Calculating with Molality

Sample Problem D A solution was prepared by dissolving 17.Ig of sucrose (table sugar, C12H22O11) 125 g of water. Find the molal concentration of this solution. 

To find molality, you need moles of solute and kilograms of solvent. The given grams of sucrose must be converted to moles. The mass in grams of solvent must be converted to kilograms. 

Use the periodic table to compute the molar mass of C12H22O11 = 342.34 g/mol 

The answer is correctly given to three significant digits. The unit mol solute/kg solvent is correct for molality. 

Sample Problem E A solution of iodine, I2, in carbon tetrachloride, CCI, is used when iodine is needed for certain chemical tests. Howmuch iodine must he added to prepare a 0.480 m solution of iodine in CCI4 if 100.0 g of CCI4 is used  

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Vapor-pressure lowering is calculated with mole fraction freezing-point depression and boiling-point elevation are calculated with molality and osmotic pressure is calculated with molarity. 

Calculate the molality of a solution with mole fraction 0.100 of C2H,OH in water. Ans. Assume 1.00 mol total, which contains ... 

Equation 2.67 indicates that the standard enthalpy and entropy of reaction 2.64 derived from Kc data may be close to the values obtained with molality equilibrium constants. Because Ar// is calculated from the slope of In AT versus l/T, it will be similar to the value derived with Km data provided that the density of the solution remains approximately constant in the experimental temperature range. On the other hand, the error in ArSj calculated with Kc data can be roughly estimated as R In p (from equations 2.57 and 2.67). In the case of water, this is about zero for most solvents, which have p in the range of 0.7-2 kg dm-3, the corrections are smaller (from —3 to 6 J K-1 mol-1) than the usual experimental uncertainties associated with the statistical analysis of the data. 

With the search variables listed above, the calculation of the remaining molalities (iterative state variables) can be easily performed sequentially by using the equilibrium expressions for the reaction shown in Table 1 and the calculated activity coefficients. The equations are used in the order in which they appear in Table 1. The sequence of calculation of molalities is OH", SO", H2S03, HSO", CO", H CO, CaOH+, CaS0°,... 

Similar relationships can be used to obtain the other thermodynamic properties. The reader is referred to the Pitzer and Brewer reference for details. This procedure provides a good method for determining the thermodynamic properties because of the nature of Bm. Figure 18.2 shows a graph of B as a function of molality for several electrolytes. We note that B changes slowly with molality (except at low m where more rapid changes are not as important in the calculation). Thus, it is easy to interpolate in a table of AB values, and an extensive table is not needed to obtain accurate values for the thermodynamic properties. 

Although not usually calculated, the molality and molarity of an alloy (a metal in a metal solution) can be calculated. Nickel steel contains nickel in small amounts mixed with iron, (a) Express the molality of the 2.5 g Ni (atomic mass = 58.69) dissolved in 1000mL Fe (atomic mass = 55.85, density = 7.66 g/cm3 under the lab conditions). (b) Express the molarity of the metal solution (no volume change). 

Let s start by calculating the molality of the solute. Ethylene glycol (HO-CH2CH2-OH, or EG for short) is an organic alcohol with a molecular mass of 62 g/mol. Since it is a molecular substance, it is a nonelectrolyte. 

Because K, depends on concentrations and the product KyKx is concentration independent, Kx must also depend on concentration. This shows that the simple equilibrium calculations usually carried out in first courses in chemistry are approximations. Actually such calculations are often rather poor approximations when applied to solutions of ionic species, where deviations from ideality are quite large. We shall see that calculations using Eq. (47) can present some computational difficulties. Concentrations are needed in order to obtain activity coefficients, but activity coefficients are needed before an equilibrium constant for calculating concentrations can be obtained. Such problems are usually handled by the method of successive approximations, whereby concentrations are initially calculated assuming ideal behavior and these concentrations are used for a first estimate of activity coefficients, which are then used for a better estimate of concentrations, and so forth. A G is calculated with the standard state used to define the activity. If molality-based activity coefficients are used, the relevant equation is... 

Molality is a bit different. It is calculated as the moles of solute per kilogram of solvent. Two main differences here first, you are measuring units of mass instead of units of volume, and second, you are using only the amount of solvent in the denominator. That s where the confusion usually comes from with molarity. With molarity, you are dividing the moles by the amount of solution, whereas in molality, you are dividing the moles by the amount of solvent. To calculate the molality of a solution where substance A is dissolved in some solvent, you would use Equation 10.3 ... 

B) In order for this to work, you need several measurements. To calculate the molality, two temperature readings are required. The first is for the pure solvent, and the second for the solution. Subtracting these values will produce A Tf. The value of Kf is also needed, but it is obtained from a reference book, not the experiment. In order to complete the calculations, two other pieces of data are required. The first is the mass of the solute. The second is the mass of the solvent. By using these two values, along with the molality (just calculated), we will be able to calculate the molar mass of the unknown. 

Practice Problem 15.11 Calculate the molality of a certain solute if a 0.512 m solution of the solute is combined with a 0.216 m solution of the solute. The first solution contains 1.34 kg of solvent, and the second solution contains 2.13 kg of the same solvent. ... 

Calculate the molality of alcohol in an aqueous solution with mole fraction alcohol 0.150. 

A knowledge of the boiling-point elevation and the appropriate constant from Table 1-4 allows one to calculate the molality of the solution, and this figure coupled with the weight of material added gives the molecular weight. The values thus determined are usually accurate to about 10 per cent. 

As with the molarity calculations, molality problems often incorporate the formula for determining the number of moles that a sample represents. Let s suppose you knew the mass of both the solute and the solvent that went into the solution. Would you be able to calculate the molality Here s an example. 

As you can see, before you can calculate the molality of the solution, you will need to determine the number of moles of solute that you are starting with. You can do this by dividing the mass of the solute (CaCl2) by its molar mass. You may recall from Example 2 that the molar mass of CaCl2 is 111.1 g/mole. Once you know the number of moles of solute that you have, you will be able to divide that value by the mass of the solute (1.5 kg of water) in order to determine the molality. Let s see what this would look like. 

Answer In solving this type of problem it is convenient to assume that we start with 100.0 g of the solution. If the mass of phosphoric acid is 35.4 percent, or 35.4 g, the percent and mass of water must be 100.0% - 35.4% = 64.6% and 64.6 g. From the known molar mass of phosphoric acid, we can calculate the molality in two steps. First we need to find the number of grams of phosphoric acid dissolved in 1000 g (1 kg) of water. Next, we must convert the number of grams into the number of moles. Combining these two steps we write... 

A solution was 2.40 m and contained 245 g of solvent. Calculate the molality of the solution after dilution with 125 g more of solvent. 

From the reported molar ratio Zr-halide/water we can calculate a molality of 0.037 m in Zr. Based on the present evaluation of the available hydrolysis and polymerisation data it cannot be accepted that monomeric species are formed, but polymeric species or colloids have to be considered to be dominant. The reported Af//° for ZrOOH of - 1132.6 kJ-moP is therefore not retained in the review. In contrast, by comparison of the measured heats of Reaction (A.3) both for X = Cl (with known values for Af//° (ZrCU, cr, 298.15 K)) with those for X = (Br, I), the unknown data for AfH° (ZrX4, cr, 298.15 K) can be determined reliably even if the stoichiometry of the dissolved or colloidal hydrolysed species is not known. The results for Reaction (A.3)... 

Comments Concentrations are molal, i.e., per kg water, base moles are calculated with the... 

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