinetic gas equation, linking molecular motion with observable gas properties.

Derivation of Graham’s Law

1. Statement of Graham’s Law: The rate of diffusion (r) of a gas is inversely proportional to the square root of its molar mass (M). Represented as $$r \propto 1/\sqrt{M}$$
2. Beginning with the Kinetic Gas Equation: The kinetic gas equation is $$PV = \frac{1}{3} mnu_{rms}^2$$ where m is the mass of one molecule, n is the number of molecules, and u_rms​ is the root-mean-square speed.
3. Relating Root-Mean-Square Speed to Molar Mass:
   • Rearranging the equation gives: $$u_{rms}^2 = \frac{3PV}{mn}$$
   • Considering mn=M (where M is the molar mass of the gas), we get: $$u_{rms}^2 = \frac{3PV}{M}$$
4. Establishing the Relationship Between RMS Speed and Molar Mass: From the above equation, we deduce: $$u_{rms} \propto 1/\sqrt{M}$$
5. Connecting RMS Speed to Rate of Diffusion: The root-mean-square speed (u_rms​) is proportional to the rate of diffusion (r), leading to: $$u_{rms} \propto r$$
6. Deriving Graham’s Law: Combining the relationships, we conclude: $$r \propto 1/\sqrt{M}$$

Summary

Graham’s Law establishes a crucial connection between the rate of diffusion of a gas and its molar mass, highlighting that gases with lower molar masses diffuse faster than those with higher molar masses. This derivation from the kinetic gas equation enhances our understanding of molecular motion’s impact on gas diffusion. It is essential for students to understand this relationship as it bridges molecular behavior with a practical, observable phenomenon in gas dynamics.

---

SAQ-4 : Derive the ideal gas equation from gas laws.

Introduction

The ideal gas equation is a fundamental relationship in chemistry and physics, derived from the combination of three empirical gas laws: Boyle’s Law, Charles’s Law, and Avogadro’s Law.

Combining Boyle’s, Charles’s, and Avogadro’s Laws

1. Boyle’s Law (Pressure and Volume): At constant temperature, the pressure (P) of a gas is inversely proportional to its volume (V). Mathematically, P ∝ 1/V or PV = constant.
2. Charles’s Law (Volume and Temperature): At constant pressure, the volume (V) of a gas is directly proportional to its temperature (T) in Kelvin. Represented as V ∝ T or V/T = constant.
3. Avogadro’s Law (Volume and Amount of Gas): At constant temperature and pressure, the volume (V) of a gas is directly proportional to the number of moles (n) of the gas. Expressed as V ∝ n or V/n = constant.

Derivation of the Ideal Gas Equation

1. Combining the Laws: To derive the ideal gas equation, we combine the proportionalities from Boyle’s, Charles’s, and Avogadro’s Laws.
2. Joint Proportionality: Combining the three laws gives PV ∝ nT.
3. Introducing the Gas Constant (R): To convert the proportionality into an equation, we introduce a proportionality constant, known as the ideal gas constant (R).
4. Ideal Gas Equation: The final equation is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

Summary

The ideal gas equation PV = nRT is derived by combining Boyle’s Law, Charles’s Law, and Avogadro’s Law. This equation provides a comprehensive description of the behavior of an ideal gas under various conditions, linking pressure, volume, temperature, and the amount of gas through a constant R. Understanding this derivation is crucial for students as it forms the basis for many calculations and concepts in gas chemistry and thermodynamics.

---

SAQ-5 : State and explain Graham’s law of diffusion.

Introduction

Graham’s law of diffusion elucidates how gases diffuse or spread out in a space. It correlates the rate of diffusion of a gas with its density, molecular weight, and vapor density, offering a predictive measure of how different gases disperse.

Graham’s Law of Diffusion Explained

1. Statement of the Law: Graham’s law states that the rate of diffusion (r) of a gas is inversely proportional to the square root of its density (d), under constant temperature and pressure. The law is mathematically expressed as r ∝ 1/d​.
2. Relation to Density: For two gases with diffusion rates r₁​ and r₂​, and densities d₁​ and d₂​, the relationship is $$r_1/r_2 = \sqrt{d_2/d_1}$$
3. Definition of Rate of Diffusion: The rate of diffusion (r) is the volume of gas diffused (v) per unit time (t), expressed as r = v/t.
4. Comparison of Two Gases: When comparing two gases, the ratio of their rates of diffusion is given by $$r_1/r_2 = (V_1/t_1) / (V_2/t_2) = (V_1 t_2) / (V_2 t_1)$$
5. Relation to Molecular Weight: The rate of diffusion (r) is also inversely proportional to the square root of the gas’s molecular weight (M), shown as r ∝ 1/M​.
6. Vapor Density and Molecular Weight: Since the molecular weight (M) is twice the vapor density (VD) of the gas (M = 2 × VD), the rate of diffusion (r) is inversely proportional to the square root of the vapor density (VD). Thus, for two gases with rates r₁​ and r_2​, and vapor densities VD₁​ and VD₂​, the formula becomes $$r_1/r_2 = \sqrt{VD_2/VD_1}$$

Summary

Graham’s law of diffusion is instrumental in determining the relative rates at which different gases diffuse. By understanding a gas’s density, molecular weight, or vapor density, we can compare its diffusion rate to that of another gas, which is crucial in applications ranging from gas mixing to pollutant dispersion analysis in the atmosphere.

---

SAQ-6 : Deduce Dalton’s law of partial pressures from kinetic gas equation.

Introduction

Dalton’s Law of Partial Pressures is a fundamental principle in gas studies. It explains how individual gases in a mixture contribute to the total pressure. This law can be logically derived from the kinetic gas equation.

Deduction of Dalton’s Law of Partial Pressures

1. Definition of Dalton’s Law: Dalton’s Law states that the total pressure exerted by a non-reacting gas mixture is equal to the sum of the individual pressures each gas would exert if it occupied the same volume and temperature alone.
2. Considering a Single Gas:
   • For a gas in a volume V, let m₁​ be its mass, n_1​ its number of moles, and u_1rms​ the root mean square velocity.
   • Using the kinetic gas equation, the pressure P₁​ is $$P_1 = \frac{1}{3} \frac{m_1 n_1 u_{1 rms}^2}{V}$$
3. Replacing with Another Gas:
   • For a second gas in the same volume V, let m₂​ be its mass, n₂​ its moles, and u_2rms​ the RMS velocity.
   • The pressure P₂​ of this gas is $$P_2 = \frac{1}{3} \frac{m_2 n_2 u_{2 rms}^2}{V}$$
4. Total Pressure in the Mixture: When both gases are in the vessel together, the combined pressure P is the sum of their individual pressures: $$P = P_1 + P_2$$

Summary

Dalton’s Law of Partial Pressures demonstrates that the total pressure in a mixture of gases is the sum of the pressures that each gas would exert independently. Deriving this law from the kinetic gas equation highlights the relationship between molecular motion and pressure in gas mixtures. This concept is vital in fields ranging from atmospheric science to industrial gas applications.