The heat of mixing and second virial cross coefficient of water + oxygen and water + nitrogen

Abstract

A vapour phase flow mixing calorimeter has been used to measure the heat of mixing $H_{\text{m}}^{\text{E}}$ of (0.5H₂O + 0.5O₂)(g) and (0.5H₂O + 0.5N₂)(g) at the pressure p = 0.101325 MPa and at temperatures from (373.15 to 493.15) K. The $H_{\text{m}}^{\text{E}}$ measurements were analysed using an association model for water in which the non-specific part of the interaction energy was calculated from the Stockmayer potential with the parameters ε/k = 233 K, σ = 0.312 nm, and t^∗ = 1.278. The specific part of the energy was calculated from an equilibrium constant for the association of two water molecules K_298 K = 0.36 MPa⁻¹ together with an enthalpy of association ΔH = −16.85 kJ · mol⁻¹. The second virial coefficients of O₂ and N₂ were calculated from the Lennard-Jones potential. Cross coefficients B₁₂ were calculated from a combining rule containing an adjustable parameter ξ which is known to be satisfactory for mixtures of (water + hydrogen, or nitrogen, or argon, or methane). For all these mixtures the combining rule gives ξ = 0.99, and this value gives a good fit to the new $H_{\text{m}}^{\text{E}}$ measurements on (water + nitrogen). For (water + oxygen) it was necessary to reduce ξ from 0.99 to 0.83 to fit the measurements. The values of B₁₂ for both mixtures are close to those obtained from measurements of the solubility of water in compressed oxygen or nitrogen, and confirm that B₁₂ for water–oxygen is less negative than that for water–nitrogen. This is in accord with recent theoretical calculations of the potential surfaces for water–oxygen and water–nitrogen.

Introduction

Second virial cross coefficients B₁₂ for water–nitrogen or water–oxygen are very difficult to measure, particularly at low temperatures. The use of pVT techniques is complicated by the need to make corrections for the adsorption of water on the walls of the apparatus. An alternative technique is to measure the solubility of water in compressed nitrogen or oxygen, a method which has the advantage that there are no adsorption errors. Another technique is to measure the isothermal Joule–Thomson coefficient ϕ of the gaseous mixture, where ϕ = B − T · (dB/dT). From know values of ϕ₁₁ and ϕ₂₂ of the pure component gases the cross coefficient ϕ₁₂ can be extracted. By fitting ϕ₁₂ to a suitable potential function values of B₁₂ can be obtained. However the design and operation of a Joule–Thomson calorimeter presents several problems, the control of heat leaks is difficult, and kinetic effects due to the high velocity of the gas passing through the throttle can spoil the accuracy of the measurements.

An alternative to Joule–Thomson calorimetry is to measure the heat of mixing of the gases, an experiment which yields experimental values of ϕ₁₂ from which values of B₁₂ can be calculated. The control of heat leaks is easier, and kinetic effects are negligible. The first calorimeter [1] designed for this purpose featured two identical flow calorimeters connected in series. The gases were mixed in the first calorimeter, and the gas mixture then flowed through the second calorimeter which acted as a reference. There is a small pressure drop across a flow mixing calorimeter, but by connecting two identical calorimeters in series the Joule–Thomson effect can be cancelled out. Alternatively the pressure drop can be measured and a correction for the Joule–Thomson effect can be made. Unlike pVT experiments flow calorimetric measurements are free from adsorption errors, any molecules which absorb are, in effect, part of the apparatus. A twin flow mixing calorimeter [2] operating at pressures close to atmospheric has been used to measure the excess enthalpy $H_{\text{m}}^{\text{E}}$ for (0.5H₂O + 0.5N₂)(g) at the standard pressure $p^{\circ }=0.101325\text{MPa}$ and at six temperatures in the range (373.15 to 423.15) K. A flow mixing calorimeter for measurements at high temperatures and pressures was then developed [3] and this was used to make measurements on (yH₂O + (1 − y)N₂) at seven temperatures in the range (448.2 to 698.2) K, at pressures from (0.35 to 12.59) MPa. A further development was the construction of a plug-in gas phase flow mixing calorimeter [4] which could be easily removed and modified as required. This calorimeter has proved to be invaluable for measurements on polar fluid mixtures [5] and is the one used for the measurements reported here.