Molality calculation

The numerators in molarity and molality calculations are identical, but their denominators differ greatly. Molarity deals with liters of solution, while molality deals with kilograms of solvent. A solution is a mixture of solvent and solute a solvent is the medium into which the solute is mixed. 

Calculate the number of moles of solute in the solution by multiplying the molality calculated in Step 3 by the given number of kilograms of solvent. 

A saturated solution of Csl- is 57.4 molal. Calculate the number of water molecules available to each ion. assuming an equal distribution between cations and anions. C omment on the result. 

The mean ionic activity coefficients of hydrobromic acid at round molalities (calculated by means of Equation 2) are summarized in Tables XI, XII, and XIII for x = 10, 30, and 50 mass percent monoglyme. Values of —logio 7 at round molalities from 0.005 to 0.1 mol-kg-1 were obtained by interpolating a least squares fit to a power series in m which was derived by means of a computer. These values at 298.15° K are compared in Figure 2 with those for hydrochloric acid in the same mixed solvent (I) and that for hydrobromic acid in water (21). The relative partial molal enthalpy (H2 — Hj>) can be calculated from the change in the activity coefficient with temperature, but we have used instead the following equations ... 

As indicated by the following example for a fuel gas. molal calculations have a simple and direct application to gaseous fuels, where the analyses are usually reported in percem on a volume basis. 

A 1.00% NaCl(aq) by mass solution has a freezing point of —0.593°C. (a) Estimate the van t Hoff i factor from the data, (b) Determine the total molality of all solute species, (c) Calculate the percentage dissociation of NaCl in this solution. (Hint The molality calculated from the freezing-point depression is the sum of the molalities of the undissociated ion pairs, the Na+ ions, and the Cl ions.)... 

Let a = fraction ionized. For every mole of acid added to the solution, there will be (1 — a) moles of un-ionized acid at equilibrium, a moles of H+, and a moles of anion base conjugate to the acid. This gives us a total of (1 + a) moles of dissolved particles. Then, the molality with respect to all dissolved particles is (1 + a) times the molality calculated without regard to ionization. 

Notice that the numerator in molality calculations is the same as the numerator in molarity calculations, but that the denominators are different. For molality, the denominator differs in two respects It is in kilograms rather than liters and it involves solvent rather than solution. For the preparation of molal solutions, a volumetric flask is not needed. This is a preparation based only on weight. Molality is expressed in moles/kilo-gram. 

The standard potential of the silver azide electrode, i.e., Ag AgN3(s) N3", is -0.2919 V at 25°C. If the solubility of silver chloride is 1.314xl0 5 molal, calculate that of silver azide at 25°C. (Complete dissociation may be assumed for the dissolved material in the saturated solution in each case.)... 

In the presence of 0.025 molal KCl, the solubility of the TlCl is 0.00869 molal calculate the mean ionic activity coefficient of TlCl in this solution. 

Although the pH at the temperatures of the experiments is never buffered and seldom considered in the experimental design, speciation calculations like those used to construct Fig. 5 indicate that organic acids are likely to be highly associated at the temperatures used in hydrous pyrolysis experiments. Therefore, it can be assumed that the molalities calculated from the yields reported for the experiments (see Appendix) can be equated with activities without taking account of acid dissociation (unlike the situtation described above for sedimentary basin brines). These activities, together with values of logK for reaction (28) at the experimental temperatures and pressures, allow estimates of log/H2 appropriate for each experiment. 

Procedure. Calculate the heats of solution of the two species, KF and KF HOAc, at each of the four given molalities from a knowledge of the heat capacity. Calculate the enthalpy of solution per mole of solute at each concentration. Find... 

Calculate the number of moles of ZnCl2 per kilogram of water in each solution (the molality m). Calculate the volume V of solution containing 1 kg of water at each solute concentration. Plot V vs. m. Use program Mathead, QQLSQ, or TableCurve... 

Molality is used in thermodynamic calculations where a temperature independent unit of concentration is needed. Molarity, formality and normality are based on the volume of solution in which the solute is dissolved. Since density is a temperature dependent property a solution s volume, and thus its molar, formal and normal concentrations, will change as a function of its temperature. By using the solvent s mass in place of its volume, the resulting concentration becomes independent of temperature. 

Thus, a measurement of the wet-bulb temperature, and the temperature T, allows the molal humidity, Y, to be calculated because is known. 

A finite time is required to reestabUsh the ion atmosphere at any new location. Thus the ion atmosphere produces a drag on the ions in motion and restricts their freedom of movement. This is termed a relaxation effect. When a negative ion moves under the influence of an electric field, it travels against the flow of positive ions and solvent moving in the opposite direction. This is termed an electrophoretic effect. The Debye-Huckel theory combines both effects to calculate the behavior of electrolytes. The theory predicts the behavior of dilute (<0.05 molal) solutions but does not portray accurately the behavior of concentrated solutions found in practical batteries. 

Table 1 gives the calculated open circuit voltages of the lead—acid cell at 25°C at the sulfuric acid molalities shown. The corrected activities of sulfuric acid from vapor pressure data (20) are also given. 

ITlie free energy of solution of a given substance from its normal standard state as a sohd, liquid, or gas to the hyj)othetical one molal state in aqueous solution may he calculated in a manner similar to that described in footnote for calculating the heat of solution. 

Consider the combustion of ethane (C H ) in pure oxygen. If 100 lb of ethane are available and 10% excess oxygen is supplied to ensure complete combustion, calculate (1) the amount of oxygen supplied, and (2) compositions of the reactants and products on mass and molal bases. 

In the event the mean molal heat capacity data are available with a reference temperature other than = 25°C (see Table 2-46 for data with = 0°C), the following equation can be used to calculate AH (Tj) ... 

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. 

Utilizing the above five experimentally derived rate constants and Eyring rate theory, the ten rate constants of Eq. 6 are all obtained. With the rate constants known, the probability of each occupancy state, /(ox) for example, can be calculated and finally the single channel current can be calculated as a function of molal activity of sodium ion. This is done for a 100 mV transmembrane potential in Fig. 9. It should be emphasized that Fig. 9 represents a calculation of single channel currents... 

The molality of a solution is readily calculated if the masses of solute and solvent are known (Example 10.3). 

The label on a bottle of concentrated hydrochloric acid. The label gives the mass percent of HCI in the solution (known as the assay] and the density (or specific gravity) of the solution. The molality, molarity, and mole fraction of HCI in the solution can be calculated from this information. 

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