Heats of dilution

To correlate measurements of the heats of dilution of aqueous sodium chloride solutions with acthity coefficients derived from measurements of e.m.f. and transport numbers. 

Heats of dilution of sodium chloride solutions have been measured at several temperatures by Gulbransen and Robinson (J. Amer. Chem. Soc. 1934, 56, 2637). In table 1 below relating to measurements at 25 C, m denotes molality and the subscripts 1 and 2 relate to the initial and final concentrations respectively. is the heat of 

Ratios of the activity coefficients of sodium chloride in aqueous solutions of various concentrations at 15 °C, 25 °C, and 35 °Chave been determined by Janz and Gordon (J. Amer. Chem. Soc. 1943, 65, 218) by combining measurements of e.m.f. of concentration cells with independent measurements of transport number. Their data can be fitted by the formula (compare problems 81 and 86) 

The theoretical values of A were calculated (compare problem 78) by taking for the dielectric constant D of water the mean of the smoothed values given by Wj man and Ingalls (J. Amer. Chem. Soc. 1938, 60, 1182) and by Drake, Pierce, and Dow (Phys. Rev. 1930, 35, 613). The x alues of dDjdT at 25 °C taken from the same sources are —0.360 deg Euxd —0.362 deg respectively. We accordingly use dD/dT = —0.361 deg-i at 25 C. 

The coeflScient of thermal expansion of water at 25 °C (Dorsey, The properties of ordinary water-substance . Reinhold, 1940) is 1 dF 

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The Debye-Htickel limiting law predicts a square-root dependence on the ionic strength/= MTLcz of the logarithm of the mean activity coefficient (log y ), tire heat of dilution (E /VI) and the excess volume it is considered to be an exact expression for the behaviour of an electrolyte at infinite dilution. Some experimental results for the activity coefficients and heats of dilution are shown in figure A2.3.11 for aqueous solutions of NaCl and ZnSO at 25°C the results are typical of the observations for 1-1 (e.g.NaCl) and 2-2 (e.g. ZnSO ) aqueous electrolyte solutions at this temperature. 

Figure A2.3.11 The mean aetivity eoeffieients and heats of dilution of NaCl and ZnSO in aqueous solution at 25°C as a fiinotion of z zjV I, where / is the ionie strength. DHLL = Debye-Htiekel limiting law.

Figure A2.3.15 Deviations (A) of the heat of dilution /7 and the osmotie eoeflfieient ( ) from the Debye-Htiekel limiting law for 1-1 and 2-2 RPM eleetrolytes aeeordmg to the DHLL + B2, HNC and MS approximations.

Absorber is a component where strong absorber solution is used to absorb the water vapor flashed in the evaporator. A solution pump sprays the lithium bromide over the absorber tube section. Cool water is passing through the tubes taking refrigeration load, heat of dilution, heat to cool condensed water, and sensible heat for solution coohng. 

The heat absorbed when unit mass of solute is dissolved in an infinite amount of solvent is the differential heat of solution for zero concentration, Lo, and this is evidently equal to the integral heat of solution for concentration s plus the integral heat of dilution for concentration s ... 

The heat absorbed when a mol of solvent is added reversibly to the solution at constant temperature (T) and pressure (P) is the heat of dilution, Q (x, P, T). 

In the above investigation Q (x, T) has the significance of a heat of dilution, i.e., it denotes the heat absorbed when more solvent is added to a solution of concentration x. If we consider a solid salt which is dissolved in a solvent, Q (x, T) has the significance of a heat of solution. If we consider a saturated solution we recover the case treated in 132. The vapour pressure p of the solution is now a function of temperature alone, since the concentration of a saturated solution is, at a given pressure, completely defined by the temperature, and it alters only very slightly with change of pressure. 

To calculate P at any other temperature we integrate Kirchhoff s equation for the heat of dilution ... 

If we assume that the heat of dilution is zero, which limits the discussion to dilute solutions ... 

It has been found, however, that this case is somewhat complicated by the formation of definite compounds in some amalgams still the general results are in agreement with the theory. Some exceptional cases found by Meyer have recently been shown to depend on the large heats of dilution of the particular amalgams (Smith, Zeitschr. anorg. Chcm., 58, 881). 

Reactions between concentrated solutions e.g., the electromotive force of the lead accumulator corresponds almost exactly with the heat of dilution of the acid when the latter is concentrated, whilst in dilute solutions the difference is very great (Nernst, Wiecl. Ann., 53, 57,1894). 

Sulfuric acid. As a 10 to 20% v/v solution, sulfuric acid can be used to clean 300 series SS, as well as other steels and metals, but not galvanized steel or magnesium. The cleaned SS can then be passivated with nitric acid. In practice, sulfuric acid is seldom used, except by specialist cleaning companies, because of its high heat of dilution and terrible burning effect on skin and other tissues. Add acid to water. 

FIG. 29 Integral heats of dilution for a solution of ammonium dodecane 1-sulfonate in water. 

The heats of dilution of sodium dodecyl sulfate in 0.0001 M NaCl and 0.145 M NaCl solutions have been determined in a study of the thermodynamics of the reaction with cetylpyridinium chloride. The heat of dilution includes the heat of dilution of the monomer, the heat of micellization, and the heat of dilution of the micelle [71]. 

The reaction is highly exothermic due to the heat of neutralization and the heat of dilution of strong acids and a strong base (50% caustic is the currently available strength). At present there are few theoretical data on the enthalpies involved in the neutralization reaction between sulfonic acid and sodium hydroxide solution. Values of about 100 kJ/gmol have been found experimentally. The following reactions and heats are involved ... 

AHx heat of dilution of sulfonic acid in water (to infinite solution)... 

AH2 heat of neutralization of LAS A//3 heat of dilution of 100% H2S04 to infinite dilution AHa heat of neutralization of H2S04 AHs heat of dilution of 50% NaOH to infinite dilution... 

The chemical potential difference —ju may be resolved into its heat and entropy components in either of two ways the partial molar heat of dilution may be measured directly by calorimetric methods and the entropy of dilution calculated from the relationship A i = (AHi —AFi)/T where AFi=/xi —/x or the temperature coefficient of the activity (hence the temperature coefficient of the chemical potential) may be determined, and from it the heat and entropy of dilution can be calculated using the standard relationships... 

The results of determinations of heats of dilution for several polymer-solvent systems over wide ranges in concentration are shown in Fig. 

In order to minimize confusion, only the curves representing the smoothed results are shown for squalene-benzene, polyisoprene-ben-zene, and rubber-benzene. Calorimetric methods were applied to those polymers of comparatively low molecular weight temperature coefficients of the activity were used for the rubber-benzene mixtures. The ratio of the heat of dilution to the square of the volume fraction t 2, which is plotted against in Fig. 112, should be independent of the concentration according to the treatment of interactions... 

Fig. 113.—Comparison of observed entropies of dilution (points and solid lines with results calculated for ASi according to Eq. (28) (broken line). Data for polydimethyl-siloxane, M =3850, in benzene, A (Newing ), obtained from measured activities and calorimetric heats of dilution. Entropies for polystyrene (Bawn et in methyl ethyl ketone,, and in toluene, O, were calculated from the temperature coefficient of the activity. The smoothed results for benzene solutions of rubber, represented by the solid curve without points, were obtained similarly.

Gee and Orr have pointed out that the deviations from theory of the heat of dilution and of the entropy of dilution are to some extent mutually compensating. Hence the theoretical expression for the free energy affords a considerably better working approximation than either Eq. (29) for the heat of dilution or Eq. (28) for the configurational entropy of dilution. One must not overlook the fact that, in spite of its shortcomings, the theory as given here is a vast improvement over classical ideal solution theory in applications to polymer solutions. 

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