Download The Physics and Chemistry of Water” Problems II – Water

”The Physics and Chemistry of Water”
Problems II – Water-solute interactions and applications
7. The solubilities of Group I halides in water are tabulated below. It appears that small
ions paired with large ions give highly soluble salts, while salts containing only small
(upper left corner in the table) or only large ions (lower right corner in the table) are
only moderately soluble. Thus, large-small ion pairs remain separated in water to a
greater extent than small-small and large-large pairs do. Explain why this is so.
Molar solubilities of Group I halides
MF MCl MBr
MI
Li
0.1
19.6 20.4
8.8
Na
1.0
6.2
8.8
11.9
K
15.9
4.8
7.6
8.7
Rb
12.5
7.5
6.7
7.2
Cs
24.2 11.0
5.1
3.0
8. The figure below shows O–O radial distribution functions for water at different applied pressures (left), and for different salt conentrations in NaCl solutions (right).
At elevated pressures and salt concentrations, respectively, these two sets have some
similarities, which are a general feature of increasingly perturbed water (and actually
ice as well). What do these data sets indicate about the structure of water, and in
what sense is this a general phenomenon? (Could anything possibly cause an opposite
effect?)
9. One quantitative measure of hydrophobic (or solvophobic, in general terms) interactions is the tendency of methane molecules to adhere to each other to form a dimer,
which is approximately equivalent to ethane.
The adjacent figure shows changes in free
energy associated with moving two separate methane molecules together, computed for several liquids using the approximate relation
δGHI = ∆µ◦Ethane − 2∆µ◦M ethane
Related data for some liquids (at 10◦ C, in
cal/mol) is shown in the table below.
a) Comment on the figures for water!
b) Hydrophobic interactions are important
in biological systems. What does the pronounced temperature dependence for water (evident in the diagram) imply for the
temperature stability of proteins?
Solvent
Water
1,4-Dioxane
1-Pentanol
Cyclohexane
Methanol
δGSI
-1990
-1613
-1486
-1359
-1278
δS SI
11
3
0
1
0
δH SI
+1500
-800
-1500
-1200
-1400
10. When studying the interactions between water and solute molecules, it is often of interest how the polarity of the solute influences the interactions; e.g. solubility, solvation
shell population and structure, or aggregation. A simple example is the simulation
results below, where the charge of two different solutes – spheres the size of Cl− and
Na+ ions – were varied (note that both positive and negative charges are assigned to
each ”ion”, which thus only serves to define the size of the cavity in the water).
a) The solvation free energies are slightly asymmetric. Explain the asymmetry, and
motivate the direction of it.
b) Explain the double peak in the solvation entropy curves.
11. The hydrogen-bond contribution to interfacial energies can be estimated using data
such as that presented in the figure below (from Grigera et al., Langmuir 12, 154
(1996), also included in the notes from lecture 9).
This figure shows the hydrogen bond distribution per water molecule for pure (bulk)
water, water near hydrophobic and hydrophilic walls. Use this data to estimate the
difference in interfacial energy for water in contact with hydrophilic and hydrophobic
surfaces, assuming the area of a water molecule is 10 Å2 . And guess what – compare
with relevant literature data, and say something about the difference. What other
contributions are there?
12. The van der Waals equation of state is a first (and slight) improvement to the ideal
gas law, in that it takes the long-range attractions and finite volume of the particles
into account (via the van der Waals constants a and b):
³
a´
p + 2 (v − b) = RT
v
where v is the molar volume, a = 0.5519 Nm4 /mol2 and b = 30.49 · 10−6 m3 /mol for
water.
Many better equations of state for water have been proposed, improving the accuracy near the critical point, at high-pressure and in the supercooled region. Although
the van der Waals constants cannot account for the complex interactions in water, improvements to excluded volume and intermolecular attraction corrections are the focus
also of modern improvements to equations of state. Some of the more recent suggestions even predict the second critical point in the supercooled region (see notes from
the last lecture). Find at least one example of such a state equation in the literature,
and describe the corrections and refinements that it embraces. You are not required
to write down the equation(s) itself, since they are sometimes given in implicit form,
but I’d be happy if you do!