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Add a little potassium iodide solution to some arsenic acid solution, and warm gently. Is iodine set free Write equation. 

If the boundaries at x = a are stress free, write down the general series solution to the problem making maximum use of symmetry. Determine all of the eigenvalues and all but the last set of coefficients explicitly (e.g., leave the solution in terms of some unknown coefficients Am). Show how you would obtain these final coefficients, but don t evaluate the integrals. 

This is exact—see Problem 11-8. Notice that Eq. 11-14 is exactly what one would write, assuming the meniscus to be hanging from the wall of the capillary and its weight to be supported by the vertical component of the surface tension, 7 cos 6, multiplied by the circumference of the capillary cross section, 2ar. Thus, once again, the mathematical identity of the concepts of surface tension and surface free energy is observed. 

The effect is to write the adsorption free energy or, approximately, the energy of adsoiption Q as a sum of electrostatic and chemical contributions. A review is provided by Ref. 156. 

The derivation that follows is essentially that given by Langmuir [9] in 1918, in which one writes separately the rates of evaporation and of condensation. The surface is assumed to consist of a certain number of sites S of which S are occupied and Sq = S - S arc free. The rate of evaporation is taken to be proportional to 5, or equal tokiSi, and the rate of condensation proportional to the bare surface So and to the gas pressure, or equal to k PSo. At equilibrium. 

If there are other kinds of work, similar expressions apply. For example, with electromagnetic work (equation (A2.1.8)1 instead of pressure-volume work, one can write for the Helmholtz free energy... 

The value of the standard free energy AG depends on the choice of reference state, as does the equilibrium constant. Thus it would be safer to write the equilibrium constant K for a gaseous reaction as... 

We consider the motion of a large particle in a fluid composed of lighter, smaller particles. We also suppose that the mean free path of the particles in the fluid, X, is much smaller than a characteristic size, R, of the large particle. The analysis of the motion of the large particle is based upon a method due to Langevin. Consider the equation of motion of the large particle. We write it in the fonn... 

A consequence of writing the partition function as a product of a real gas and an ideal g part is that thermod)mamic properties can be written in terms of an ideal gas value and excess value. The ideal gas contributions can be determined analytically by integrating o the momenta. For example, the Helmholtz free energy is related to the canonical partitii function by ... 

Write out the ehitrge density diagTiiiiis for the positive ion. free radical, and negative ion of the cyclopropyl system. 

Draw bond order and free valency index diagrams for the butadienyl system. Write a counter into program MOBAS to detemiine how many iterations are executed in solving for the allyl system. The number is not the same for all computers or operating systems. Change the convergence criterion (statement 300) to several different values and determine the number of iterations for each. 

Write a structural formula for the most stable of the free radi... 

Write equations for the initiation and propagation steps for the formation of dichloromethane by free radical chlorination of chloromethane... 

The chemical potential p, of the adsorbate may be defined, following standard practice, in terms of the Gibbs free energy, the Helmholtz energy, or the internal energy (C/,). Adopting the last of these, we may write... 

On the basis of these ideas, the observed volume of a sample can be written as the sum of the volume occupied by the molecules (subscript 0) and the free volume (subscript f). Acknowledging that each of these is a function of temperature, we write... 

Polymer propagation steps do not change the total radical concentration, so we recognize that the two opposing processes, initiation and termination, will eventually reach a point of balance. This condition is called the stationary state and is characterized by a constant concentration of free radicals. Under stationary-state conditions (subscript s) the rate of initiation equals the rate of termination. Using Eq. (6.2) for the rate of initiation (that is, two radicals produced per initiator molecule) and Eq. (6.14) for termination, we write... 

We divide by Avogadro s number to convert the partial molar Gibbs free energy to a molecular quantity, and the minus sign enters because the force and the gradient are in opposing directions. Recalling the definition of chemical potential [Eq. (8.13)], we write jUj + RT In aj = ii2 + RT In 7jC, where aj... 

Alkaline Fuel Cell. The electrolyte ia the alkaline fuel cell is concentrated (85 wt %) KOH ia fuel cells that operate at high (- 250° C) temperature, or less concentrated (35—50 wt %) KOH for lower (<120° C) temperature operation. The electrolyte is retained ia a matrix of asbestos (qv) or other metal oxide, and a wide range of electrocatalysts can be used, eg, Ni, Ag, metal oxides, spiaels, and noble metals. Oxygen reduction kinetics are more rapid ia alkaline electrolytes than ia acid electrolytes, and the use of non-noble metal electrocatalysts ia AFCs is feasible. However, a significant disadvantage of AFCs is that alkaline electrolytes, ie, NaOH, KOH, do not reject CO2. Consequentiy, as of this writing, AFCs are restricted to specialized apphcations where C02-free H2 and O2 are utilized. 

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