i. Boyle’s law states that at constant temperature:
Answer: C) P ∝ 1V
Explanation: Pressure is inversely proportional to volume at constant T.
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Loading home…Solids have fixed shape and volume; particles vibrate about fixed positions in a lattice. Liquids have fixed volume but take the shape of the container; particles move and slide past one another. Gases have neither fixed shape nor fixed volume; particles move rapidly and fill the available space. Intermolecular forces are strongest in solids and weakest in gases. Heating increases kinetic energy and can cause melting or vaporisation. These differences explain compressibility and diffusion rates of the three states.
Boyle’s law: at constant temperature, the pressure of a fixed mass of gas is inversely proportional to its volume (P ∝ 1V). Equivalently, PV = constant for a given amount of gas at fixed T. Charles’s law: at constant pressure, volume is directly proportional to absolute temperature (V ∝ T). A plot of V versus T (kelvin) is a straight line that extrapolates toward zero volume near −273 °C. Both laws are limiting laws for ideal gases. They combine with Avogadro’s law into the ideal gas equation PV = nRT.
An ideal gas is a hypothetical gas whose particles have negligible volume and no intermolecular attractions, and undergo elastic collisions. Real gases approach ideal behaviour at low pressure and high temperature. The ideal gas equation is PV = nRT. R is the universal gas constant; its value depends on the units of P, V and T (e.g. 0.0821 dm³ atm K⁻¹ mol⁻¹ or 8.314 J K⁻¹ mol⁻¹). n is amount in moles and T must be in kelvin. The equation links the four measurable variables of a gaseous sample.
In ice, water molecules form an open three-dimensional hydrogen-bonded network. Each molecule is tetrahedrally hydrogen-bonded, leaving empty space in the lattice. This open structure gives ice a larger volume for the same mass than liquid water. Hence the density of ice is lower than that of liquid water, and ice floats. On melting, the open framework partially collapses and molecules pack more closely. Hydrogen bonding is therefore responsible for this important anomaly of water.
Vapour pressure is the pressure exerted by a vapour in equilibrium with its liquid (or solid) at a given temperature. It increases with temperature as more molecules escape to the vapour phase. Boiling occurs when vapour pressure equals the external atmospheric pressure. The normal boiling point is the temperature at which vapour pressure equals 1 atm. Liquids with stronger intermolecular forces have lower vapour pressures and higher boiling points. At high altitude, lower external pressure lowers the boiling point of water.
Crystalline solids have long-range ordered arrangement of particles and sharp melting points. They show characteristic crystal faces and anisotropic properties in many cases. Amorphous solids lack long-range order and soften over a temperature range rather than melting sharply. Glass and many plastics are amorphous; NaCl and diamond are crystalline. X-ray diffraction gives sharp patterns for crystals but not for amorphous solids. The distinction is structural: order versus disorder in particle packing.
Kinetic molecular theory models a gas as a large number of tiny particles in continuous random motion. The volume of the particles themselves is negligible compared with the container volume. Intermolecular attractions are assumed negligible in the ideal case. Collisions with the walls are elastic and cause pressure. Average kinetic energy is proportional to absolute temperature.
If volume decreases at constant T, particles hit the walls more often, so pressure rises—Boyle’s law. If temperature rises at constant P, particles move faster and the volume must expand to keep pressure constant—Charles’s law. At constant V, higher T means higher pressure—Gay-Lussac’s relation. Equal numbers of particles at the same T and P occupy equal volumes—Avogadro’s law.
Real gases deviate when particles’ own volume and attractions matter, especially at high P and low T. The van der Waals equation introduces corrections a and b for attractions and finite volume. Nevertheless, kinetic theory remains the conceptual foundation of gas behaviour in school chemistry.
Combining Boyle’s law (V ∝ 1P), Charles’s law (V ∝ T) and Avogadro’s law (V ∝ n) gives V ∝ nT/P. Introducing the constant R yields PV = nRT, the ideal gas equation. R is the same for all ideal gases; only units change with the pressure–volume system used. The equation of state allows calculation of any one variable when the others are known.
Ideal behaviour assumes point masses and no attractions. At high pressure, molecular volume is no longer negligible, so measured volume is larger than ideal predictions. At low temperature, attractions pull molecules together, reducing pressure relative to the ideal value. Compressibility factor Z = PV/nRT equals 1 for an ideal gas and varies for real gases.
Gases with low critical temperatures and weak intermolecular forces (H₂, He) are closer to ideal under ordinary conditions. Polar or easily liquefied gases (NH₃, CO₂) deviate more. Understanding deviations is important in industry where high pressures are used.
A heating curve of ice shows temperature rising as solid warms, then a plateau at 0 °C while ice melts at constant temperature. Latent heat of fusion is absorbed to break part of the hydrogen-bonded lattice. Liquid water then warms until 100 °C (at 1 atm), where another plateau marks boiling as latent heat of vaporisation is absorbed.
During phase changes, kinetic energy stays roughly constant while potential energy of particle arrangement changes. Steam at 100 °C contains more energy than liquid water at 100 °C because of the large enthalpy of vaporisation.
Ice is less dense than liquid water because of the open hydrogen-bonded structure of the solid. Water reaches maximum density near 4 °C; further cooling toward 0 °C expands the liquid slightly as hydrogen-bond order increases. Floating ice and the 4 °C density maximum shape climate and aquatic ecosystems.
Phase diagrams summarise solid–liquid–gas equilibria and the unique negative slope of water’s melting curve. These features all trace back to hydrogen bonding in water.
London (dispersion) forces arise from temporary dipoles in all atoms and molecules. They increase with molecular size and polarisability; hence boiling points rise down the noble gases and in larger hydrocarbons. Dipole–dipole attractions occur between permanent dipoles in polar molecules and are stronger than dispersion forces of similar mass in many cases.
Hydrogen bonding is a specially strong dipole interaction involving H bonded to F, O or N. It explains high boiling points of H₂O, HF and NH₃ compared with H₂S, HCl and PH₃. It also explains the open structure and low density of ice relative to liquid water.
Stronger intermolecular forces raise melting and boiling points, increase viscosity and surface tension, and lower vapour pressure. Solubility follows “like dissolves like”: polar and hydrogen-bonding solutes dissolve in polar solvents. Recognising the dominant intermolecular force predicts many physical trends without detailed calculation.
Ionic solids are lattices of cations and anions (e.g. NaCl). They are hard, brittle, have high melting points, and conduct when molten or dissolved but not as solids.
Molecular solids consist of discrete molecules held by intermolecular forces (e.g. I₂, ice, sucrose). They are relatively soft and have low to moderate melting points; ice’s properties are dominated by hydrogen bonding.
Covalent network solids have atoms linked by continuous covalent bonds (diamond, SiO₂, SiC). They are very hard, have very high melting points, and are usually electrical insulators (graphite is an exception with delocalised electrons in layers).
Metallic solids have cations in a sea of delocalised electrons. They are malleable, ductile, lustrous, and good conductors of heat and electricity. Alloy properties can be tuned by composition.
Structure determines properties: knowing the solid type predicts mechanical, thermal and electrical behaviour.