Lewis and Randall rule

With sufficient data, equation (6.47) can be integrated to give o,. However, adequate data are available for only a few mixtures, and approximate relationships are used to estimate o,. The simplest approximation uses the Lewis and Randall rule given by11... 

Note the similarity between the Lewis and Randall rule... 

Dalton s law is based on the assumption of ideal gases so that each behaves independently and exerts the same partial pressure as it would il alone in the container. The Lewis and Randall rule assumes that the fugacitv of the gases is independent so that the gas has the same fugacity coefficient as it would have at the same total pressure when other gases were not present. 

The fugacity of species B in an ideal solution of gases is given by the Lewis and Randall rule... 

Activity coefficients of solutes at infinite dilution, jT, are nearly constant (i.e., by Henry s law). By the Lewis and Randall rule, the activity coefficients of nearly pure solutes approach unity as xf 1.0. In this case. Equation (10.11) is approximately... 

Insofar as the distribution coefficient, Kp- or Dp is constantf and not a function of composition, then Nemst s law [35] is obeyed, especially for nomeactive, simple systems. The lack of a composition dependence may be taken as an indication that a particnlar system is not reactive. In snch cases, the distribution of solute between the two phases is primarily determined by its solnbility in each phase hence Henry s law and/or the Lewis and Randall rule apply. 

The fugacity coefficient ratio J can be estimated by assuming that the Lewis and Randall rule 1 applies, at least approximately, for the mixture, so that each component has the same fugacity coefficient that it would have if it were a pure gas at the same total pressure. The Principle of Corresponding States can then be used to compare the fugacity coefficients of the three components. At p — 60 atm (61 bar) and in the temperature range from 900 to 1600 K, the reduced temperatures and pressures for the components of the equilibrium... 

It can be shown that the maximum conversion of nitrogen and hydrogen into ammonia occurs when the gases are mixed with the stoichiometric ratio. (See Problem PI5.1.) hSee Section 11.3a of Chapter 11 for a discussion of the effect of pressure on the fugacity, including the Lewis and Randall rule. 

THE LEWIS AND RANDALL RULE From Eqs. (14-3) and (14-18), it follows that... 

If, over the interval from 0 to P, the partial molar volume V for component i is equal to the molar volume v for pure component i (that is V = v then the Lewis and Randall rule holds for component / over the pressure interval 0 to P. (Note that for the ideal solution behavior to exist over the interval 0 to P, it is necessary that the Lewis-Randall rule hold for each component of the mixture over the interval 0 to P.) Thus, if V = then Eq. (14-49) reduces to... 

Similarly, if over the interval 0 to P, V = for component i in the liquid phase, then it follows as a consequence that the Lewis and Randall rule holds for component i over the pressure interval 0 to P... 

Equation (7-106) is the Lewis and Randall rule for computing the fugacity of a pure real gas. (Further methods of calculation are discussed in Gilbert Newton Lewis and Merle Randall, Thermodynamics and the Free Energy of Chemical Substances, chap. 17, McGraw-Hill Book Company, Inc., New York, 1923.)... 

The Lewis and Randall rule is found to be applicable outside the range for which Eq. (7-180) is valid. 

An alternative expression for can be obtained by utilizing the Lewis and Randall rule [Eq. (7-184)]. By use of this rule, Eq. (8-79) reduces to... 

This is expressed by the relationship known as the Lewis and Randall rule which can be stated as,... 

The applicability of the ideal solution model (or of the Lewis and Randall rule which is equivalent) may be tested on those few mixtures whose true fugacities have been obtained directly from (3 68). In Gibson and Sosnick s studies on argon-ethylene mixtures it was found that fugacities calculated by means of the rule were not in error by more than 20%, up to a pressure of 60 atm. However, at a pressure of 100 atm the error was much larger and was as much as 100 % in certain mixtures. The examination of the data on the... 

Na—system by Merz and Whittakerf shows that this mixture obeys the Lewis and Randall rule fairly closely and the errors do not exceed 20 % at 1000 atm. 

Let it be assumed, for purposes of trial, that the mixtureN2—TL2— behaves as an ideal gaseous solviiou equivalent to assuming that it obeys the Lewis and Randall-rule, equation (3 72). This rule may be... 

Using the Lewis and Randall rule and the fugacity data of Newton (Industr. Engng Chem. 27 (1935), 302) calculate the maximum percentage yield of NHg in a 1 3 nitrogen-hydrogen mixture at 450 C and 200 atm pressure. 

A useful description of an ionic solution (electrolyte) is ionic strength. The Lewis and Randall rule is stated, In dilute solutions, the activity coefficient of a given strong electrolyte is the same in all solutions of the same ionic strength. For a heterogeneous solution, this rule is expressed mathematically as... 

The Lewis and Randall rule that strong electrolytes at the same ionic strength exhibit similar ionic effects is valid to S 0.1. Solutions of higher strength... 

Gas Law Deviation. In the ideal solution the partial pressure, or activity, of a component was equal to the mol fraction times the vapor pressure of the pure component at the temperature in question. If the pressures are such that the vapor under these conditions does not obey the perfect-gas law, then a fugacity correction should be applied. For such a case, the Lewis and Randall rule would be... 

Partial pressures were replaced with fugacities calculated according to Lewis and Randall rules, and the data sets were recalculated. The rate constant k still showed considerable variations with operating conditions. Below 400 °C it decreased with space velocity and above 400 °C it increased. It decreased with both pressure and H2/N2 ratio. In view of this, Adam and Comings resorted to a graphical approach to reactor design. 

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