We obtain uranium- 235 from U-238 by fluorinating the...

We obtain uranium- 235 from $U-238$ by fluorinating the uranium to form 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

Isotopic Separation Techniques

Using differences in molecular mass for separating isotopes is a common industrial application of effusion and diffusion principles. By exploiting the slight mass differences between isotopic compounds, separation methods such as gas centrifugation or effusion can enrich specific isotopes, which has significant applications in nuclear technology.

Graham's Law of Effusion

This law states that the rate at which a gas effuses is inversely proportional to the square root of its molecular mass. It provides the basis for comparing how quickly different gases—or isotopic variants of a gas—can escape through a small opening, which is fundamental in processes like gas separation.

Molecular Mass Influence on Effusion

The molecular mass of a gas is a key determinant of its kinetic behavior. In effusion, lighter molecules move faster on average than heavier ones, resulting in higher rates of passage through an aperture. This concept is crucial for quantitatively predicting separations based on the square root ratio of molecular masses.

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