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The relationship of the size of finite lattice systems and their distribution functions per particle in the grand canonical ensemble is considered. Connections between the conditional distribution functions of the one-dimensional systems of different sizes are expressed in terms of recursion expressions for different boundary conditions. The application of the proposed method of computation of distribution functions per particle in the grand canonical ensemble shows that for one-dimensional finite-size systems with interactions between nearest-neighbors, phenomena analogous to first-order phase transitions can be observed

A method for adsorption measurements on catalysts with small surface areas has been devised. The adsorption of argon has been examined on membrane catalysts made from Pd−Ni and Pd−Ru alloys before and after catalytic experiments. A sharp change of the adsorption properties and an increase in the surface areas of catalysts after reactions have been observed.

Using X-ray photoelectron spectroscopy (XPS) and differential flow methods, the surface composition and surface area of Pd−Ru alloys have been examined before and after their use as catalysts. The increase in the catalytic activity of the alloys leads to the enrichment of their surface in ruthenium. It is concluded that the catalytic activity of these alloys is governed by the composition, structure and (to a lesser degree) the roughness of the surface.

1. The catalytic activity of binary alloys of palladium containing 4.4–9.2% Ru was investigated as a function of' the conditions of their heat treatment in an atmosphere of various gases (air, H2, Ar). 2. The results of the investigation were treated according to a program permitting calculation of the parameters of the Arrhenius equation on the assumption of normal and logarithmic-normal distributions of their values. The correctness of the hypothesis of a logarithmic-normal distribution was demonstrated. 3. Raising the temperature of treatment of the alloys in a stream of air from 350 to 750°, as well as repeated treatment in a stream of air at 750°, caused an appreciable increase in the catalytic activity, associated with an increase in the preexponential factors. An even greater increase in the activity, due to a decrease in the activation energy, is also achieved as a result of treatment of the catalyst with air, and then with H2, at 750° with rapid cooling in H2.