Question

Uranium- 235 can be separated from U-238 by fluorinating the 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 U-235 is $235.054 \mathrm{amu}$ and that of $\mathrm{U}-238$ is $238.051$ amu.

Name: Problem 53, Chapter 5: Principles of Chemistry: A Molecular Approach
Uploaded: 2024-01-05T02:30:48-08:00
Duration: 3 min 8 s
Channel: Dominique Jan Tan
Description: Uranium- 235 can be separated from U-238 by fluorinating the uranium to form UF6 (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 UF6 and ^235 UF6. The atomic mass of U-235 is 235.054 amu and that of U-238 is 238.051 amu.

   Uranium- 235 can be separated from U-238 by fluorinating the 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 U-235 is $235.054 \mathrm{amu}$ and that of $\mathrm{U}-238$ is $238.051$ amu.

Principles of Chemistry: A Molecular Approach

Nivaldo J. Tro 1st Edition

Chapter 5, Problem 53

Instant Answer

Solved by Expert Dominique Jan Tan

01/05/2024

Step 1

Effusion is the process by which gas molecules escape through a tiny hole into a vacuum. The rate of effusion of a gas is inversely proportional to the square root of its molar mass (Graham's law of effusion). Show more…

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Uranium- 235 can be separated from U-238 by fluorinating the 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 U-235 is $235.054 \mathrm{amu}$ and that of $\mathrm{U}-238$ is $238.051$ amu.

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Key Concepts

Graham's Law of Effusion

Graham's Law states that the rate at which a gas effuses is inversely proportional to the square root of its molar mass. This means that lighter gas molecules escape through a small opening faster than heavier ones, making the difference in molecular weight a key factor in separation techniques that rely on effusion.

Isotope Separation via Effusion

Isotope separation can be accomplished by exploiting the slight differences in the rates at which molecules containing different isotopes effuse. Because the rate of effusion depends on the square root of the molecular mass, even small differences between isotopes’ masses, as applied in the case of uranium isotopes, can lead to measurable differences in effusion rates that allow them to be separated.

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