The state of matter, focusing on gases and liquids, is a fundamental topic in JEE Chemistry. Understanding the behavior of gases and liquids, the laws governing them, molecular interactions, and physical properties is essential to solve a variety of problems efficiently. This comprehensive guide covers ideal and real gases, kinetic molecular theory, gas laws, liquefaction of gases, properties of liquids such as viscosity and surface tension, and phase equilibria.
Matter exists primarily in three states: solid, liquid, and gas. Each state differs in particle arrangement, intermolecular forces, and properties. Gases and liquids are fluids, meaning they flow and take the shape of their container, but differ significantly in density and compressibility.
Gas laws relate pressure (P), volume (V), temperature (T), and amount (n) of gas:
At constant temperature, pressure and volume are inversely proportional:
P \times V = \text{constant}
At constant pressure, volume is directly proportional to temperature (in Kelvin):
\frac{V}{T} = \text{constant}
At constant volume, pressure is directly proportional to temperature (in Kelvin):
\frac{P}{T} = \text{constant}
At constant temperature and pressure, volume is proportional to the number of moles:
V \propto n
Combining all laws:
PV = nRT
Where R = 0.0821 L·atm/mol·K (ideal gas constant)
The total pressure exerted by a mixture of non-reacting gases equals the sum of partial pressures of individual gases.
P_{\text{total}} = P_1 + P_2 + \cdots + P_n
The rate of diffusion or effusion of a gas is inversely proportional to the square root of its molar mass:
\frac{\text{Rate}_1}{\text{Rate}_2} = \sqrt{\frac{M_2}{M_1}}
KMT explains gas behavior based on particle motion:
Pressure arises from collisions of gas molecules with container walls. Mathematically:
P = \frac{1}{3} \frac{N}{V} m \overline{v^2}
Where:
v_{\text{rms}} = \sqrt{\frac{3RT}{M}}
Where R is gas constant, T temperature, and M molar mass in kg/mol.
E_k = \frac{3}{2} RT
Real gases deviate from ideal behavior at high pressure and low temperature due to:
Corrects ideal gas equation to account for volume and pressure deviations:
\left(P + \frac{a}{V_m^2}\right)(V_m - b) = RT
Where \(V_m\) = molar volume, \(a\) = measure of attraction, \(b\) = volume correction.
Indicates deviation from ideal gas:
Z = \frac{PV}{RT}
Process of converting gases into liquids by cooling and/or applying pressure.
Maximum temperature at which a gas can be liquefied by pressure alone.
Minimum pressure required to liquefy a gas at critical temperature.
Temperature change in a real gas when it expands without performing external work.
Liquids have definite volume but no fixed shape. Molecules are close with moderate intermolecular forces.
Force acting on surface molecules that minimizes surface area.
\gamma = \frac{F}{l}
Where \(F\) is force and \(l\) length.
Resistance to flow due to internal friction.
\eta = \frac{F}{A \times (dv/dx)}
Where \(F\) force, \(A\) area, and \(dv/dx\) velocity gradient.
Vapor pressure is pressure exerted by vapor in equilibrium with liquid.
Boiling point is temperature at which vapor pressure equals external pressure.
Describes coexistence of phases at equilibrium.
F = C - P + 2
Where F = degrees of freedom, C = components, P = phases present.
| Concept | Formula/Relation |
|---|---|
| Boyle's Law | P × V = constant (at constant T) |
| Charles's Law | V/T = constant (at constant P) |
| Ideal Gas Equation | PV = nRT |
| Van der Waals Equation | (P + a/V_m²)(V_m - b) = RT |
| Graham's Law | Rate₁/Rate₂ = √(M₂/M₁) |
| Root Mean Square Velocity | v_rms = √(3RT/M) |
| Surface Tension | γ = F/l |
| Viscosity | η = F/(A × dv/dx) |
Mastery over the state of matter concepts will not only help you score well in JEE Chemistry but also build a strong foundation for physical chemistry and thermodynamics.