V

Published:17 May 2024
Concepts in Physical Chemistry, Royal Society of Chemistry, 2nd edn, 2024, pp. 342351.
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Physical chemistry is the part of chemistry that seeks to account for the properties and transformations of matter in terms of concepts, principles, and laws drawn from physics. This glossary is a compilation of definitions, descriptions, formulae, and illustrations of concepts that are encountered throughout the subject. This section describes the concepts that begin with the letter V; where appropriate, the entries also describe subsidiary but related concepts. Refer to the Directory for a full list of all the concepts treated.
Valence Bond Theory
The overall wavefunction of a polyatomic molecule is the product of such wavefunctions for all the bonds in the molecule as expressed by one of its canonical structures, a structure exhibiting the topological layout of bonds, such as one of the Kekulé structures of benzene. The basic theory is augmented by allowing resonance, which is the improvement of the description by the superposition of wavefunctions corresponding to different canonical structures, including ionic structures. The geometry of molecules is matched by allowing for the promotion of atoms and the hybridization of their atomic orbitals, and the resulting localized bonds are classified as σ and π. See promotion, hybrid orbitals, and resonance.
Valence Electron
A valence electron is an electron in the outermost occupied shell of an atom and is the focus of bond formation. It occupies one of the valence orbitals of an atom, an orbital in that shell.
van der Waals Equation
van der Waals Forces
van der Waals forces are the forces of attraction between closedshell atoms and molecules, and specifically the interactions for which the potential energy is proportional to 1/R ^{6}, where R is the internuclear separation. (The force itself is proportional to 1/R ^{7}.) They are commonly classified as dipole–dipole, dipole–induced dipole, and induced dipole–induced dipole (London, dispersion) interactions. A van der Waals molecule is a loose cluster of closedshell molecules or atoms held together by van der Waals forces.
van der Waals Loops
van der Waals loops are the unphysical oscillations of the isotherms predicted by the van der Waals equation of state below the critical temperature. They are replaced by straight lines by using the Maxwell construction.
van ’t Hoff Equation
The kinetic explanation of this dependence notes that the activation energy of the reverse of an exenthalpic reaction is greater than that of the forward reaction (Figure V.2). Therefore, the rate of the reverse reaction increases with temperature more than the rate of the forward reaction increases. As a result, the equilibrium shifts towards reactants and K decreases.
Vapour Pressure
The boiling temperature, T_{b}, is the temperature at which the vapour pressure of a liquid becomes equal to the ambient pressure. The standard boiling point is the boiling temperature when the ambient pressure is 1 bar. The normal boiling point (the ‘boiling point’) is the boiling temperature when the ambient pressure is 1 atm.
Variation Principle
The implication is that the best form of a trial wavefunction, the form that most closely matches the true wavefunction of the system, is the one with values of the parameters that result in the lowest energy (Figure V.3). When the trial wavefunction is written as a linear combination with the coefficients the variable parameters, then the optimum form, the best values of the coefficients, is obtained by solving the secular equations.
Vector Model
The vector model of angular momentum is a pictorial depiction of the state with quantum numbers j, m_{j} in which a vector of length {j(j + 1)}^{1/2} and zcomponent m_{j} lies at a stationary but indeterminate azimuthal angle on a cone around the zaxis (Figure V.4). In the presence of a magnetic field, the vector precesses on the cone at the Larmor frequency. The vector model can be elaborated to depict the coupling of angular momenta, when the contributing vectors are drawn with definite phases to acquire the correct resultant vectors: see singlet and triplet states.
Vertical Transition
A vertical transition is an electronic transition that, in accord with the Franck–Condon principle, occurs without change of the nuclear coordinates and therefore is depicted by a vertical line on a molecular potentialenergy diagram.
Vibrational Motion
See harmonic oscillator. A nonlinear molecule with N atoms has 3N − 6 normal modes of vibration with a restoring force which is in general a function of stretching and bonding contributions and an effective mass which depends on the quantity of matter that moves in the course of the vibration. When the displacements are so great that the potential can no longer be regarded as parabolic, the motion is anharmonic. See Morse potential.
Vibrational Temperature
Virial Theorem
For a harmonic oscillator, b = 2, so 〈E_{k}〉 = 〈E_{p}〉; for a hydrogenic atom, b = −1, so $\u2329 E k \u232a=\u2212 1 2 \u2329 E p \u232a$ , which implies that $E= 1 2 \u2329 E p \u232a$ .
Virtual Orbital
A virtual orbital of an atom is an atomic orbital that is not occupied in the ground state of an atom but which is a member of the basis used to construct molecular orbitals as linear combinations of atomic orbitals.
Virtual Transition
It is sometimes said that the molecule has made a virtual transition to one of those excited states because if it is inspected there is a probability equal to c_{n}^{2} that it would be found in the excited state $ \psi n ( 0 ) $ .
Viscosity
The physical inspiration for this definition is that if the flow of the fluid is Newtonian (that is, can be regarded as a series of layers moving past each other at different rates), then the migration of a molecule from a slowly moving layer to a faster layer slows that layer and hence retards the flow of the liquid (Figure V.7). The SI units of η are kg m^{−1} s^{−1}, but it is commonly reported in poise (P), with 1 P = 10^{−1} kg m^{−1} s^{−1}. See also diffusion.
It follows that the viscosity of a perfect gas is independent of the pressure and increases as the temperature is increased. The independence of pressure arises because the increase of the number of molecules cancels a decrease in mean free path, so although there are more transporting molecules, they carry the momentum for a shorter distance. The increase with temperature (as T ^{1/2}) is due to the greater transport of momentum at higher temperatures.
In this case, the migration of molecules is an activated process because a molecule must escape from the attraction of its neighbours.