Vapor density method

This was exactly the measurement you made in Experiment 6—it is called the vapor-density method for molecular weight determination. To... 

Exactly the same type of behavior is found for the freezing point of a solution except that the freezing point is lowei than that of the pure solvent. Thus we have two methods for molecular weight determination which are applicable to compounds with such low vapor pressure or which decompose so readily that the vapor density method cannot be used. 

Prior to the work of Eaoult, who developed (1882-1885) the cryo-scopic method for determining molecular weights of dissolved substances, and to van t Hoff s formulation (1886-1888) of the solution laws, no method was available for quantitatively determining the molecular weights of substances in solution. The vapor density method obviously could not be applied to any but very low polymers. No means was at hand for determining the state of polymerization even in instances where polymerization was suspected. 

Musculus and Meyer (12) measured the diffusion rates of some starches and dextrins in 1881. The work was designed to determine the relationship of these "isomeric or polymeric" forms to the simple sugars from which they were formed. They concluded that dextrin molecules must be much larger than those of the sugars. This work, however, preceeded Raoult s (13) development of the cryoscopic technique for the determination of the molecular weights of dissolved substances, and van t Hoff s (14) formulation of the solution laws. Further, since the vapor density method was obviously inapplicable, it was not possible for them to actually determine the degree of polymerization. 

Ealy, Jr., "Determining the Molecular Weight of a Gas," Chemical Demonstrations, A Source-book for Teachers, Vol. 1 (American Chemical Society, Washington, DC, 1988), pp. 19-20. The molar mass of butane is determined by the vapor density method. 

You are to determine the molar mass of a volatile liquid using the vapor density method. Assume you have the following equipment available to you ... 

Sometimes the density of the vapor is calculated from P, V, m, and T, and authors speak of a vapor density method. There are also a few cases in which the vapor is actually weighed. The general treatment and usefulness of these procedures zire the same as those described for PVT. 

An old method that is used occasionally is the vapor density method. In this method, a known volume of gas is weighed at a known temperature. After converting the volume of the gas to standard temperature and pressure, we can determine what fraction of a mole that volume represents. From that fraction, we can easily calculate the molecular mass of the substance. 

The monometalUc carbonyls are sufficiently volatile to permit molecular-weight determinations by the vapor-density method at temperatures generally below 100° In addi-... 

Correlation Methods Vapor densities are not correlated as functions of temperature alone, as pressure and temperature are both important. At high temperatures and very low pressures, the ideal gas law can be applied whde at moderate temperature and low pressure, vapor density is usually correlated by the virial equation. Both methods will be discussed later. 

Vapor Density Prediction A myriad of methods exist for pre-dic tion of vapor density as a function of temperature and pressure. This section will only present the most accurate and generally used methods. 

For prediction of vapor density of pm e hydi ocaihon and nonpolar gases, tbe corresponding states method of Pitzer et al. is tbe most accurate method, witb errors of less than 1 percent except in tbe critical region where errors of up to 30 percent can occur. Tbe method correlates tbe compressibibty factor by Eq. (2-75), after which tbe density can be calculated by Eq. (2-75) ... 

For hydrocarbon and nonpolar gas mixtures, the Pitzer pure component method can be used to predict vapor density by replacing the true critical properties with pseudocritical properties defined in... 

For pure organic vapors, the Lydersen et al. corresponding states method is the most accurate technique for predicting compressibility factors and, hence, vapor densities. Critical temperature, critical pressure, and critical compressibility factor defined by Eq. (2-21) are used as input parameters. Figure 2-37 is used to predict the compressibihty factor at = 0.27, and the result is corrected to the Z of the desired fluid using Eq. (2-83). 

No specific mixing rules have been tested for predicting compressibility factors for denned organie mixtures. However, the Lydersen method using pseudocritical properties as defined in Eqs. (2-80), (2-81), and (2-82) in place of true critical properties will give a reasonable estimate of the compressibihty faclor and hence the vapor density. 

Vapor densities for pure compounds can also be predicted by cubic equations of state. For hydrocarbons, relatively accurate Redlich-Kwong-type equations such as the Soave and Peng-Robinson equations are often used. Both require only T, and (0 as inputs. For organic compounds, the Lee-Erbar-EdmisteF" equation (which requires the same input parameters) has been used with errors essentially equivalent to those determined for the Lydersen method. While analytical equations of state are not often used when only densities are required, values from equations of state are used as inputs to equation of state formulations for thermal and equilibrium properties. 

If critical pressure and critical temperature are given in Pa and K, respectively, viscosities in centipoise result. The variable Io is either the low pressure pure component or mixture viscosity according to whether a pure component or mixture is being considered. For mixtures, simple molar average pseiidocritical temperature (Kay s rule), pressure, and density, and molar average molecular weight are used. The vapor density can be predicted by the methods previously discussed. Errors of above 5 percent are common for hydrocarbons and their mixtures. Experimental densities will reduce the errors slightly. 

The temperature-independent parachor [P] may be calculated by the additive scheme proposed by Quale.The atomic group contributions for this method, with contributions for silicon, boron, and aluminum from Myers,are shown in Table 2-402. At low pressures, where Pi. pc, the vapor density term may be neglected. Errors using Eq. (2-168) are normally less than 5 to 10 percent. 

Liquid surface tension is calculated using the Sugden Parachor method [242]. Neglecting vapor density, surface tension for the liquid mixture is ... 

Dihydro-lH-l,5,2-azasilaboroles derive from the 2,5-dihydro-lH-l,2-aza-boroles ( 6.5.3.3) by substitution of the carbon neighboring N by a silicon atom. They may act as four-electron donors using electron density from the C=C double bond and the N atom. The B atom behaves as an acceptor center. Two pathways are known for complex synthesis reaction with a generated transition-metal complex fragment and reaction with metal atoms by the metal-vapor synthesis method. 

The UNSAT-H model estimates evaporation from the soil in two ways. In the isothermal mode, the user must supply PET data for each day or daily climate data from which the model calculates PET by the Penman method. In the thermal mode, the model estimates evaporation from the difference in vapor density in the atmosphere and in the surface soil layer. 

Fig. 11 Wet thickness (H) of PAAm in water as a function of the PAAm graft density for samples prepared by surface-initiated ATRP on substrates with gradient of initiator density. The initiator was immobilized by the vapor-diffusion method using mixtures of l-trichlorosilyl-2-(fn/p-chloromethyl phenyl)ethan n-octyl trichlorosilane (w/w) 1 1 (squares), 1 2 (circles), and 1 5 (triangles). The inset shows a cartoon illustrating the polymer behavior. Reproduced with permission from [134] (Copyright 2003 American Chemical Society)...

Jean Baptiste-Andr Dumas, 1800-1884. Professor of chemistry at the Athenaeum and at the Sorbonne. He devised a method of determining vapor density, and developed the theory of types m organic chemistry, which he defended against Berzelius duahstic electrochemical theory. From a study of the aliphatic alcohols, Dumas and Pehgot developed the conception of homologous series, See also ref. (62). 

The first synthesis of an organic fluoride was devised by the French chemists, Dumas and Peligot.10 During a detailed study of the chemistry of methanol (wood spirit), dimethyl sulfate and anhydrous potassium fluoride were heated together in a glass vessel. Fluoromethane was formed, and characterized, its vapor density being determined (presumably by Dumas method). 

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