Molar mass from vapor pressure

There are a variety of ways to do the calculations. Most of these, however, involve the calculation of the number of moles (n) from the ideal gas equation n = PV/RT. The mass of the vapor sample is calculated from the difference between measurements 1 and 2. The temperature (measurement 3) is converted to kelvin. The pressure (measurement 4) is converted to atmospheres. Measurement 5 is converted to liters. Inserting the various numbers into the ideal gas equation allows you to calculate the number of moles. The molar mass is calculated by dividing the mass of the sample by the moles. 

Number-average molar masses were determined using a vapor pressure osmometer (VPO) (Hitachi 117 Molecular Weight Apparatus) at 54.8 0.1°C in toluene (Fisher Scientific, certified A.C.S.) which was distilled from freshly crushed CaH2. The VPO apparatus was calibrated with pentaerythritol tetrastearate (Pressure Chemical). Gel permeation chromatographic (GPC) analyses were performed in tetrahydrofuran by HPLC (Perkin-Elmer 601 HPLC) using six y-Styragel columns (106, 105, 10l, 103, 500, and 100 A) after calibration with standard polystyrene samples. 

B,155,1 m Z. Shakhashiri, "Determination of the Molecular Mass of a Volatile Liquid," Chemical Demonstrations, A Handbook for Teachers of Chemistry, Vol. 1 (The University of Wisconsin Press, Madison, 1983) pp. 51-54. A boiling-water bath is used to heat a volatile liquid until it is vaporized, completely filling an Erlenmeyer flask covered by aluminum foil with a pinhole orifice. From atmospheric pressure, bath temperature, volume of the flask, and mass of recondensed vapor, the molar mass of the volatile liquid is determined. 

According to equation (2.3), the Henry s law constant can be estimated by measuring the concentration of X in the gaseous phase and in the liquid phase at equilibrium. In practice, however, the concentration is more often measured in one phase while concentration in the second phase is determined by mass balance. For dilute neutral compounds, the Henry s law constant can be estimated from the ratio of vapor pressure, Pvp, and solubility, S, taking the molecular weight into consideration by expressing the molar concentration ... 

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. 

Section 12.1 introduces the concept of pressure and describes a simple way of measuring gas pressures, as well as the customary units used for pressure. Section 12.2 discusses Boyle s law, which describes the effect of the pressure of a gas on its volume. Section 12.3 examines the effect of temperature on volume and introduces a new temperature scale that makes the effect easy to understand. Section 12.4 covers the combined gas law, which describes the effect of changes in both temperature and pressure on the volume of a gas. The ideal gas law, introduced in Section 12.5, describes how to calculate the number of moles in a sample of gas from its temperature, volume, and pressure. Dalton s law, presented in Section 12.6, enables the calculation of the pressure of an individual gas—for example, water vapor— in a mixture of gases. The number of moles present in any gas can be used in related calculations—for example, to obtain the molar mass of the gas (Section 12.7). Section 12.8 extends the concept of the number of moles of a gas to the stoichiometry of reactions in which at least one gas is involved. Section 12.9 enables us to calculate the volume of any gas in a chemical reaction from the volume of any other separate gas (not in a mixture of gases) in the reaction if their temperatures as well as their pressures are the same. Section 12.10 presents the kinetic molecular theory of gases, the accepted explanation of why gases behave as they do, which is based on the behavior of their individual molecules. 

Large quantities of liquefied natural gas (LNG) are shipped by ocean tanker. At the miloading port provision is made for vaporization of the LNG so that it may be delivered to pipelines as gas. The LNG arrives in tlie tanker at atmospheric pressure and 77i.7 K, and represents a possible heat sink for use as the cold reservoir of a heat engine. For unloading of LNG as a vapor at the rate of 9000 ni s . as measured at 298.15 (25°C) and 1.0133 bar, and assuming tlie availability of an adequate heat source at 303.15 K (30°C), what is tlie maximum possible power obtainable and what is the rate of heat transfer from the heat source Assume that LNG at 298.15 K (25°C) and 1.0133 bar is an ideal gas with the molar mass of 77. Also assume that the LNG vaporizes only, absorbing only its latent heat of 512 kJ kg at 113.7 K. 

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). 

Three mechanisms have been invoked to describe the transfer of water vapor from the feed-membrane interface to the strip-membrane interface, namely Poiseuille flow, Knudsen diffusion, and Fickian (molecular) diffusion. The operative mechanism in a particular system depends on the pore diameter and on whether or not the pores are filled with stationary air. The membrane mass transfer co-efficient (as kgm h Pa ) applicable to each of these mechanisms can be estimated using Eqs. (4), (5), and (6), respectively. Here, r is the pore radius, e is the membrane porosity, is the molar mass of water, is the mean water vapor pressure in the pores, is the membrane thickness, x is the pore tortuosity, is the viscosity of water vapor, R is the gas constant, T is the absolute temperature, is the diffusion co-efficient of water vapor in air,... 

The transpiration method is a simple and versatile method for vapor pressure measurement at high temperatures. An inert carrier gas is passed over the condensed substance in a constant temperature furnace zone. The flow rate of the carrier gas is constant and sufficiently small so that the carrier gas is saturated with vapor, which condenses at some point downstream. The mass of vapor transported by a known volume of carrier gas is determined. If the total vapor pressure is known, from the boiling point method, the results from the transpiration method may be used to calculate the average molar mass of the vapor. 

The average molar mass M2 then can be calculated from the measured values of m2, Pf, and i, when the vapor pressure P2i and the parameter C are known at a fixed temperature T. 

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.)... 

In addition, the proportionality between vapor pressure and concentration (Raoult s law) and that between osmotic pressure and concentration (van t Hoff s law) had to be satisfied. Both requirements were adequately fulfilled within the limits of experimental error by the covalent crystalloids then studied, but not by the colloids. This error concerning the two laws made the high molar masses of the colloids also seem suspect. However, we know today that both laws are only limiting laws for infinite dilution. A molar mass apparently dependent on concentrations, i.e., calculated from the limiting laws, is also the rule rather than the exception for low-molar-mass substances. This effect, dependent on the interaction between the molecules in the solution, was known as early as 1900 from ebullioscopic measurements by Nastukoff, who also proposed an extrapolation to zero solute concentration. Caspari obtained a molar mass of 100 000 g/mol for rubber using osmotic measurements by a similar extrapolation procedure. 

In the Dumas-bulb technique for determining the molar mass of an unknown liquid, you vaporize the sample of a liquid that boils below 100 °C in a boiling-water bath and determine the mass of vapor required to fill the bulb (see drawing, next page). From the following data, calculate the molar mass of the unknown liquid mass of unknown vapor, 1.012 g volume of bulb, 354 cm pressure, 742 torr temperature, 99 "C. 

Stream Information. Directed arcs that represent the streams, with flow direction from left to right wherever possible, are numbered for reference. By convention, when streamlines cross, the horizontal line is shown as a continuous arc, with the vertical line broken. Each stream is labeled on the PFD by a numbered diamond. Furthermore, the feed and product streams are identified by name. Thus, streams 1 and 2 in Rgure 3.19 are labeled as the ethylene and chlorine feed streams, while streams 11 and 14 are labeled as the hydrogen chloride and vinyl-chloride product streams. Mass flow rates, pressures, and tempera-mres may appear on the PFD directly, but more often are placed in the stream table instead, for clarity. The latter has a column for each stream and can appear at the bottom of the PFD or as a separate table. Here, because of formatting limitations in this text, the stream table for the vinyl-chloride process is presented separately in Table 3.6. At least the following entries are presented for each stream label, temperature, pressure, vapor fraction, total and component molar flow rates, and total mass flow rate. In addition, stream properties such as the enthalpy, density, heat capacity, viscosity, and entropy, may be displayed. Stream tables are often completed using a process simulator. In Table 3.6, the conversion in the direct chlorination reactor is assumed to be 100%, while that in the pyrolysis reactor is only 60%. Furthermore, both towers are assumed to carry out perfect separations, with the overhead and bottoms temperatures computed based on dew- and bubble-point temperatures, respectively. 

Polycarbonate from bisphenol-A served as the EP. It was obtained from the Bayer A.G., Leverkusen, Germany. The number-average molar mass was determined by vapor pressure osmosis = 18700gmol . The mass average was estimated by... 

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