Preparation of nuclear fuel.By far the most important application of Graham's law is in thepreparation of fuel for nuclear energy reactors. The process of isotope enrichmentincreases theproportion of fissionable, but rarer, 235U (only 0.7% by mass of naturally occurring uranium) tothe nonfissionable, more abundant 238U (99.3% by mass). Because the two isotopes haveidentical chemical properties, they are extremely difficult to separate chemically. But, one wayto separate them takes advantage of a difference in a physical property—the effusion rate ofgaseous compounds. Uranium ore is treated with fluorine to yield a gaseous mixture of 238UF6and 235UF6that is pumped through a series of chambers separated by porous barriers.Molecules of 235UF6are slightly lighter (= 349.03) than molecules of 238UF6(= 352.04),so they move slightly faster and effuse through each barrier 1.0043 times faster. Many passesmust be made, each one increasing the fraction of 235UF6, until the mixture obtained is 3–5%by mass 235UF6. This process was developed during the latter years of World War II and2. IEB Wireframe...9 of 1611/3/14, 10:37 AM
produced enough 235U for two of the world's first atomic bombs. Today, a less expensivecentrifuge process is used more often. The ability to enrich uranium has become a keyinternational concern, as more countries aspire to develop nuclear energy and nuclear arms.The Process of DiffusionClosely related to effusion is the process of gaseous diffusion,the movement of one gas throughanother. Diffusion rates are also described generally by Graham's law:For two gases at equal pressures, such as NH3and HCl, moving through another gas or a mixture ofgases, such as air, we findThe reason for this dependence on molar mass is the same as for effusion rates: lighter molecules havehigher average speeds than heavier molecules, so they move farther in a given time.If gas molecules move at hundreds of meters per second (see Figure 5.14), why does it take a secondor two after you open a bottle of perfume to smell it? Although convection plays an important role inthis process, another reason for the time lag is that a gas particle does not travel very far before itcollides with another particle (Figure 5.22). Thus, a perfume molecule travels slowly because itcollides with countless molecules in the air. The presence of so many other particles means thatdiffusion rates are much lower than effusion rates.Imagine how much quicker you can walk throughan empty room than through a room crowded with other moving people.Figure 5.22Diffusion of gases. When different gases (black, from the left, and green, from the right) movethrough each other, they mix. For simplicity, the complex path of only one black particle is shown (inred). In reality, all the particles have similar paths.