Molar mass from freezing-point

When determining a molar mass from freezing-point depression, it is possible to make each of the following errors (among others). In each case, predict whether the error would cause the reported molar mass to be greater or less than the actual molar mass. 

The expressions commonly used for determination of molalities or molar mass from freezing-point depressions are derived with the following approximations ... 

Molar Mass from Freezing-Point Depression... 

Suppose that 10.0 g of an organic compound used as a component of mothballs is dissolved in 80.0 g of benzene. The freezing point of the solution is 1.20°C. (a) What is an approximate molar mass of the organic compound (b) An elemental analysis of that substance indicated that the empirical formula is C3H2C1. What is its molecular formula (c) Using the atomic molar masses from the periodic table, calculate a more accurate molar mass of the compound. 

Molar masses from gas density, freezing-point, and boiling-point measurements... 

Measurements of osmotic pressure generally give much more accurate molar mass values than those from freezing-point or boiling-point changes. 

Strategy First, we can determine the empirical formula from mass percent data. Then, we can determine the molar mass from the freezing-point depressioiL Finally, from the empirical formula and the molar mass, we can find the molecular formula. 

How to Calculate the Molar Mass of a Solute from Freezing-Point Depression or Boiling-Point Elevation Data... 

In carrying out a molar mass determination by freezing point depression, we must choose a solvent in which the solute is readily soluble. Usually, several such solvents are available. Of these, we tend to pick one that has the largest kf. This makes ATf large and thus reduces the percent error in the freezing point measurement From this point of view, cyclohexane or other organic solvents are better choices than water, because their kf values are larger. 

SELF-TEST 8.14B When 200. mg of linalool, a fragrant compound found in cinnamon oil from Sri Lanka, was added to 100. g of camphor, it lowered the freezing point of camphor by 0.51°C. What is the molar mass of linalool ... 

Colligative1 properties of dilute polymer solutions depend only on the number of dissolved molecules and not on properties of the molecules themselves, such as mass or size. Osmotic pressure, freezing point depression, boiling point elevation, and vapour pressure lowering are the most prominent examples. These methods essentially allow one to count the number n of solute molecules. From n and the known total mass m of the solute the molar mass M is readily obtained as... 

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. 

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. 

A 4.51 g sample of an unknown compound was dissolved in 98.0 g of solvent. From the freezing point depression, the concentration was found to be 0.388 mol/kg. Calculate the molar mass of the unknown. 

One of the laboratory requirements for the course, and also the topic of former test questions, is the determination of the molar mass of a substance from the freezing-point depression. Actually, any of the colligative properties can be used to determine the molar mass, but the only one that you are required to know is the freezing-point depression method. It is easier to illustrate the technique within the framework of a problem, so the discussion of this process will be done within a sample problem. 

We wish to derive expressions for calculating the molality m of the solution (or the molar mass Mof the solute) from a measured freezing-point depression AT. The molality of the solution is given by... 

In this experiment the freezing point of a solution containing a known weight of an unknown solute in a known weight of cyclohexane is determined from cooling curves. From the result at each of two concentrations, the molar mass of the unknown is determined. 

For the determination of very high molar masses, freezing-point depressions, boiling-point elevations, and vapor-pressure lowerings are too small for accurate measurement. Osmotic pressures are of a convenient order of magnitude, but measurements are time-consuming. The technique to be used in this experiment depends on the determination of the intrinsic viscosity of the polymer. However, molar-mass determinations from osmotic pressures are valuable in calibrating the viscosity method. 

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. 

Calculate the molar mass of a nonvolatile solute from the changes it causes in the colligative properties (vapor-pressure lowering, boiling-point elevation, freezing-point lowering, or osmotic pressure) of its dilute solution (Section 11.5, Problems 41-56). 

The elemental analysis of an organic solid extracted from gum arabic (a gummy substance used in adhesive, inks, and pharmaceuticals) showed that it contained 40.0 percent C, 6.7 percent H, and 53.3 percent O. A solution of 0.650 g of the solid in 27.8 g of the solvent diphenyl gave a freezing-point depression of 1.56°C. Calculate the molar mass and molecular formula of the solid. K for diphenyl is 8.00°C/ot.)... 

Lysozyme is an enzyme that cleaves bacterial cell walls. A sample of lysozyme extracted from egg white has a molar mass of 13,930 g. A quantity of 0.100 g of this enzyme is dissolved in 150 g of water at 25°C. Calculate the vapor-pressure lowering, the depression in freezing point, the elevation in boiling point, and the osmotic pressure of this solution. (The vapor pressure of water at 25°C is 23.76 mmHg.)... 

Each colligative property relates concentration to some measurable quantity—the number of degrees the freezing point is lowered, the magnitude of osmotic pressure created, and so forth. From these measurements, we can determine the amount (mol) of solute particles and, for a known mass of solute, the molar mass of the solute as well. 

Two grams of benzoic acid dissolved in 25 g of benzene, Xy = 4.90 Kkg/mol, produce a freezing-point depression of 1.62 K. Calculate the molar mass. Compare this with the molar mass obtained from the formula for benzoic acid, CgHjCOOH. 

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