An ideal gas is a hypothetical model. Real gases have molecular volume and intermolecular forces, so they deviate from the equation of state.
Basic Knowledge
Three representative types of intermolecular force are as follows.
① van der Waals forces (dispersion forces): weak attractions caused by instantaneous charge imbalances. They exist in all molecules.
② Dipole–dipole interactions: act between polar molecules, such as HCl and acetone.
③ Hydrogen bonds: particularly strong interactions in which H directly bonded to F, O, or N interacts with another F, O, or N. They are important in H2O, NH3, HF, proteins, and DNA.
As molecular mass increases, van der Waals forces become stronger and the boiling point rises (clearly seen when comparing the boiling points of halogens in the same group).
van der Waals forces (dispersion forces caused by instantaneous dipoles)
Hydrogen bond (particularly strong F/O/N-H...F/O/N interaction)
Compressibility factor Z (Z = PV/(nRT); Z=1 for an ideal gas)
van der Waals equation ((P+an2/V2)(V-nb)=nRT)
Polarizability (ease with which an electron cloud is distorted by an external electric field)
London dispersion force (attraction between nonpolar molecules; strengthened as molecular mass increases)
Further Study (Principles and Applications)
Real gases approach ideal-gas behavior at high temperature and low pressure. At low temperature, intermolecular attractions make the actual volume smaller than predicted, giving Z<1. At high pressure, the intrinsic volume of molecules cannot be ignored, giving Z>1.
Hydrogen bonds are extremely important in life science. They are the driving force that maintains DNA base pairs (A-T, G-C) in the double helix and the secondary structures of proteins (α-helix, β-sheet). The high boiling point and large specific heat of water, as well as the density anomaly of ice, are all caused by hydrogen bonding and are closely connected with the conditions necessary for life.
- Ideal gas ⇒ molecular size and intermolecular forces are ignored
- Real gases approach ideal behavior at high temperature and low pressure
- Strength of intermolecular forces: hydrogen bonds>dipole interactions>dispersion forces
- Hydrogen bonding: only F-H, O-H, and N-H
- Boiling points within a group rise with molecular mass (dispersion forces ↑)
- Real gases are evaluated using the compressibility factor Z=PV/nRT
- Unusually high boiling point of water ⇒ hydrogen bonding
Important Notes (Common Confusions and Frequent Mistakes)
① Do not confuse covalent bonds (within molecules) with hydrogen bonds (between molecules). Hydrogen bonds are several tens of kJ/mol and are weaker than covalent bonds (several hundred kJ/mol). ② H bonded to elements other than F, O, and N (such as Cl) does not form hydrogen bonds. ③ The comparisons H2O > H2S, NH3 > PH3, and HF > HCl in boiling point provide evidence of hydrogen bonding. ④ van der Waals force may be used broadly to mean dispersion force + dipole interaction.
Practice
- Select the valid combination of atoms for forming a hydrogen bond: ① O-H...N ② C-H...O ③ S-H...O
- Which has the higher boiling point, H2O or H2S? Answer with the reason.
- Explain what can be determined when the compressibility factor Z = PV/(nRT) is greater than or less than 1.