States Of Matter: Class 11 Chemistry Chapter Notes

Key Terms and Definitions

Boyle's Law

For a fixed amount of gas at constant temperature, the pressure of a gas is inversely proportional to its volume (P ∝ 1/V).

Charles's Law

For a fixed amount of gas at constant pressure, the volume of a gas is directly proportional to its absolute temperature (V ∝ T).

Avogadro's Law

At the same temperature and pressure, equal volumes of all gases contain an equal number of molecules (V ∝ n).

Ideal Gas

A hypothetical gas whose molecules occupy negligible space and have no intermolecular forces of attraction. It obeys all gas laws under all conditions of temperature and pressure.

Dalton's Law of Partial Pressures

The total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases.

Compressibility Factor (Z)

A correction factor which describes the deviation of a real gas from ideal gas behaviour. It is the ratio of the molar volume of a gas to the molar volume of an ideal gas at the same temperature and pressure (Z = PV/nRT).

Critical Temperature (Tc)

The temperature above which a gas cannot be liquefied, no matter how much pressure is applied.

Absolute Zero

The lowest possible temperature at which a gas would theoretically have zero volume. It is 0 Kelvin (-273.15 °C).

Must-Remember Formulas & Constants

• Ideal Gas Equation: PV = nRT. Master the units for each variable.
• Value of Gas Constant (R): 8.314 J K⁻¹ mol⁻¹ (SI units), 0.0821 L atm K⁻¹ mol⁻¹ (common unit). Use the value that matches the units of P and V in the problem.
• Combined Gas Law: (P₁V₁)/T₁ = (P₂V₂)/T₂ for a fixed amount of gas.
• Dalton's Law: P_total = P₁ + P₂ + P₃ + .... Partial Pressure Pᵢ = xᵢ * P_total, where xᵢ is the mole fraction.
• Graham's Law of Diffusion: rate₁/rate₂ = √(M₂/M₁), where M is molar mass. The rate of diffusion is inversely proportional to the square root of molar mass.
• Compressibility Factor (Z): For an ideal gas, Z = 1. For real gases, Z > 1 (repulsive forces dominate, hard to compress) or Z < 1 (attractive forces dominate, easier to compress).
• van der Waals Equation for Real Gases: (P + an²/V²)(V - nb) = nRT. Here, 'a' accounts for intermolecular forces and 'b' for molecular volume.
• Kinetic Gas Equation: PV = (1/3)mnc², where c is the root mean square speed.
• STP vs NTP: Standard Temperature & Pressure (STP) is 273.15 K (0°C) and 1 bar. Molar volume = 22.7 L/mol. Older convention (Normal Temperature & Pressure, NTP) used 1 atm pressure, molar volume = 22.4 L/mol. Check what your exam specifies.
• Temperature Conversion: Always use Kelvin for gas law calculations. K = °C + 273.15.

The Gas Laws at a Glance

Kinetic Molecular Theory of Gases

The Kinetic Molecular Theory of Gases (KMT) provides a microscopic model to explain the macroscopic behavior of gases described by the gas laws. It is based on a set of postulates about the nature of gas molecules:

1. Particles and Separation: Gases consist of a large number of tiny particles (atoms or molecules) that are so far apart from each other that the actual volume of the molecules is negligible compared to the total volume of the container.
2. Constant, Random Motion: Gas particles are in continuous, rapid, and random motion in all possible directions. They move in straight lines until they collide with another particle or the walls of the container.
3. No Intermolecular Forces: There are no forces of attraction or repulsion between the particles of a gas. This is why gases expand to fill their container.
4. Elastic Collisions: Collisions between gas particles and between particles and the container walls are perfectly elastic. This means that there is no net loss of kinetic energy during collisions; energy may be transferred, but the total kinetic energy of the system remains constant.
5. Kinetic Energy and Temperature: The average kinetic energy of the gas particles is directly proportional to the absolute temperature (in Kelvin) of the gas. At any given temperature, molecules of all gases have the same average kinetic energy.

These assumptions form the basis of an 'ideal gas'. Real gases deviate from these assumptions, particularly at high pressures and low temperatures.

Ideal Gas vs. Real Gas

Worked Example: Ideal Gas Equation

• {"problem":"Calculate the volume occupied by 8.8 g of CO₂ at 31.1°C and 1 bar pressure. (R = 0.083 L bar K⁻¹ mol⁻¹)","solution":"Step 1: Convert units and find moles (n).\nMolar mass of CO₂ = 12 + 216 = 44 g/mol.\nMoles (n) = given mass / molar mass = 8.8 g / 44 g/mol = 0.2 mol.\nTemperature (T) in Kelvin = 31.1 + 273.15 = 304.25 K.\nPressure (P) = 1 bar.\n\nStep 2: Apply the Ideal Gas Equation (PV = nRT).\nWe need to find Volume (V).\nV = nRT / P\n\nStep 3: Substitute the values.\nV = (0.2 mol 0.083 L bar K⁻¹ mol⁻¹ * 304.25 K) / 1 bar\nV = 5.05 L\n\nAnswer: The volume occupied by 8.8 g of CO₂ is 5.05 L."}

Common Exam Traps

Unit Consistency is King! A huge number of marks are lost due to incorrect units. If you use R = 0.0821 L atm K⁻¹ mol⁻¹, your pressure must be in atm and volume in L. If you use R = 8.314 J K⁻¹ mol⁻¹, pressure must be in Pascals (Pa) and volume in cubic meters (m³). Always convert temperature to Kelvin before starting any calculation involving gas laws.

Practice Questions with Solutions

• Under what two conditions do real gases behave most like ideal gases? High temperature and low pressure.
• What is the physical significance of the van der Waals constant 'a'? It accounts for the magnitude of intermolecular forces of attraction between gas particles.
• Why is the graph of P vs V for a gas at constant temperature a hyperbola? Because Boyle's law states that P is inversely proportional to V (P = k/V), which is the equation for a rectangular hyperbola.
• If you have two balloons, one with Helium (4g/mol) and one with Nitrogen (28g/mol) at the same temperature and pressure, which will deflate faster? Why? The Helium balloon will deflate faster. According to Graham's Law of Diffusion, the rate of effusion is inversely proportional to the square root of the molar mass. Since Helium has a lower molar mass, it will effuse (leak) out of the balloon faster.

Frequently Asked Questions

Frequently Asked Questions