!!! the heat exchanged between the system and its surroundings must be exchanged at constant pressure when enthalpy is used!!!
4 Gibbs was an American, died in 1903. In Polish: Free enthalpy
Gibbs free energy is that part of enthalpy that can be effectively used (from the process, e.g. a reaction) or changed into work. The remaining part is
dissipated for the increase in disorder. In the defining formulae all the symbols refer to the reaction. (enthalpic term and entropic term). The latter term defines energy contained in the system in a disordered form.
11 In Polish: just free energy. Also A – work function.
These conditions (normal pressure, 1.013105 Pa, and 273,15 K ) are known in English as NPT (normal pressure and temperature), which is chemically speaking WRONG. The pressure given is NOT standard pressure, which is exactly 1105 Pa, and there is NOT such a concept as standard temperature. The value of 298,15 K is only a reference temperature.
Molecular interactions reduce both the impetus of the molecules hitting the wall and the frequency of hitting, this way reducing the pressure. Because both effects are directly proportional to the density of molecules, hence, inversely proportional to the molar volume, the latter quantity is squared.
The shaded parabolic area represents the P-V-T conditions where gaseous and liquid phases coexist.
„Van der Waals” loops are artefacts, true shape of isotherms is represented by the horizontal piece of straight line.
This straight line should be drawn in such a way to produce the equal
surface areas (integrals) between the straight line and the artefact line above and under the straight line.
The importance of the supercritical
fluids in analytics and technology
24 Due to some weaknesses of the Van der Waals equation some other equations
of state for real gases were suggested (Berthelot, Dieterici, Beattie- Bridgeman).
The virial equation is also too complex, esp. if we allow for the dependence of its coefficients on T.
The approach of transforming some expressions as exponential (power) series is frequently found in physical chemistry. First term alone gives the perfect gas equation of state..
For helium one can see the dependence on temperature, for a number of gases, the dependence on molar mass at 273K.
28 Equation (1, Newton) defines viscosity, where F is a force of frictioni between
two adjacent layers contacting each other on surface area A, and at velocity gradient along an axis normal to the layers equal to dv/dx.
Equation (2) is Poiseuille’s equation, where r is the radius of a capillary tube, l – its length, P – difference of pressure between its inlet and outlet, - flow time, and v – volume of gas that had flown through the tube in this time.
In the picture is mean free path of gas molecules.
x axis is a vertical axis here.
Last equation includes density =m·NA/Vm.
29 Some symbols are already explained, see „Maxwell Distribution (2)” slide.
In Sutherland (semiempiric) constants 0 and c are substance specific contants.
30 cV is specific heat (per one gram) at constant volume.
32 The last equation (Graham’s law) was experimentally discovered as early as
Equipartition comes from Latin and means equal partition (distribution) of something, here energy.
The three degrees of freedom of translation mean motion along the three axes of a 3D system of coordinates, x, y, z.
This energy is gained (rotation begins) at higher temperatures. Some light gases can hardly be excited totationally at low temperatures (just above the boiling point) and therefore deviations from the Trouton’s rule (see earlier lectures) may be observed.
Heating curve T=f(H), shown before is meant.
Increase in CV above 5/2RT and CP above 7/2RT occurs not stepwise but smoothly (gradually more and more molecules begin to vibrate.
Energy of electrons and nuclei of atoms is constant (at least it does not depend on temperature) and therefore, it is not reflected in heat capacities.
37 There are exxceptions from the D-P rule (light elements rigidly bound in the
crystal lattice, e.g. diamond 0.735R, beryllium 2R), but Einstein’s theory allows for it via exclusion of some (impossible) oscillations .
38 Z may be a measure of deviations from the Boyle’s law.
The fact that at low pressures virial equation becomes Clapeyron’s equation (dropping the second and higher virial coefficients) doesnot mean that real gases become perfect, just only that Clapeyron’s equation does describe their behaviour correctly.