Molality molar mass

Equation (88) is the expression used commonly for solutions of synthetic polymers, but, where the nature of adsorption and binding is of critical interest, alternative forms exist. These differ mainly in the modes of expressing concentration (e.g. activity, molality, molarity, mass/unit volume). Interrelations among the units and expressions have been presented very clearly by Timasheff and Townend15. ... 

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. 

Molal boiling point constant, 269,270t Molal freezing point constant, 269,270t Molality (m) A concentration unit defined as the number of moles of solute per kilogram of solvent, 259,261-262 Molar mass The mass of one mole of a substance, 55,68-68q alcohol, 591 alkane, 591... 

Self-Tfst 8.9A Calculate the molality of toluene dissolved in benzene, given that the mole fraction of toluene is 0.150. The molar mass of benzene is 78.11 g-mol-1. 

Lewis and Randall stated that in dilute solutions the activity coefficient of a strong electrolyte is the same in all solutions of the same ionic strength this statement was confirmed in thermodynamic deductions of activity coefficients. The molality version of 7 can be applied in a fully analogous way and allows a more straightforward treatment of solution properties. [Conversion of molality into molarity requires the solution densities e.g., for a solute of molar mass M and a solution of density q we have... 

First compute the molality of the benzene solution, then the number of moles of solute dissolved, and finally the molar mass of the unknown compound. 

From this relationship, we can see that each Na2S04 produces three ions. The production of three ions means that the van t Hoff factor, i, is 3. We need to know the molality of the solution to find our answer. To determine the molality, we will begin by determining the moles of sodium sulfate. Sodium sulfate has a molar mass of 142.04 g/mol. Thus, the number of moles of sodium sulfate present is ... 

D—To calculate the molar mass, the mass of the solute and the moles of the solute are needed. The molality of the solution may be determined from the freezing-point depression, and the freezing-point depression constant (I and II). If the mass of the solvent is known, the moles of the solute may be calculated from the molality. These moles, along with the mass of the solute, can be used to determine the molar mass. 

Because the concentration of CO is not negligible, we can no longer apply the simple relationship between molality and concentration (mi = cjp) to write the equilibrium constant in terms of concentrations. The correct relationship between these two quantities is now given by equation 14.23, where M and n are the molar mass and the amount of substance of the solvent, respectively, and M and , are the corresponding quantities for the three solutes. 

Temperature, Heat capacity. Pressure, Dielectric constant. Density, Boiling point. Viscosity, Concentration, Refractive index. Enthalpy, Entropy, Gibbs free energy. Molar enthalpy. Chemical potential. Molality, Volume, Mass, Specific heat. No. of moles. Free energy per mole. 

Here, p and m are the standard chemical potential and concentration (molal scale) of the /-component (z = 1 for solvent, z = 2 for biopolymer) A2 is the second virial coefficient (in molal scale units of cm /mol, i.e., taking the polymer molar mass into account) and m° is the standard-state molality for the polymer. 

Figure 6.10 Effect of CITREM on the molecular and thermodynamic parameters of maltodextrin SA-2 (DE = 2) in aqueous medium (phosphate buffer, pH = 7.2, ionic strength = 0.05 M 20 °C) (a) weight average molar mass, Mw (b) radius of gyration, Ra (c) structure sensitive parameter, p, characterizing die architecture of maltodextrin associates (d) second virial coefficient, A2 or A2, on the basis of the weight ( ) and molal (A) scales, respectively. The parameter R is defined as the molar ratio of surfactant to glucose monomer units in the polysaccharide. The indicated cmc value refers to the cmc of the pure CITREM solution. Reproduced from Anokhina et al. (2007) with permission.

Mt is lhe molar mass of the solvent, AJin its latent heat of vaporization in kcal per mole at temperature 7 . ms the molality of solute v 0e is called... 

To calculate the molality of a solution prepared by dissolving 10.5 g of sodium chloride in 250 g of water, we convert the mass of sodium chloride to moles of NaCl (by dividing the mass by the molar mass) and divide it by the mass of water in kilograms ... 

The main feature that distinguishes molality from molarity is its definition in terms of the mass of solvent used to make up the solution the molarity is expressed in terms of the volume of the resulting solution (not the volume of solvent used to make the solution). As a result, the molality is useful when we want to emphasize the relative numbers of molecules of the components of a mixture. That will be required only rarely in this text, so molality will appear much less frequently than molarity (it is used only in Chapter 8). If a concentration given as a molarity needs to be converted into molality, the mass of solvent in the solution must be known. To calculate this mass, the density of the solution is needed. 

STRATEGY The molality is the number of moles of solute per kilogram of solvent. Therefore, consider a solution made with exactly 1 kg of solvent and work out the mass of solute present from the number of moles and the molar mass. Then calculate the mass percentage of solute by dividing the mass of solute by the total mass of the solution and multiply by 100%. 

Take the freezing-point constant from Table 8.9. Use this -molality to calculate the moles of solute in the sample by multiplying it by the mass of solvent in kilograms. At this stage, determine the molar mass of the solute by dividing the given mass of solute by the number of moles present. For the molecular formula, decide how many atoms of sulfur are needed in each molecule to account for the molar mass. 

To prepare a 1.000 m solution of KBr in water, for example, you would dissolve 1.000 mol of KBr (119.0 g) in 1.000 kg (1000 mL) of water. You can t say for sure what the final volume of the solution will be, although it will probably be a bit larger than 1000 mL. Although the names sound similar, note the differences between molarity and molality. Molarity is the number of moles of solute per volume (liter) of solution, whereas molality is the number of moles of solute per mass (kilogram) of solvent. 

What is the molality of a solution made by dissolving 1.45 g of table sugar (sucrose, C12H22O11) in 30.0 mL of water The molar mass of sucrose is 342.3 g/mol. 

PROBLEM 11.9 The density at 20°C of a 0.500 M solution of acetic acid in water is 1.0042 g/mL. What is the concentration of this solution in molality The molar mass of acetic acid, CH3C02H, is 60.05 g. 

The solubility of a solid in a liquid is the amount of the solid that will dissolve in the liquid to form an equilibrated saturated solution (Faure, 1998), 111. In the literature, the solubility of a particular solid substance in water has been traditionally derived from laboratory measurements of the mass or moles of the solid that dissolves in a given mass or volume of distilled and deionized water. These values are often listed in milligrams per liter, grams per 100 milliliters (Lide, 2007), grams per liter, micrograms per liter Oigl-1), molal, molar, or micromolar ( iM) (Table 2.8). 

Other measures of the solubility of a gaseous solute are readily derived from its mole fraction. The Henry s law constant is KH lim(pjxj30) atp2 —> 0, which becomes on the molal scale Km lim(1000 p2/Mjc2) with Mj the molar mass of the solvent in g mob1 for use in Eq. (2.13) below. The Ostwald coefficient is the limit of y2 = RT(xJp lVl atp2 -> 0 and is related to the mass fraction w2 by ... 

The molar mass of ethyl alcohol is 46.1. Since the molality is 1.54, 1 kg of water dissolves 1.54 mol C2H5OH. The amount of C2H5OH that 2.5 kg water dissolves is... 

For a solute of molar mass, M, show that the molar concentration, M, and molality, m, of the solution are related by... 

The freezing point of pure camphor is 178,4°C and its molal freezing-point constant, kf, is 40.0° dm. Find the freezing point of a solution containing 1.50 g of a compound that has the molar mass (M) 125 g/mol dissolved in 35.0 g of camphor. 

The assumption that the molality and molarity are equal does not introduce serious error into the calculations for dilute aqueous solutions. The relationships discussed in Chapter 12 show that M m when the density is 1 g/mL (1 g/cm3) and M < 1000/m. Urea has a molar mass of 60.0 g/mol. Then, 0.280 mol/L may be used for the molarity in the osmotic pressure equation. 

A solution contains 10.6 g of a nonvolatile substance dissolved in 740 g of ether. The boiling point of the solution is 0.284°C over the boiling point of pure ether. Molal boiling-point constant for ether is 2.11°C kg/mol. What is the molar mass of the substance ... 

The freezing point of a sample of naphthalene was found to be 80.6°C. When 0.512 g of a substance were dissolved in 7.03 g naphthalene, the solution s freezing point was 75.2°C. What is the molar mass of the solute (Molal freezing-point constant for naphthalene is 6.80°C kg/mol.)... 

You dissolve 90 g of sucrose (molar mass = 342 g/mol) in 1000 g of water. What is the molality of the solution If the cryoscopic constant for water is 1.9 degrees/molal, what is the freezing point of the solution ... 

Supposing the solution has a solute present at molality, msoiute and that the solvent has a molar mass, M then ... 

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