Calculating Molal Concentration

Sample Problem D a water solution containing an unknown quantity of a nonelectrolyte solute is found to have a freezing point of - 0.23 C. What is the molal concentration of the solution  

Q ANALYZE Given freezing point of solution = —0.23 C Unknown molality of the solution 

CHECK YOUR A shown by the unit cancellation, the answer gives the molality, as desired. WORK Thfi answer is properly limited to two significant digits. 

A solution consists of 10.3 g of the nonelectrolyte glucose, CgHj20g, dissolved in 250. g of water. What is the freezing-point depression of the solution  

In a laboratory experiment, the freezing point of an aqueous solution of glucose is found to be —0.325°C. What is the molal concentration of this solution  

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The ability of Equation 22 to reproduce the experimental data was checked by means of the calculated molal concentration of reference solution from the relation... 

Calculate the concentrations of each of the following solutions (a) the molality of 13.63 g of sucrose, C 2H22Om, dissolved in 612 mL of water (h) the molality of CsCl in a 10.00% by mass aqueous solution (c) the molality of acetone in an aqueous solution with a mole fraction for acetone of 0.197. 

Calculate the concentrations of each of the following solutions (a) the molality of chloride ions in an aqueous solution of magnesium chloride in which xMgCU s 0.0120 ... 

Fig. 8.7. Molal concentrations m, and activities a, of calcium and sulfate species in equilibrium with gypsum at 25 °C as functions of NaCl concentration, calculated using the B-dot equation (left) and the hmw activity model (right).

His procedure was used for the calculation of the activity coefficients in the aqueous solution of two electrolytes with a common ion from isopiestic data (3). Kelly, Robinson, and Stokes (4) proposed a treatment of isopiestic data of ternary systems with two electrolytes by a procedure based on the assumption that at all values of molal concentrations, mi,m2, the partial derivatives may be expressed by a sum of two functions in their differential form as follows ... 

Since the vapor pressure of the solvent is lowered by the presence of solutes, the temperature at which the vapor pressure equals atmospheric pressure (where the solution boils) is higher than for the pure solvent, as shown in Figure 11-1. Detailed calculations show that the increase in boiling point for a dilute solution is proportional to the total molal concentration of solutes ... 

Table 3.2 summarizes the chemistries that lead to the precipitation of solid phases. The actual parameters for these equilibria are in Appendix B. The range of temperatures used in model parameterizations or validation and the maximum molal concentrations are both fundamentally important in properly applying the model. Extrapolations outside these tempera-ture/compositional ranges require careful scrutiny of model calculations. 

The first term on the right is the salt dependence of In Kohs, expressed in molal concentration units. The second term can be calculated from the dependence of the salt activity coefficient on salt concentration... 

Since the solution for this problem calls for the calculation of AT, which is dependent on molal concentration, we must calculate the moles of solute. 

Chloroacetic acid, amonoprotic acid, has a Ka of 1.40 x 10 3. Calculate the freezing point of a 0.10 M solution of this acid. Assume that the numerical value of the molar and molal concentrations are the same. 

In all of the examples given, a temperature of 25°C and 1 atm total pressure are assumed. The task will be to calculate the concentration of all of the carbonic acid system components, pH, At, CO2, Pcc>2< Ca2+ concentration, ionic strength, and the appropriate ion activity coefficients. The values of the thermodynamic constants used in these calculations were calculated from appropriate equations in Chapter 1. Concentrations are on the molal scale, and results for each case are summarized in Table 2.4. 

To maintain equal cell concentrations at equivalent levels of sucrose and CKlt amount of these substances required to give indicated molal concentration added to usual volume (3.45 ml.) of uptake buffer containing glucose and L-Cu-glutamic acid. Incubation for 100 minutes at37°C. Amount of glutamate calculated from isotope content of cell extracts... 

Calculate the concentration of a 7.500% solution of NaCl in water in (a) molality (b) mole fraction NaCl. 

The predicted values for the various solid phases shown in Table IV were calculated using the hydroxide and carbonate activity printout of the model. These values were used to calculate the equilibrium trace cation activities in the brine. The activity values were then divided by the predicted single ion activity coefficients and thereby converted to the molal concentration scale. These molal units were then converted to molar units, and then into the milligrams per kilogram of solution units reported. 

Ba, Sr, and B. Consistency between programs was evaluated by comparing the log of the molal concentrations of free ions and complexes for two test solutions a hypothetical seawater analysis and a hypothetical river water analysis. Comparison of the free major ion concentrations in the river water test case shows excellent agreement for the major species. In the seawater test case there is less agreement and for both test cases the minor species commonly show orders of magnitude differences in concentrations. These differences primarily reflect differences in the thermodynamic data base of each chemical model although other factors such as activity coefficient calculations, redox assumptions, temperature corrections, alkalinity corrections and the number of complexes used all have an affect on the output. 

A bottle of wine contains 12.5% ethanol by volume. The density of ethanol (C2H5OH) is 0.789 g/cm3. Calculate the concentration of ethanol in wine in terms of mass percent and molality. 

The raising of the boiling point and the lowering of the freezing point are therefore proportional to the molal concentration. The constant of proportionality can be calculated from the latent heat of evaporation or fusion, and from the boiling or freezing point of the solvent. 

Example 2.3. Activity and Activity Coefficient of Aqueous NaCl Water vapor pressures have been measured over NaCl solutions of varying molal concentrations. Results of such measurements allow calculations of relative vairor pressure lowering, 4>, and 7., for a range of NaCl concentrations in water. Robinson and Stokes (1959) provide such data for concentrations ranging fn)m 0.1 to 6.0 molal. Table 2.1 shows results for three different concentrations. The mole fraction of H2O, Xfy, is also included. From such data the activity of aqueous NaCl can be computed, (see also Figure 2.4.)... 

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