Molar mass from effusion

The enrichment procedure uses the small mass difference between the hexafluorides of uranium-235 and uranium-238 to separate them. The first procedure to be developed converts the uranium into uranium hexafluoride, UFfl, which can be vaporized readily. The different effusion rates of the two isotopic fluorides are then used to separate them. From Graham s law of effusion (rare of effusion l/(molar mass)1/2 Section 4.9), the rates of effusion of 235UFfe (molar mass, 349.0 g-mol ) and 238UF6 (molar mass, 352.1 g-mol ) should be in the ratio... 

Self-Test 4.13A It takes 30 mL of argon 40 s to effuse through a porous barrier. The same volume of vapor of a volatile compound extracted from Caribbean sponges takes 120 s to effuse through the same barrier under the same conditions. What is the molar mass of this compound ... 

The formula mass of CjHj is 27.04 g -mol From the effusion data, we can calculate the molar mass of the sample ... 

The Process of Effusion One of the early triumphs of the kinetic-molecular theory was an explanation of effusion, the process by which a gas escapes from its container through a tiny hole into an evacuated space. In 1846, Thomas Graham studied this process and concluded that the effusion rate was inversely proportional to the square root of the gas density. The effusion rate is the number of moles (or molecules) of gas effusing per unit time. Because density is directly proportional to molar mass, we can state Graham s law of effusion as follows the rate of effusion of a gas is inversely proportional to the square root of its molar mass,... 

Plan The effusion rate is inversely proportional to fE, so we find the molar mass of each substance from the formula and take its square root. The inverse of the ratio of the square roots is the ratio of the effusion rates. 

SECTION 10.8 It follows from Idnetic-molecular theory that the rate at which a gas undergoes effusion (escapes through a tiny hole) is inversely proportional to the square root of its molar mass (Graham law). The diffusion of one gas through the space occupied by a second gas is another phenomenon related to the speeds at which molecules move. Because molecules undergo frequent collisions with one another, the mean fiee path—the mean distance traveled between collisions- -is short. Collisions between molecules limit the rate at which a gas molecule can diffuse. 

A gas evolved from the fermentation of glucose is found to effuse through a porous barrier in 15.0 min. Under the same conditions of terr5)erature and pressure, it takes an equal volume of N2 12.0 min to effuse through the same barrier. Calculate the molar mass of the gas and suggest what the gas might be. 

Analyze We are given information related to the relative rate of effusion of an unknown gas, and from that we are asked to find its molar mass. Thus, we need to connect relative rates of effusion to relative molar masses. 

Because the average molecular speed essentially equals V3/f77M , where M is the molar mass, the rate of effusion is proportional to Va/ . That is, the rate of effusion is inversely proportional to the square root of the molar mass (or molecular weight), as Graham s law states. The derivation of Graham s law from kinetic theory was considered a triumph of the theory and greatly strengthened confidence in its validity. 

The Knudsen and torsion-effusion methods have been combined in a single apparatus, for example by Lindscheid and Lange. In this work the torsion cell was suspended from a microbalance, thus enabling simultaneous observations of mass loss and cell rotation to be made. The values of vapour pressure calculated from the two sets of results can be combined through the Knudsen and torsion-effusion equations to obtain the molar mass of the vapour species. Lindscheid and Lange carried out such measurements for Fe, Co, and Ni, and for Ni + Co alloys. 

According to Graham s law, the rates of diffusion (mixing of gases) and effusion (escape of a gas from a container into a vacuum) are inversely proportional to the square root of the molar mass of the gas. 

A process related to diffusion is effusion, the process by which a gas escapes from a container into a vacuum through a small hole (Figure 5.21 ). The rate of effusion is also related to root mean square velocity— heavier molecules effuse more slowly than lighter ones. The rate of effusion—the amount of gas that effuses in a given time—is inversely proportional to the square root of the molar mass of the gas as follows ... 

Effusion If you have ever seen a tire deflate from a puncture, you are familiar with effusion. Effusion is the escape of a gas through a small opening in its container. Graham s law of effusion states that the rate of effusion for a gas is inversely proportional to the square root of its molar mass. 

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