The Dimerization Constant of Nitrobenzene in Benzene: A Critique of Partition as a Thermodynamic Method

Abstract

The dimerization constant (K) of nitrobenzene in benzene was determined at 5.5 and 25 °C by means of partition (solvent extraction). A hydration study was performed at these temperatures to determine the extent of hydration of nitrobenzene in the benzene phase. Published freezing point depression data for the anhydrous benzene–nitrobenzene system were used to obtain a value of K at 5.5 °C. The heats of solution of nitrobenzene in benzene (anhydrous) were determined at 25 °C. The heat of solution and freezing point depression data were combined to obtain a value of K for the anhydrous system at 25 °C. At each of 5.5 and 25 °C the value of K determined by partition was significantly smaller than the corresponding value of K for the anhydrous system, and the discrepancy was larger at 25 than at 5.5 °C. It was found that by fitting a simple electrostatic model to the difference in the values of K found at 5.5 °C, the difference at 25 °C could be predicted.

The activity coefficients of some polar solutes in benzene

“…The result that the activity coefficients of o-C6H4C12 fall below those of C6H5N02 at low concentrations, despite the fact that C6H,N02 has a 'The uncertainty in the h value of benzene is about 0.025 deg/rnolal (7). In the C6H,-o-C6H,C1, system for example this uncertainty produces an uncertainty of about 0.020 units in y when the concentration is 0.50 molal.…”

“…The connection between the j-function and the activity coefficient is (7): [2] and doing the integrations provides a closed form expression for In yTfthat is lengthy but straightforward enough to use (7). This expression, together with the entries in Table 2, provides the smoothed values of yTF given at rounded molalities in Table 3.…”

The Calculation of Effective Pair Potentials in Solution from Activity Coefficient Data: Nitrobenzene in Benzene

“…20 where v, -the molecular volume of the pure solvent, D, ' -the partial molecular volume of the solute in the solvent at infinite dilution of the solute, V -volume of the system, W,, E the potential of mean force (see below) between two solute molecules at positions r, and r, in the infinitely dilute solution, W,, -the potential of -mean force between one solute molecule and one solvent molecule at positions r, and r, in the infinitely dilute solution. It is taken as understood in [5] that all the terms are functions of pressure and temperature.…”

“…This system has been extensively studied by a variety of methods including freezing point depression (1,(13)(14)(15)(16)(17), vapor pressure lowering (1 8), polarization measurements (1,19), and calorimetry (20). In a previous article (20) freezing point depression and calorimetric data were combined to obtain values for the dimerization constant (or equivalently the stoichiometric activity coefficient) of nitrobenzene in benzene over the range 5.5 (freezing point of benzene) to 25 "C. In the present work, Hill's Constant Pressure Solution Theory (21)(22)(23), and the connection between this theory and McMillan-Mayer theory (23), are used to derive a relationship between the dimerization constant of nitrobenzene in benzene and the sum of two cluster integrals. One of these integrals involves the nitrobenzene-nitrobenzene pair potential in benzene, and the other, the nitrobenzene-benzene pair potential in benzene.…”