Hertz—Knudsen equation

This equation is commonly designated the Hertz-Knudsen equation. 

The assumptions inherent in the derivation of the Hertz-Knudsen equation are (1) the vapor phase does not have a net motion (2) the bulk liquid temperature and corresponding vapor pressure determine the absolute rate of vaporization (3) the bulk vapor phase temperature and pressure determine the absolute rate of condensation (4) the gas-liquid interface is stationary and (5) the vapor phase acts as an ideal gas. The first assumption is rigorously valid only at equilibrium. For nonequilibrium conditions there will be a net motion of the vapor phase due to mass transfer across the vapor-liquid interface. The derivation of the expression for the absolute rate of condensation has been modified by Schrage (S2) to account for net motion in the vapor phase. The modified expression is... 

The third, fourth, and fifth assumptions inherent in the Hertz-Knudsen equation are also used in the derivation of Eq. (60). Maa (M3) has shown by experimental studies that Eq. (60) provides a good model for predicting the net rate of phase change. Maa (M4) and O Connor (Ol) have shown that if these assumptions are replaced by significantly less restrictive ones, and the derivation repeated, the calculated values of the net rate of phase change differ by less than 10% under the most extreme conditions. 

If a surface with a finite number of sites is exposed to a gas, the number of molecules hitting the surface is given by the Hertz-Knudsen equation ... 

According to Turkdogan [5] the maximum value of in Eq.(9.65) is obtained by setting t equal to unity and zero activation (adsorption) energy (Eg = 0). Equation (9.65) then transforms to the classical Hertz-Knudsen equation for the number of moles striking a imit surface area per unit time Rma ... 

During the CVD process, the molecules to be incorporated into the lattice of substrate must be delivered to the surface from the bulk gas. The flux of incident molecules onto the substrate surface is defined by the Hertz-Knudsen equation [3,... 

The method of quantitative vaporization is based on the Hertz Knudsen equation [87]. The mass loss rate dm/dt of a substance A, vaporized at the temperature T in the Knudsen cell, is determined by weighing, in addition to the ion intensity measurement, k is obtained by the equatiop... 

What does this correlation imply concerning the relationship between activation energy for chemisorption and fractional surface coverage Hint Start your derivation with the Hertz-Knudsen equation as given in the text). 

The maximum theoretical rate of vaporization V (kgm s ) from the surface of a pure liquid or solid under its own vapour pressure is given by the Hertz-Knudsen equation, which can be derived from the kinetic theory of gases ... 

Eq,(3) is approximately reduced to the so-called Hertz-Knudsen equation in which the Interference of evaporation and condensation fluxes is not taken into account. Under the condition (4), Eq.(3) becomes Identical with Eq.(2), in consequence, we obtain... 

The surface sites occupied by adsorbed molecules are not available for other molecules. In this case, only free sites of the surface are available for further adsorption. This part is equal to (1 - 0). And if we assume that the adsorption sites are equivalent and have unit fixed occupancy, then in accordance with the Hertz-Knudsen equation [9], the adsorption rate of molecules from the gaseous phase is determined by the following equation ... 

From the kinetic theory of gases, an expression for the net-mass flux at the interphase can be derived based on the works of Hertz [223] and Knudsen [224]. From a statistical consideration under the assumption of a Maxwell-Boltzmann distribution for the velocity of the gas molecules, the maximum condensation mass flux can be calculated. The evaporation mass flux has to equal the condensation mass flux at equilibrium. The resulting Hertz-Knudsen equation for calculating the area specific net-mass flux is given below ... 

In the calculations of partial pressures (Hastie et al., 1968), ionization of dimeric molecules accompanied by loss of more than one atom (especially in reaction steps that can interfere with ionization of monomers) was assumed to be improbable. This assumption was experimentally confirmed in studies of the congruent evaporation of SmCl3 (Chervoimyi et al., 1974). Isothermal evaporation of a sample of known weight was carried out at several temperatures, and the saturated vapor pressure was determined by the Hertz-Knudsen equation. In each experiment, the state of an imsaturated vapor caused by the presence of an nonvolatile species ( 1.5% SmCl2) was determined in the end of... 

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