Mole fractions converting molality

Convert between molality and mole fraction or molarity (Toolbox 8.1 and Examples 8.6 and 8.7). 

Note that it is not possible to convert from molarity to molality or mole fraction unless some information about the density or weight composition of the solution is given. 

It is important to be able to convert among the different concentration units. Conversions between molality and mole fraction are performed by considering a solution containing 1 kg of solvent ... 

The molar mass of one component is required to convert molality to mole fraction or mole fraction to molality. 

Both molality and mole fraction are intensive properties, which is useful for an easy method to convert from one to the other. In such a problem, we can assume that we have any quantity of solution that will make our solving process easiest. 

You want to convert among molarity, molality, and mole fraction of a solution. You know the masses of solute and solvent and the volume of solution. Is this enough information to carry out all the conversions Explain. 

It is snggested the reader keep in mind the definitions of all concentrations given earlier and, most importantly, be able to convert from one concentration scale to another (see Section 1.4). Some of the listed concentrations depend on temperature and pressure (e.g., molarity and volume fraction) while others do not (e.g., molality and mole fractions). Note the lUPAC [1] recommends using some other names and units of concentrations, but they are not stiU sufficiently accepted by electrochanists and electrochanical engineers. In this book, molality, molarity, and mole fraction will mainly be used. 

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 phase rule is often used in the form t = c - p + 2 to ascertain the number of degrees of freedom of a system even when the concentration units in the aqueous phase are molal (m) or molar. This is not correct because the phase rule is derived 1n terms of mole fractions (X). Thus, an additional quantity, the total number of moles, is required to convert X into m. This is illustrated by equations below which we shall find useful later on. 

Frequently it is necessary to convert solute activity coefficients based on mole fraction to a molality basis, or vice versa. The equation for making this conversion can be derived in the following way. 

The left term is the relative vapor pressure lowering, which is solely dependent on the mole fraction concentration of a single solute or the sum of mole fraction of each solute dissolved in the solution. Thus, the relative vapor pressure lowering is a direct measure of the total number of dissolved solute particles, irrespective of their physicochemical nature. The mole fractions can be converted into molality (m moles of solute per 1000 g of solvent) to result in the following equation for water as the solvent ... 

The molal activity coefficient f is the activity coefficient usually measured experimentally and reported, rather than the unsymmetric or symmetric mole fraction activity coefficients. Most activity coefficient models, however, yield values of the symmetric or the unsymmetric mole fraction activity coefficient. It is therefore often necessary to convert back and forth between activity coefficients and chemical potentials in the various systems. 

Note When converting from one concentration unit to another, it is convenient to assume one of the following (1) the solution has a volume of one liter molarity molality), (2) the total amount of solvent and solute is one mole mole fraction o molality), or (3) the mass of the solvent in the solution is one kilogram molality mole fraction). 

Other measures of composition such as mole fraction and mass fraction are less commonly used to express chemical reaction rates. Weight measurements are frequently used to prepare solutions or fill reactors. The resulting composition will have a known ratio of moles and masses of the various components, but the numerical value for concentration requires that the density be known. Good practice is to prepare solutions in mass units and then convert to standard concentration units based on the known or observed density of the solution under reaction conditions. To avoid ambiguity, modern analytical chemists frequently define both molarity and molality in weight units as moles per kilogram of solution or moles per kilogram of solvent. 

E5.4(b) In Exercise 5.3(b), the Henry s law constant was determined for concentrations expressed in mole fractions. Thus the concentration in molality must be converted to mole fraction. 

Water-treatment plants commonly use chlorination to destroy bacteria. A by-product is chloroform (CHCI3), a suspected carcinogen, produced when HOCl, formed by reaction of CL and water, reacts with dissolved organic matter. The United States, Canada, and the World Health Organization have set a limit of 100. ppb of CHCI3 in drinking water. Convert this concentration into molarity, molality, mole fraction, and mass percent. 

Plan In converting concentration units based on the mass or moles of solute and solvent (mass percentage, mole fraction, and molality), it is usefril to assume a certain total mass of solution. Let s assume that there is exactly 100 g of solution. Because the solution is 36% HCl, it contains 36 g of HCl and (100 — 36) g = 64gofH20. We must convert grams of solute (HCl) to moles to calculate either mole fraction or molality. We must convert grams of solvent (H2O) to moles to calculate mole fractions and to kilograms to calculate molality. 

We must convert grams of solute (HCl) to moles to calculate either mole fraction or molality. We must convert grams of solvent (H2O) to moles to calculate mole fractions and to kilograms to calculate molality. 

Concentrations of solutions can be expressed quantitatively by several different measures, including mass percentage [(mass solute/mass solution) X 100] parts per million (ppm), parts per billion (ppb), and mole fraction. Molarity, M, is defined as moles of solute per liter of solution molality, m, is defined as moles of solute per kilogram of solvent. Molarity can be converted to these other concentration units if the density of the solution is known. 

The preceding considerations are based on the use of the mole fraction scale. Chemists and chemical engineers who use other scales for the composition of mixtures and solutions, for example, weight percent and mole percent for mixtures or molality, molonity, and molarity for solutions (see Section LA) must convert chemical potentials and activity coefficients to these scales. Conversion is based on the fact that changes in composition scales do not change the chemical potential, for example, conversion from the mole fraction scale p,f°, foi) to the molality scale (M -Ki) ... 

We can use a Raoultian standard state (pure water) for the solvent, but its deviation from ideal behavior, whether based on a mole fraction or a molality scale, is often converted to the osmotic coefficient , which does not actually have a standard state. It is an absolute system property. 

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