We separate uranium- 235 from U-238 by fluorinating a sample...

We separate uranium- 235 from U-238 by fluorinating a sample of uranium to form $\mathrm{UF}_{6}$ (which is a gas) and then taking advantage of the different rates of effusion and diffusion for compounds containing the two isotopes. Calculate the ratio of effusion rates for ${ }^{238} \mathrm{UF}_{6}$ and ${ }^{235} \mathrm{UF}_{6}$. The atomic mass of $\mathrm{U}-235$ is $235.054$ amu and that of $\mathrm{U}-238$ is $238.051$ amu.

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Key Concepts

Graham's Law of Effusion

Graham's Law of Effusion states that the rate at which a gas effuses is inversely proportional to the square root of its molar mass. This principle allows us to compare the effusion rates of different gases by relating these rates to their molecular masses, making it a fundamental tool in processes that separate gases based on their mass differences.

Isotopic Separation

Isotopic separation involves differentiating compounds that contain isotopes, which are atoms of the same element having slightly different masses. Using techniques such as gas effusion, even minor differences in molecular mass—due to the presence of different isotopes—can be exploited to achieve separation, providing a method for enriching one isotope over another.

Molecular Mass Calculations

Accurate molecular mass calculations are essential when applying Graham's Law to real substances. By summing the atomic masses of the constituent atoms in a molecule, one determines the overall molar mass, which then directly influences the predicted rate of effusion, highlighting how small differences in mass can result in measurable differences in behavior between isotopic compounds.

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