Chapter 31, Water as a Solvent Video Solutions, Molecular Driving Forces

Problem 1

Compute the extrema of $\Delta \mu^{*}(T)$ and $\Delta \mu^{6}(T) / R T$.
(a) Use the Gibbs-Helmholtz equations $(13.40)$ and (13.41) to show that $\Delta s^{*}=0$ at the temperature at which $\mu^{*}(T)$ is a maximum or minimum.
(b) Show that $\Delta h^{*}=0$ at the temperature at which $\Delta \mu^{*} / R T$ is a maximum or minimum.

Vikash Ranjan

Numerade Educator

06:03

Problem 2

The heat capacity of protein unfolding. Figure $31.15$ shows the enthalpy of folding a protein.
(a) Determine $\Delta C_{p}$ for folding from this graph.
(b) If $\Delta S_{\text {fold }} \approx 0$ at $T=28^{\circ} \mathrm{C}$, compute $\Delta S_{\text {fold }}$ at $T=$ $100^{\circ} \mathrm{C} .$
(c) Compute $\Delta G$ fold at $T=25^{\circ} \mathrm{C}$.

Narayan Hari

Numerade Educator

04:12

Problem 3

The forces of micelle formation. A micelle contains 80 sodium dodecyl sulfate molecules, each of which has a headgroup with one negative charge at the surface. The micellar radius is $15 \mathrm{~A}$.
(a) Compute the electrostatic energy required to charge up the head groups at the surface of the spherical micelle in water at $T=300 \mathrm{~K}$.
(b) The free energy of transfer of a $\mathrm{CH}_{2}$ group from water to oil is $-0.8 \mathrm{kcal} \mathrm{mol}^{-1}$. Dodecyl chains have $12 \mathrm{CH}_{2}$ groups. Is hydrophobic association sufficient to overcome the electrostatic repulsions to form micelles?

Narayan Hari

Numerade Educator

02:25

Problem 4

'Icebergs' are less ordered than ice. Compare the entropy per molecule of inserting a nonpolar solute into water with the entropy of freezing water.

Supratim Pal

Numerade Educator

04:52

Problem 5

The electrostriction of ions in water. Formic acid (HCOOH) at infinite dilution in water at $T=298.15 \mathrm{~K}$ has partial molar volume $v=34.69 \mathrm{~cm}^{3} \mathrm{~mol}^{-1}$. The change in volume upon ionization is $\Delta v=-8.44 \mathrm{~cm}^{3} \mathrm{~mol}^{-1}$. If this $\Delta v$ is distributed uniformly among the first-shell water molecules, how much volume reduction can be attributed to each first-shell water molecule?

Sima Sarker

Numerade Educator

01:21

Problem 6

Ion solvation enthalpies scale inversely with ion radius. Ionic radii increase from $\mathrm{Li}^{*}$ to $\mathrm{Na}^{*}$ to $\mathrm{K}^{*}$, yet the enthalpies of solution decrease (see Figure 22.17). Write an electrostatic expression to rationalize this trend.

Hitendra Singh

Numerade Educator

02:55

Problem 7

Estimating the cavity size distribution in water. Suppose that the energy cost of creating a spherical cavity of radius $r$ in water is
$$
\varepsilon(r)=4 \pi r^{2} \gamma,
$$
where $y=7.2 \times 10^{-2} \mathrm{~N} \mathrm{~m}^{-1}$ is the surface tension of water at $T=300 \mathrm{~K}$.
(a) Write an expression for the size distribution $p(r)$ of cavities in water.
(b) Compute the average radius $\langle r\rangle$ of a cavity at $T=$ $300 \mathrm{~K}$.

Adriano Chikande

Numerade Educator