Molality, different from molarity

Molality (m) is a temperature-independent measure of concentration, defined as the number of moles of solute per kilogram of solvent. It differs from molarity (M) in that it is based on a mass of solvent, rather than a volume of solution. Like molarity, molality can be used as a factor to solve problems (Section 15.4). Molality is also used in problems involving freezing-point depression and boiling-point elevation. 

We have information about molarity (mol/L) and density (g/mL) and are asked to find molality (mol/kg) and mole fraction (mol/mol). A good way to approach conversions from molarity to another measure is to choose a convenient volume for the solution, determine its mass and the mass of solute, and find the mass of water by difference. Then convert mass of water to kilograms and to moles to complete the calculations. 

The correct answer is (E). You should be very clear on the differences between molarity and molality. Molality is the measure of the number of moles of solute dissolved per kilogram of solvent. The molarity is a measure of the moles of solute dissolved in a given volume of solution. If you know that a given solution has a molarity of 1.00, then you know there is 1.00 moles of solvent per liter of solution. Knowing the density will allow you to determine the mass of a solution. If the mass of the solute is subtracted from the mass of the solution, the result will be the mass of the solvent, which is required for the determination of molality. 

Repeat Exercise 3.5.2 when molality is used in place of molarity and is referred to unit molality as the standard chemical potential. How do your results differ from those cited in the text ... 

With the adoption of qf =x = I for a pure material, and by employing standard conditions on setting P = 1, we automatically satisfy the requirement that a, (T, 1, X ) = 1. For, it is only with this choice that Eq. (3.4.4) reduces to an identity. However, as shown later in Section 3.7, at any other pressure a/(r, P,xf) differs from unity, although under normal experimental conditions the deviations from unity are small. The selection of molarity or molality engenders complications that are addressed later. 

Many molality problems do not differ in solving technique from molarity problems. As usual, be very careful with the units. 

Here, cs denotes the concentration in mol/kg (molality scale), and [s] is the concentration in mol/liter (molarity scale). Both units are related in that [s] = pwcs where pw= 1 kg/dm3 is the density of water. Its variation with temperature causes the molarity scale to depend on temperature, whereas the molality scale does not. In the temperature range 0-25°C, however, the density of water differs from unity by less than 0.3%, so that [s] = cs with reasonable accuracy. Most Henry coefficients are less well known. From the definitions in Eqs. (8-7) and (8-8), the coefficients involved are related by... 

Explain how the molarity of a solution is different from its molality. (Chapter 14)... 

Molality is typically reported in moles of solute per kilogram of solvent (mol kg" ). This unit is sometimes (but unofficially) denoted m, with 1 m = 1 mol kg" . An important distinction between molar concentration and molality is that whereas the former is defined in terms of the volume of the solution, the molality is defined in terms of the mass of solvent used to prepare the solution. A distinction to remember is that molar concentration varies with temperature as the solution expands and contracts, but the molality does not. For dilute solutions in water, the numerical values of the molality and molar concentration differ very little because 1 dm of solution is mostly water and has a mass close to 1 kg for concentrated aqueous solutions and for all nonaqueous solutions with densities different from 1 g cm" , the two values are very different. 

In view of Equations 1.53 and 1.55 it is evident that in the defined ideal solutions the activity is equal to the molarity or to the molality, respectively. It follows, therefore, that the aetivity may be thought of as an idealized molarity (or molality), which may be substituted for the aetual molarity (or molality) to allow for departure from ideal dilute solution behaviour. The aetivity eoeffieient is then the ratio of the ideal molarity (or molality) to the aetual molarity (or molality). At infinite dilution both f and y must, by definition, be equal to unity, but at appreeiable eoncentrations the aetivity eoeffieients differ from unity and from one another. However, it is possible to derive an equation relating f and y, and this shows that the difference between them is quite small in dilute solutions. 

Suppose we prepare a solution at 20 °C by using a volumetric flask calibrated at 20 °C. Then suppose we warm this solution to 25 °C. As the temperature increases from 20 to 25 °C, the amount of solute remains constant, but the solution volume increases slightly (by about 0.1%). The number of moles of solute per liter—the molarity—decreases slightly (by about 0.1%). This temperature dependence of molarity can be a problem in experiments demanding a high precision. That is, the solution might be used at a temperature different from the one at which it was prepared, and so its molarity is not exactly the one written on the label. A concentration unit that is independent of temperature, and also proportional to mole fraction in dilute solutions, is molality (m)—the number of moles of solute per kilogram of solvent (not of solution). A solution in which... 

The use of two different polymer concentrations, C2 and v, in preceding equations results from deference to custom in expressing electrolyte concentrations in molarities (or in molalities). Confusion might have been minimized in Eq. (45) by substituting C2m = V2m/yu-... 

This equation implies an experimental determination of AH as a function of the mole numbers. The experimental data that are required may be published in many different ways. For example, the change of enthalpy per mole of solution may be given as a function of the mole fractions, molalities, or molarities. The methods required to calculate (Hk — Hf) for the components from such data are exactly those discussed in Sections 6.3 and 6.5. 

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 ... 

Molality. Molarity is the number of gram moles of solute per 10(X) g of solvent. Take note of the drastic difference between this definition of molality and the difinition of molarity. The solvent is now separate from the solute. The symbol used for molality is m. 

Both these considerations would be taken into accoimt if the activation process were assumed to occur at a constant pressure, p, such that the partial molar volume of the solvent is independent of the temperature, though this possibility does not appear to have been considered. A full discussion is beyond the scope of this chapter, but the resulting heat capacities of activation are unlikely to differ greatly from those determined at a constant pressme of, say, 1 atm. (see p. 137). Unfortunately, this approach requires the definition of rather clumsy standard states for solutes, e.g., hypothetically ideal, 1 molal, under a pressure such that a given mass of the pure solvent occupies a particular volume. 

Show that the free energy of dilution of a solution from one molality (m) to another (m ), i e., the difference in the partial molar free energy (y) of the solute in the two solutions, is equal to... 

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