Problem 5-16

First see the answer to problem 5-24

(a) Dispersion interactions (induced dipole-induced dipole) only since the molecule has no dipole moment and is not an ionic compound.

(b) Covalent compound consisting of atoms of different electronegativities.  The ClF bond is a polar covalent bond and the molecule has a net dipole moment (unlike CCl₄ for instance where the bond dipoles cancel giving the molecule no net dipole moment).  The intermolecular interactions will be made up of dipole-dipole interactions and dispersion interactions.  The strongest of these is the dipole-dipole interaction, and consequently, it will dominate.

(c) This is a covalent compound (compound from non-metals) with no dipole moment.  Consequently, only dispersion interactions will be present.

(d) An ionic compund (compound between a metal and non-metal, difference in electronegativity >2) so ionic interactions and dispersion interactions.  Ion-ion interactions are very strong so they will dominate.  

Problem 5-22

IF₅ solid, BrF₅ liquid, ClF₅ gas

The compound with the strongest intermolecular interactions is expected to be the solid, the one with the weakest interactions the gas, and the intermediate case the liquid. Intermolecular interactions are discussed in detail below in Problem 5-24. For these molecules, the applicable intermolecular interactions are dipole and induced dipole interactions. The induced dipole or dispersion interactions increase with molecular weight. Hence, considering these interactions alone, IF₅ is the predicted to be the solid, BrF₅ the liquid, and ClF₅ the gas. Dipole-dipole interactions are also important for these interhalogen compounds; their bond dipoles do not cancel thereby giving rise to a permanent dipole. (draw Lewis structures to convince yourself, Hint: the X atom is central and has an expanded valence shell). Considering the electronegativity differences in the compounds and hence the magnitude of the bond dipoles, IF₅ is expected to have the strongest dipole-dipole interactions, followed by BrF₅, and the weakest interactions are expected with ClF₅. As with the induced dipole forces, this predicts IF₅ is the solid, BrF₅ the liquid, and ClF₅ the gas.

Problem 5-24

Ordering of boiling points:

He < Ar < SO₂ < HF < CaF₂

The ordering parallels the strength of the intermolecular interactions that attract molecules to one and other. The greater the attractive interactions, the higher the boiling point.

Before discussing intermolecular interactions, it is first necessary to introduce the idea of a dipole. A dipole can be represented as two charges, equal in magnitude but opposite in sign, at a fixed distance from one and other. The positive end of one dipole interacts attractively with the negative end of another dipole and vice versa. The electron density of atoms is continuously fluctuating. Thus, at any given instant the electron density about an atom may be asymmetrically distributed thus giving rise to a transient dipole (see Figure below). The transient dipole on one atom can induce a dipole on a neighboring atom by distorting the neighbor’s electron cloud, thereby resulting in an attractive interaction that reduces the energy of the system (see Figure).

Caption: A snapshot in time of two Ar atoms. The shading represents the instantaneous electron density about the atoms. The deltas indicate the partial charge distribution. The arrow with a plus symbol on its tail is a symbol for a dipole (note the orientation relative to the specifed partial charges).

It is important to realize that these are not permanent dipoles, they are transient since the electron density is continually fluctuating. Despite this continual fluctuation, the net result is an attractive interaction. Induced dipole interactions are also termed dispersion interactions, and they result in the condensation of noble gases such as Ar or Ne. They are weak interactions (see table below) and consequently elements such as Ar or Ne have very low boiling points (For Ar, T_b = -186^oC, for Ne, T_b = -246^oC). Ne has a lower boiling point than Ar because dispersion interactions increase with increasing molecular weight. In small atoms, the electrons are held tightly by the nucleus and are not as readily polarized (distorted) as in larger atoms with electrons further from the nucleus.

In many molecules, there are permanent dipoles which interact attactively. Bonds between different atoms, such as in HCl, generally involve some unequal sharing of electron density and hence give rise to a dipole. Such bonds are termed polar covalent bonds. The magnitude of the dipole depends on the difference in the electronegativies of the bonded atoms. The larger the difference, the large the bond dipole. In molecules such as HCl, the bond dipole is the same as the molecules dipole. Larger molecules, however, have dipole moments that are the vector sum (both the magnitude and direction of the dipole are important in the summation) of bond dipoles. In carbon tetrachloride (CCl₄), for instance, there is no molecular dipole because all of the bond dipoles cancel (draw a Lewis structure and/or build a model to convince yourself ( see a model of CCl₄). In SO₂, however, there is a permanent dipole as shown in the Figure below (see a model of SO₂).

The presence of dipole-dipole forces result in SO₂ having a higher boiling point (T_b = -10^oC) than Ar, even higher than Kr (T_b = -156^oC) which has a larger molecular weight than SO₂.

With compounds containing a hydrogen bonded to F, O or N, a special type of bond, termed a hydrogen bond, is common. In water for instance, a hydrogen bound to an oxygen in one molecule can form a weak bond with the oxygen of another water molecule. Generally, hydrogen bonds are indicated as X-H · · · X’ where typically X=F, O, or N. Hydrogen bonds are much weaker than typical covalent bonds as indicated in the table below. The are exceptionally important in the chemistry of biological systems such as ourselves. The presence of hydrogen bonding in HF results in its boiling point being higher than that of SO₂ (T_b = 20^oC for HF).

Finally, the interaction between ions is very strong (see table below). Hence, ionic compounds such as CaF₂ have very high melting and boiling points (For CaF₂, T_melt = 1400^oC and T_boiling » 2500^oC).

Note: For reference, a typical C-C bond energy is 350 kJ mole^-1. Values from P.W. Atkins, Physical Chemistry 5^th Ed., W.H. Freeman, New York, 1994.

Problem 5-46.

Empirically, one component phase diagrams are determined by measuring the melting, boiling, and sublimation temperatures of a material as a function of external pressure (see note 1 below). These measurements trace out the solid-liquid, liquid-gas, and solid-gas coexistence curves, respectively (see note 2 below). These three curves meet at the triple point which is the temperature and pressure at which solid, liquid and gas coexist. The solid-liquid and solid-gas coexistence curves extend from the triple point indefinitely, whereas the liquid-gas coexistence curve terminates at the critical point. At temperatures above the critical temperature, changing the pressure of the system will never result in a two-phase, liquid-gas system. The pressure simply changes the density of the single-phase, supercritical fluid. By "moving around" the critical point one can transform between a liquid and gas without ever passing through a two-phase state (i.e. two substances with different densities). Rather, the transformation between liquid and gas is simply observed as a continuous change in density.

The problem provides us with enough information to sketch qualitatively, the phase diagram of N₂ (see Figure below). First plot the triple point and the critical point. The gas-liquid coexistence curve connects these two points. The liquid-solid coexistence curve extends up from the triple point consistent with our expectation that upon isobaric (constant pressure) cooling a liquid will transform into a solid. The slope of the liquid-solid coexistence curve (whether it points left or right) depends on the relative densities of the liquid and solid. With most substances, including N₂ (see data provided in problem), the solid is more dense than the liquid, and a sufficient increase in pressure will convert liquid to solid. The slope of the liquid-solid coexistence curve is therefore positive. Water is the most notable exception (ice floats on water), and the liquid-solid coexistence curve for water has negative slope. Finally, the solid-gas coexistence curve extends from the triple point with positive slope. The slope is positive because a solid is always more dense than a gas.

The problem also asks us to plot the "normal" boiling and freezing points for N₂. "Normal" transition temperatures are defined to be for a pressure of 1atm. Hence the intersection of a horizontal line drawn at 1atm of pressure with the coexistence curves gives the normal transition temperatures. For N₂ and most substances, both a normal melting and boiling point are observed because the P_{triple point} < 1 atm. For substances where P_{triple point} > 1 atm, the only transition (neglecting the possibility of solid-solid phase transformations as with the NiTi "shape memory metal" demonstrated in class) observed at 1atm is sublimation as with CO₂.

Note1:

It is important to understand the relation between vapor pressure, evaporation and boiling (similar statements can be made regarding sublimation). Consider a liquid that is introduced into a closed, thermostated, and evacuated container of fixed volume and fitted with a pressure gauge. Some of the condensed phase will vaporize resulting in an increase in pressure. Vaporization will continue until a dynamic equilibrium is reached. The pressure of the vapor observed in equilibrium with the condensed phase is called the vapor pressure (if all of the liquid vaporized we would have to introduce more liquid into the vessel to get a measure of its vapor pressure).

The situation in an open container is somewhat different. As in the closed container, vaporization occurs at the surface of the liquid, but it continues indefinitely because the vapor is continually swept away (say by air currents or diffusion). Equilibrium is never achieved and the liquid can evaporate completely. So how is boiling different from evaporation? Both involve conversion of liquid to gas. As we raise the temperature, the vapor pressure of the liquid increases. When the vapor pressure equals atmospheric pressure, vaporization can happen throughout the bulk of the material (hence the formation of bubbles) rather than simply at the surface. At the boiling point, the vapor pressure is sufficient to overcome the externally imposed pressure (say from the atmosphere), and the liquid can vaporize freely: boil. In a sealed, fixed-volume container, heating results in a continual increase in pressure and boiling is not observed.

Above, I said that the liquid-solid coexistence curve can be empirically determined by measuring the boiling point of a liquid as a function of external pressure. From this discussion, it is hopefully apparent that the liquid-solid coexistence curve can also be constructed by measuring the vapor pressure of a liquid as a function of temperature. A similar commentary applies to the solid-gas coexistence curve.

Note2: In sketching the phase diagram, the coexistence curves were drawn as straight lines - an oversimplification. Thermodynamic considerations can be used to predict the shapes of the various coexistence curves; later in the course we will learn some of the tools used in such calculations, but we will not calculate the forms of phase coexistence curves specifically.

Problem 5-50

a. The vapor pressure of the solid is 0.069atm. See Note 1 of problem 4-9.

b.  As Pext < Ptriple point, the solid hydrogen will sublime to gaseous hydrogen, see 4-9.