Class 11 Chemistry — Chapter 305: States of Matter

Key concepts: States of Matter (Class 11 Chemistry)

Whether a substance is a gas, a liquid or a solid is decided by a tug of war between the intermolecular forces pulling its particles together and the thermal energy driving them apart. This chapter first surveys those forces — London dispersion, dipole-dipole and hydrogen bonding — and then studies the gaseous state in detail: the laws of Boyle, Charles, Gay-Lussac and Avogadro, which combine into the ideal gas equation PV = nRT, together with Dalton's law of partial pressures and Graham's law of diffusion. The kinetic molecular theory explains why these laws work and introduces the Maxwell distribution of molecular speeds. Finally, real gases are shown to deviate from ideality at high pressure and low temperature, a deviation measured by the compressibility factor and described by the van der Waals equation, which leads on to critical constants, liquefaction and the properties of the liquid state.

London dispersion forces

Momentary fluctuations in the electron cloud of an atom or molecule create an instantaneous dipole that induces a dipole in its neighbour. These forces act between all particles, including non-polar ones such as He and CH₄, and grow stronger as the number of electrons and the size of the molecule increase.

Dipole-dipole interaction

Molecules with a permanent dipole moment, such as HCl or SO₂, line up so that the positive end of one faces the negative end of the next. These attractions are stronger than dispersion forces between molecules of comparable size, so polar substances usually boil higher than non-polar ones.

Hydrogen bonding

A special, unusually strong dipole-dipole attraction that arises when hydrogen is covalently bonded to the small, highly electronegative atoms F, O or N. It explains the abnormally high boiling points of HF, H₂O and NH₃, the high viscosity of glycerol, and the fact that ice is less dense than water.

Boyle's law

At constant temperature, the volume of a fixed mass of gas varies inversely with the pressure, so that PV stays constant. A plot of P against V is a hyperbola while a plot of P against 1/V is a straight line through the origin, which is the usual way of testing the law.

Charles' law

At constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature, so V/T is constant. Extrapolating the straight line of V against Celsius temperature for every gas gives a common intercept at −273.15 °C, which defines absolute zero and the kelvin scale.

Gay-Lussac's law

At constant volume, the pressure of a fixed mass of gas is directly proportional to its absolute temperature, so P/T is constant. This is the law behind pressure cookers, sealed aerosol cans that burst on heating, and the constant-volume gas thermometer.

Avogadro's law and molar volume

Equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules, so V is proportional to n. It follows that one mole of any ideal gas occupies 22.4 L at STP, taken here as 273 K and 1 atm, whatever the identity of the gas.

Ideal gas equation

Combining the three gas laws with Avogadro's law gives PV = nRT, the equation of state of an ideal gas. Since n = mass ÷ molar mass, the same equation rearranges to M = dRT/P, which is the standard route from a measured gas density to a molar mass.

Dalton's law of partial pressures

In a mixture of non-reacting gases each component exerts the pressure it would exert alone, and the total pressure is the sum of these partial pressures. The rule is essential when a gas is collected over water, where the aqueous tension must be subtracted to obtain the pressure of the dry gas.

Graham's law of diffusion

At the same temperature and pressure the rate of diffusion or effusion of a gas is inversely proportional to the square root of its density, and hence of its molar mass. This is why hydrogen diffuses four times as fast as oxygen and why the law can be used to separate gaseous isotopes.

Kinetic molecular theory

Gases are pictured as very large numbers of tiny particles in ceaseless random motion, whose own volume is negligible, between which there are no appreciable attractions, and whose collisions are perfectly elastic. The average kinetic energy of the particles depends only on the absolute temperature.

Maxwell distribution of speeds

At any temperature the molecules do not all move at the same speed; the fraction having each speed follows a skewed bell-shaped curve. Raising the temperature flattens and broadens the curve and shifts its peak to the right, so more molecules move fast, while heavier gases give narrower curves peaking at lower speeds.

Three molecular speeds

The most probable speed lies at the peak of the Maxwell curve, the average speed is the arithmetic mean, and the root mean square speed is the square root of the mean of the squared speeds. Because the curve is skewed, they always stand in the fixed ratio 1 : 1.128 : 1.224.

Deviation of real gases

Real gases obey PV = nRT closely only at low pressure and high temperature. At high pressure the molecules occupy a significant fraction of the container and at low temperature the attractions between them can no longer be ignored, so both simplifying assumptions of the kinetic theory break down.

van der Waals equation

Written as (P + an²/V²)(V − nb) = nRT, it repairs the ideal gas equation with two constants: a measures the intermolecular attraction that lowers the observed pressure, and b is the excluded volume of the molecules themselves. Large values of a and b mark a gas that is easily liquefied.

Compressibility factor Z

Defined as Z = PV/nRT, it equals exactly 1 for an ideal gas. Z below 1 at moderate pressure shows that attractive forces make the gas more compressible than ideal, while Z above 1 at high pressure shows that molecular volume and repulsion make it harder to compress.

Critical constants and liquefaction

The critical temperature Tc is the temperature above which a gas cannot be liquefied by pressure alone; the pressure needed to liquefy it at Tc is the critical pressure Pc and the volume of one mole there is the critical volume Vc. A high Tc, as in NH₃ or SO₂, means strong attractions and easy liquefaction.

Vapour pressure and boiling point

The vapour pressure of a liquid is the pressure exerted by its vapour in equilibrium with the liquid at a given temperature, and it rises steeply with temperature. A liquid boils when its vapour pressure equals the external pressure, which is why water boils below 100 °C at high altitude.

Surface tension

Molecules at the surface of a liquid experience an unbalanced inward pull, so the liquid behaves as if covered by a stretched skin and tries to minimise its surface area. This explains spherical droplets, capillary rise and the cleaning action of detergents, and its value falls as temperature rises.

Viscosity

Viscosity is the internal resistance to flow, caused by friction between adjacent layers of a liquid moving at different speeds. Stronger intermolecular forces mean higher viscosity, so glycerol with its three hydroxyl groups is far more viscous than water, and heating always makes a liquid flow more freely.