Kcal/mol

Metals A and B form an alloy or solid solution. To take a hypothetical case, suppose that the structure is simple cubic, so that each interior atom has six nearest neighbors and each surface atom has five. A particular alloy has a bulk mole fraction XA = 0.50, the side of the unit cell is 4.0 A, and the energies of vaporization Ea and Eb are 30 and 35 kcal/mol for the respective pure metals. The A—A bond energy is aa and the B—B bond energy is bb assume that ab = j( aa + bb)- Calculate the surface energy as a function of surface composition. What should the surface composition be at 0 K In what direction should it change on heaf)pg, and why ... 

Assuming that for water AGd is 7 kcal/mol, calculate the rate of nucleation for ice nuclei for several temperatures and locate the temperature of maximum rate. Discuss in terms of this result why glassy water might be difficult to obtain. 

Other properties of association colloids that have been studied include calorimetric measurements of the heat of micelle formation (about 6 kcal/mol for a nonionic species, see Ref. 188) and the effect of high pressure (which decreases the aggregation number [189], but may raise the CMC [190]). Fast relaxation methods (rapid flow mixing, pressure-jump, temperature-jump) tend to reveal two relaxation times t and f2, the interpretation of which has been subject to much disagreement—see Ref. 191. A fast process of fi - 1 msec may represent the rate of addition to or dissociation from a micelle of individual monomer units, and a slow process of ti < 100 msec may represent the rate of total dissociation of a micelle (192 see also Refs. 193-195). 

When plotted according to the linear form of the BET equation, data for the adsorption of N2 on Graphon at 77 K give an intercept of 0.004 and a slope of 1.7 (both in cubic centimeters STP per gram). Calculate E assuming a molecular area of 16 for N2. Calculate also the heat of adsorption for the first layer (the heat of condensation of N2 is 1.3 kcal/mol). Would your answer for Vm be much different if the intercept were taken to be zero (and the slope the same) Comment briefly on the practical significance of your conclusion. 

As a simple model of a heterogeneous surface, assume that 20% of it consists of sites of Q= 2.5 kcal/mol 45% of sites Q = 3.5 kcal/mol and the remainder, of sites of Q= 4.5 kcal/mol. Calculate Q(P, T) for nitrogen at 77 K and at 90 K, assuming the adsorption to follow the Langmuir equation with bo given by Eq. XVII-15. Calculate qsi for several 6 values and compare the result with the assumed integral distribution hinction. 

The nitrogen adsorption isotherm is determined for a finely divided, nonporous solid. It is found that at = 0.5, P/P is 0.05 at 77 K, gnd P/F is 0.2 at 90 K. Calculate the isosteric heat of adsorption, and AS and AC for adsorption at 77 K. Write the statement of the process to which your calculated quantities correspond. Explain whether the state of the adsorbed N2 appears to be more nearly gaslike or liquidlike. The normal boiling point of N2 is 77 K, and its heat of vaporization is 1.35 kcal/mol. 

Some early observations on the catalytic oxidation of SO2 to SO3 on platinized asbestos catalysts led to the following observations (1) the rate was proportional to the SO2 pressure and was inversely proportional to the SO3 pressure (2) the apparent activation energy was 30 kcal/mol (3) the heats of adsorption for SO2, SO3, and O2 were 20, 25, and 30 kcal/mol, respectively. By using appropriate Langmuir equations, show that a possible explanation of the rate data is that there are two kinds of surfaces present, 5 and S2, and that the rate-determining step is... 

Calculate the energy release in kilocalories per mole (kcal/mol) of He for the cold fusion reaction... 

Calculate also the activation energy for the reaction, again in kcal/mol, assuming that the Coulomb repulsion maximizes at 3 -y 10 cm separation of the nuclear centers. Assuming a successful cold-fusion device, how many fusions per second would generate one horsepower (1 hp) if the conversion of heat into work were 10% efficient ... 

Figure A3.7.5. Velocity-flux contour plot for FIF product from the reaction F + para- i2 HF + F1 at a reactant collision energy of 1.84 kcal mol ...

Figure B2.3.6. CM angle-velocity contour plot for the F + D2 reaction at an incident relative translational energy of 1.82 kcal mol [26], Contours are given at equally spaced intensity intervals. This CM differential cross section was used to generate the calculated laboratory angular distributions given in figure B2.3.4. (By pennission from AIP.)...

The values of this (approximate) fi (qx) calculated from this equation are smaller than 0.08 kcal/mol over the entire nuclear configuration space involved, and to a very good approximation can be neglected. 

The combination is in this case an out-of-phase one (Section I). This biradical was calculated to be at an energy of 39.6 kcal/mol above CHDN (Table ni), and to lie in a real local minimum on the So potential energy surface. A normal mode analysis showed that all frequencies were real. (Compare with the prebenzvalene intermediate, discussed above. The computational finding that these species are bound moieties is difficult to confimi experimentally, as they are highly reactive.)... 

Although extraction of lipids from membranes can be induced in atomic force apparatus (Leckband et al., 1994) and biomembrane force probe (Evans et al., 1991) experiments, spontaneous dissociation of a lipid from a membrane occurs very rarely because it involves an energy barrier of about 20 kcal/mol (Cevc and Marsh, 1987). However, lipids are known to be extracted from membranes by various enzymes. One such enzyme is phospholipase A2 (PLA2), which complexes with membrane surfaces, destabilizes a phospholipid, extracts it from the membrane, and catalyzes the hydrolysis reaction of the srir2-acyl chain of the lipid, producing lysophospholipids and fatty acids (Slotboom et al., 1982 Dennis, 1983 Jain et al., 1995). SMD simulations were employed to investigate the extraction of a lipid molecule from a DLPE monolayer by human synovial PLA2 (see Eig. 6b), and to compare this process to the extraction of a lipid from a lipid monolayer into the aqueous phase (Stepaniants et al., 1997). 

We assume in the following that the ligand is bound in a binding pocket of depth 6 —a = 7 A involving a potential barrier AU = 25 kcal/mol, similar to that of streptavidin (Chilcotti et al., 1995). We also assume that the diffusion coefficient of the ligand is similar to the diffusion coefficient of the heme group in myoglobin (Z) = 1 A /ns) as determined from Mofibauer spectra (Nadler and Schulten, 1984). 

This result reflects the Kramers relation (Gardiner, 1985). A millisecond time of unbinding, i.e.. Tact 1 ms, corresponds in this case to a rupture force of 155 pN. For such a force the potential barrier AU is not abolished completely in fact, a residual barrier of 9 kcal/mol is left for the ligand to overcome. The AFM experiments with an unbinding time of 1 ms are apparently functioning in the thermally activated regime. 

Equilibrium constants for protein-small molecule association usually are easily measured with good accuracy it is normal for standard free energies to be known to within 0.5 kcal/mol. Standard conditions define temperature, pressure and unit concentration of each of the three reacting species. It is to be expected that the standard free energy difference depends on temperature, pressure and solvent composition AA°a also depends on an arbitrary choice of standard unit concentrations. 

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