Saturation molal

If equilibrium has not been reached between a mixture of components, the condition is referred to as partial saturation. At partial saturation the gas mixture obeys real gas laws. There are several ways to express the concentration of a vapor in a mixture of gases. Most often, weight or mole fraction is used. Other definitions are relative saturation (relative humidity), molal saturation (molal humidity) and absolute saturation (absolute humidity). 

Another way to express vapor concentration is by molal saturation, which is the ratio of the moles of vapor to the moles of vapor-free gas. 

Define relative saturation (humidity), molal saturation (humidity), absolute saturation (humidity), and humidity by formulas involving partial pressures of the gas components. 

Figure 28 shows the key features of the humidity chart. The chart consists of the following four parameters plotted as ordinates against temperature on the abscissas (1) Humidity H, as pounds of water per pound of dry air, for air of various relative humidities (2) Specific volume, as cubic feet of dry air per pound of dry air (3) Saturated volume in units of cubic feet of saturated mixture per pound of dry air and (4) latent heat of vaporization (r) in units of Btu per pound of water vaporized. The chart also shows plotted hiunid heat (s) as abscissa versus the humidity (H) as ordinates, and adiabatic humidification curves (i.e., humidity versus temperature). Figure 28 represents mixtures of dry air and water vapor, whereby the total pressure of the mixture is taken as normal barometric. Defining the actual pressure of the water vapor in the mixture as p (in units of mm of mercury), the pressure of the dry air is simply 760 - p. The molal ratio of water vapor to air is p/(760-p), and hence the mass ratio is ... 

In the case of a sparingly soluble substance, if each of the quantities in (64) is divided by Avogadro s constant, we confirm the statement made above— namely, that, if AS at per ion pair is added to the contribution made to the entropy of the crystal by each ion pair, in this way we evaluate the contribution made by one additional ion pair to the entropy of the saturated solution and it is important to grasp that this contribution depends only on the presence of the additional pair of ions in the solution and does not depend on where they have come from. They might have been introduced into the solution from a vacuum, instead of from the surface of a solid. In (64) the quantities on the right-hand side refer to the solution of a crystal, but the quantity (S2 — Si) does not it denotes merely a change in the entropy of a solution due to the presence of additional ions, which may have come from anywhere. When Si denotes the entropy of a sufficiently large amount of solution, (S2 — Si) is the partial molal entropy of the solute in this solution. 

When solid AgCl is in contact with its saturated aqueous solution, we have found that, if additional ion pairs are transferred from the surface of the crystal to the solution, the total change of entropy is equivalent to 52.8 e.u Since the entropy of the solid is 23.0 e.u., we find that the partial molal entropy of AgCl in its saturated aqueous solution at 25°C is... 

Since the saturated solutions of AgT and AgCl are both very dilute, it is of interest to examine their partial molal entropies, to see whether we can make a comparison between the values of the unitary terms. As mentioned above, the heat of precipitation of silver iodide was found by calorimetric measurement to be 1.16 electron-volts per ion pair, or 26,710 cal/mole. Dividing this by the temperature, we find for the entropy of solution of the crystal in the saturated solution the value... 

The entropy of solid Agl is a little larger than that of AgCl, namely, 27.1 e.u., as compared with 23.0 e.u. Using (64) we find for the partial molal entropy of Agl in its saturated solution the value... 

Let x and x denote the mole fractions of the two sparingly soluble solids in their respective saturated solutions let y and y denote their mole ratios, m and ml their molalities, and a and a their activities on the molality scale. If the saturated solutions are sufficiently dilute, we may, with sufficient accuracy, neglect the differences between the four ratios x/x, y/yf, m/m, and a/a. We can express the difference between the cratic terms by means of any of these quantities, thus,... 

In agreement with (98), the left-hand side is just the standard free energy of solution AF°. Here y, as defined by (106), is the usual activity coefficient on the molality scale. In particular, when the solid is in contact with its saturated solution, there is no change in the free energy when additional ions are taken into solution. In this case, if in (108) we write m, t and y,at, the values of m and y in the saturated solution, we may set AF equal to zero. This will be discussed in Sec. 100. 

Finally, as an example of a highly soluble salt, we may take sodium chloride at 25° the concentration of the saturated solution is 6.16 molal. The activity coefficient of NaCl, like that of NaBr plotted in Fig. 72, passes through a minimum at a concentration between 1.0 and 1.5 molal and it has been estimated2 that in the saturated solution the activity coefficient has risen to a value very near unity. Writing y = 1.0, we find that the work required to take a pair of ions from the surface of NaCl into pure water at 25° has the rather small value... 

Lithium Carbonate in Aqueous Solution. As an illustration, we shall evaluate the conventional AF° and AS0 for lithium carbonate in aqueous solution. At 25°C the concentration of the saturated solution is 0.169 molal.1 In this solution the molality of the Li+ ion is of course 0.338. The activity coefficient of the Li2CO.t in the saturated solution is not accurately known, but its value is not far from y,at = 0.59. Substituting in (186) we have then... 

The saturated solution of silver sulfate in water at 25°C has a molality equal to 0.02689, and the activity coefficient y of tho solute in this saturated solution is 0.533. 

The saturated solution of potassium iodate in water at 25°C has a molality equal to 0.43. Taking the activity coefficient y in this saturated solution to be 0.52, find the conventional free energy of solution at 25°C, and calculate in electron-volts per ion pair the value of L for the removal of tho ions K+ and (IOs) into water at 25°C. 

C12-0037. A saturated solution of hydrogen peroxide in water contains 30.% by mass H2 O2 and has a density of 1.11 g/mL. Calculate the mole fractions, molarity, and molality of this solution. 

Metal Temp. °C Molality of saturated solution Temp. °C Molality of saturated solution... 

They used a value of 4.1 x 10-11 molal s-1 for rmax, the maximum reaction rate, and 1.4 x 10-5 molal for KA, the half saturation constant. We consider application of this kinetic law in detail in Chapter 28. 

Since the enzyme concentration was not observed separately from the rate constant, we carry the product k+ m. in this equation as rmax, the maximum reaction rate. Bekins el al. (1998) fitted their results using values of 1.4 mg kg-1 day-1 (or 1.7 x 10-10 molal s-1) for rmax, and 1.7 mg kg-1 (1.8 x 10-5 molal) for Ka, the half-saturation constant. In a field application lasting many years, of course, the assumption that enzyme concentration remains constant might not be valid,... 

Following the calculations in Section 18.5, we take a rate constant k+ for sulfate reduction of 10-9 mol mg-1 s-1, a half-saturation constant for acetate of 70 p, molal, and a growth yield of 4300 mg mol-1 from a study of the kinetics of Desulfobacter postgatei by Ingvorsen el al. (1984). We set a value for KA, the half-saturation constant for sulfate, of 200 p molal, as suggested by Ingvorsen el al. (1984) and Pallud and Van Cappellen (2006). 

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