![]() Meyer vigorously pointed toward this same statement in "the spontaneity of processes generally described as "mixing", that is, combination of two different gases initially each at pressure, p, and finally at total pressure, p, has absolutely nothing to do with the mixing itself of either" ( 7). Thus, the mixing process for gases is actually a spontaneous process due to an increase in volume. Then, on a molecular basis, because the density (closeness) of energy levels increases in the larger volume, and therefore there is greater dispersal of the molecular energies on those additional levels, there are more possible arrangements (more microstates) for the mixture than for the individual constituents. From a macro viewpoint, the initial energy of each constituent becomes more dispersed in the new larger volume provided by the combined volumes of the components. The entropy effects in gas expansion into a vacuum, as described previously, are qualitatively similar to gases mixing. Therefore, this means closer energy levels, far more than were available for the motional energy in the liquid - and a greatly increased number of microstates for the vapor. (All of the enthalpy of vaporization is needed to break intermolecular bonds in the liquid.) However in the case of liquid to vapor, there is a huge expansion (a thousand times increase)in volume. Similarly, a liquid at its vaporization temperature has the same energy as its gas molecules. Thus, that previous motional energy of intermolecular vibration that was in the crystal is now distributed among a far greater number of new translational energy levels, and that means that there are many more accessible microstates than in the solid. This might be compared to a fantastically huge dance in which the individual participants don't move very far (takes a water molecule >12 hours to move a cm at 298K) but they are holding hands and then releasing to grab new partners far more frequently than billions of times a second. ![]() When the liquid forms, there is rapid breaking of hydrogen bonds (trillionths of a second) and forming new ones with adjacent molecules. However, a change in the motional energy - not an increase in the quantity of energy - occurs from the transfer of vibrational energy in the ice crystal to the liquid. Of course, it is released when the temperature of the system drops below the freezing/melting point).The process is isothermal, and therefore there is no energy transferred to the system to increase motional energy. (This potential energy remains unchanged in a substance throughout heating, expansion, mixing, subsequent phase change to a vapor, or mixing. Because melting involves bond-breaking, it is an entropy increase in the potential energy of the substance involved. ![]() The rigid tetrahedral structure is no longer present in liquid water but the presence of a large number of hydrogen bonds is shown by the greater density of water than ice due to the even more compact hydrogen-bonded clusters of H 2O.) Quantitatively, the entropy increase in this isothermal dispersal of energy from the surroundings is ΔH Fusion /T. Many, but not all of the hydrogen bonds in crystalline ice are broken. (“To the degree required” has special significance in the melting of ice. ![]() To change a solid to a liquid at its melting point requires large amounts of energy to be dispersed from the warmer surroundings to the solid for breaking the intermolecular bonds to the degree required for existence of the liquid at the fusion temperature. ![]() The entropy change is unknown (but likely not zero) because there are equal numbers of molecules on both sides of the equation, and all are gases.\) ![]()
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