Liquid water calculations

Fig. 14. The Gibbs free energy of liquid water calculated from the Weres-Rice Model (from...

Fig. 15. The enthalpy of liquid water calculated from the Weres-Rice model (from Ref. 64>) Fig. 16. The entropy of liquid water calculated from the Weres-Rice model (from Ref. 84>) Fig. 17. The specific heat of liquid water calculated from the Weres-Rice model (from Ref. 64>)...

Figure 26. Comparison of the FIR absorption spectra of liquid water calculated for the hat-curved model (solid lines) and the rectangular-well model (dashed lines) with the same u and p values at 22.2°C (a) and 27°C (b). The parameters w. p. r./ of the hat-curved model are given in Table VII.

Kongsted, J., Osted A., Mikkelsen K.V. and Christiansen O., Molecular electric properties of liquid water calculated using the combined coupled cluster/molecular mechanics method. J. Mol.Struct. (THEOCHEM) (2003) 632 207-225. 

There is also a binding energy, though a small one, of about 15, 20 and 31 kcal/mole of substance M for most of the 6, 8 and 15 H20 compounds, respectively, reckoned on gaseous M and liquid water calculated with respect to ice these figures are approximately equal to 6—10 kcal/mole of substance M for all three groups. 

Fig. 4. (a) The radial distribution functions goH r), goo r), and gHH r)) of flexible TIP3P liquid water calculated using the NHC-RESPA and ISO-NHC-RESPA methods, (b) The error in the distribution functions as a function of time, where the exact distributions are those that have been generated from a long run with a small time step. The legends report the large time step... 

Benzene (CgHg) bums in air to produce carbon dioxide and liquid water. Calculate the heat released (in kilojoules) per gram of the compound reacted with oxygen. The standard enthalpy of formation of benzene is 49.04 kJ/mol. 

In Figs. 20c and 20d for comparison the solid curves represent analogous spectra for liquid water calculated at the temperature 27°C using the same molecular model the employed parameters are also given in Table X. The experimental data obtained by Downing and Williams [22] and Liebe et al. [19] are marked by open circles. The symbol D in Fig. 20d marks the relaxation band of water, in which the loss peak is placed at the microwave region. The profiles of the hat well, estimated for ice and water, are depicted, respectively, in Figs. 21a and 21b. 

Figure 22.1. Power spectrum of flie Raman scattering intensity of liquid water calculated from IS analysis. The solid line is for the instantaneous structures and the dashed line is for the ISs along a trajectory. The dashed-dotted straight line indicates f with a = 1.3 (f is frequency). The system contains 216 water molecules. Adapted with permission from Acc. Chem. Res., 32 (1999), 741. Copyright (1999) American Chemical Society.

Osted, A., J. Kongsted, K. V. Mikkelson, P.-O. Astrand, and 0. Christiansen, Statistical mechanically averaged molecular properties of liquid water calculated using the combined coupled cluster/molecular dynamics method. Chem. Phys., 2006.124 124503-124516. 

The boiling-point rise can be considered negligible as well as the heat of solution. Each evaporator has a 1000-ft surface area and the heat-transfer coefficients are Ui = 500 and U2 = 700 btu/h ft °F. The feed enters evaporator number 2 and steam at 100 psia is fed to number 1. The pressure in the vapor space of evaporator number 2 is 0.98 psia. Assume that the heat capacity of all liquid solutions is that of liquid water. Calculate the feed rate F and the product rate Z, of a solution containing 25% solids. Hint Assume a feed rate of, say, F = 1000 Ib /h. Calculate the area. Then calculate the actual feed rate by multiplying 1000 by 1000/calculated area.)... 

Fig. 7.5 EOM-CCSD/aug-cc-pVTZ results for the absorption spectrum of liquid water. Calculations with n = 20. Vertical lines are the experimental peak positions from Heller [58] (Expl) and Hayashi [59] (Exp2)...

Temperature dependences of the fraction of water molecules with tetrahedral arrangement of the nearest four neighbors in liquid water calculated at the liquid-vapor coexistence curve for two water models are shown in Fig. 5. There are less than 10% of such water molecules at the liquid-vapor critical point. Upon cooling, more water molecules gain tetrahedral ordering and their fraction achieves 50% at ambient conditions. At some temperatures below the freezing temperature, fraction of tetrahedrally ordered water molecules in supercooled liquid water shows a rapid or even a stepwise increase. 

The reports were that water condensed from the vapor phase into 10-100-/im quartz or pyrex capillaries had physical properties distinctly different from those of bulk liquid water. Confirmations came from a variety of laboratories around the world (see the August 1971 issue of Journal of Colloid Interface Science), and it was proposed that a new phase of water had been found many called this water polywater rather than the original Deijaguin term, anomalous water. There were confirming theoretical calculations (see Refs. 121, 122) Eventually, however, it was determined that the micro-amoimts of water that could be isolated from small capillaries was always contaminated by salts and other impurities leached from the walls. The nonexistence of anomalous or poly water as a new, pure phase of water was acknowledged in 1974 by Deijaguin and co-workers [123]. There is a mass of fascinating anecdotal history omitted here for lack of space but told very well by Frank [124]. 

TIk experimentally determined dipole moment of a water molecule in the gas phase is 1.85 D. The dipole moment of an individual water molecule calculated with any of thv se simple models is significantly higher for example, the SPC dipole moment is 2.27 D and that for TIP4P is 2.18 D. These values are much closer to the effective dipole moment of liquid water, which is approximately 2.6 D. These models are thus all effective pairwise models. The simple water models are usually parametrised by calculating various pmperties using molecular dynamics or Monte Carlo simulations and then modifying the... 

Fig. 7.12 Experimental and calculated infrared spectra for liquid water. The black dots are the experimental values. The thick curve is the classical profile produced by the molecular dynamics simulation. The thin curve is obtained by applying quantum corrections. (Figure redrawn from Guilbt B 1991. A Molecular Dynamics Study of the Infrared Spectrum of Water. Journal of Chemical Physics 95 1543-1551.)...

In Fig. 5.21, from Dawson s paper, the uptake at X for the 250°C-outgassed sample is dose to the calculated value for a monolayer of water with a (H20) = 101 A. Point X has therefore been ascribed to a close-packed monolayer of water on a hydroxylated surface of rutile. The fact that the differential entropy of adsorption relative to the liquid state (calculated from the isosteric heat of adsorption) changes sharply from negative to positive values in this region with A s 0 at X was regarded as supporting evidence. ... 

The diagram in Fig. 11-101 presents enthalpy data for LiBr-water solutions. It is needed for the thermal calculation of the cycle. Enthalpies for water and water vapor can be determined from the table or properties of water. The data in Fig. 11-101 are apphcable to saturated or subcooled solutions and are based on a zero enthalpy of liquid water at 0°C and a zero enthalpy of solid LiBr at 25°C. Since... 

Heat of combustion is the heat liberated or absorbed when one gram mole of the substance is completely oxidized to liquid water and CO2 gas at one atmosphere and 20°C or 25°C. (Cj-C hydrocarbons and cyclohexane at 25°C, others at 20°C). The gross heating value in Btu/ft could be calculated as follows ... 

In this case, Ptot is the measured pressure. The partial pressure of water vapor, Ph2o, is equal to the vapor pressure of liquid water. It has a fixed value at a given temperature (see Appendix 1). The partial pressure of hydrogen, PH2, can be calculated by subtraction. The number of moles of hydrogen in the wet gas, h2, can then be determined using the ideal gas law. 

E6.2 The fugacity of liquid water at 298.15 K is approximately 3,17 kPa. Take the ideal enthalpy of vaporization of water as 43.720 TmoD1, and calculate the fugacity of liquid water at 300 K. 

For the flow of steam, a highly non-ideal gas, it is necessary to apply a correction to the calculated flowrate, the magnitude of which depends on whether the steam is saturated, wet or superheated. Correction charts are given by Lyle<5) who also quotes a useful approximation16 — that a steam meter registers 1 per cent low for every 2 per cent of liquid water in the steam, and 1 per cent high for every 8 per cent of superheat. 

He placed two 150.-g samples of water at 0.00°C (one ice and one liquid) in a room kept at a constant temperature of 5.00°C. He then observed how long it took for each sample to warm to its final temperature. The liquid sample reached 5.00°C after 30.0 min. However, the ice took 10.5 h to reach 5.00°C. He concluded that the difference in time that the two samples required to reach the same final temperature represented the difference in heat required to raise the temperatures of the samples. Use Black s data to calculate the enthalpy of fusion of ice in kj-mol-1. Use the known heat capacity of liquid water. 

Calculate the standard entropy of vaporization of water at 85°C, given that its standard entropy of vaporization at 100.°C is 109.0 J-K -mol 1 and the molar heat capacities at constant pressure of liquid water and water vapor are 75.3 J-K -mol 1 and 33.6 J-K -mol, respectively, in this range. 

We will illustrate the necessity of including solute from CCN by a simple calculation, recalling that pH = 5.6 is the supposed equilibrium value for water in contact with 300 ppm of CO2. (That calculation will appear later.) In clean, marine air, the concentration of submicrometer aerosol particles (by far the most numerous) is small, say 0.25 pg m . It is known from measurements that the molecular form is often NH4HSO4, and we assume it is all dissolved in 0.125 g/m of liquid water in a cloud - which is typical for fair-weather marine clouds. Thus the average concentration of sulfate ion [SO4 ], mol/L, is... 

Fig. 16-4 pH sensitivity to SO4- and NH4. Model calculations of expected pH of cloud water or rainwater for cloud liquid water content of 0.5 g/m. 100 pptv SO2, 330 ppmv CO2, and NO3. The abscissa shows the assumed input of aerosol sulfate in fig/m and the ordinate shows the calculated equilibrium pH. Each line corresponds to the indicated amoimt of total NH3 + NH4 in imits of fig/m of cloudy air. Solid lines are at 278 K, dashed ones are at 298 K. The familiar shape of titration curves is evident, with a steep drop in pH as the anion concentration increases due to increased input of H2SO4. (From Charlson, R. J., C. H. Twohy and P. K. Quinn, Physical Influences of Altitude on the Chemical Properties of Clouds and of Water Deposited from the Atmosphere." NATO Advanced Research Workshop Acid Deposition Processes at High Elevation Sites, Sept. 1986. Edinburgh, Scotland.)... 

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