Naturally found uranium consists of 99.274% ²³⁸U, 0.720% ²³⁵U, and 0.006% ²³³U. As we have seen, ²³⁵U is the isotope that can undergo a nuclear chain reaction. Most of the ²³⁵U used in the first atomic bomb was obtained by gaseous diffusion of uranium hexafluoride, UF₆(g).

(a) What is the mass of UF₆ in a 30.0-L vessel of UF₆ at a pressure of 695 torr at 350 K?

(b) What is the mass of ²³⁵U in the sample described in part (a)?

(c) Now suppose that the UF₆ is diffused through a porous barrier and that the change in the ratio of ²³⁸U and ²³⁵U in the diffused gas can be described by Equation 10.23. What is the mass of ²³⁵U in a sample of the diffused gas analogous to that in part (a)?

(d) After one more cycle of gaseous diffusion, what is the percentage of ²³⁵UF₆ in the sample?

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