The 235U isotope (atomic mass = 235.00) undergoes fission when bombarded with neutrons. However, its natural abundance is only 0.72 percent. To separate it from the more abundant 238U isotope (atomic mass = 238.00), uranium is first converted to UF6, which is easily vaporized above room temperature. The mixture of 235UF6 and 238UF6 gases is then subjected to many stages of effusion. Calculate how much more quickly 235UF6 effuses than 238UF6. Give the answer as the ratio of rates of 235UF6 to 238UF6 to four decimal places.

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maacastrobr maacastrobr · Answer 1 · 2019-12-11T12:10:03+01:00

Answer:

So ²³⁵UF₆ effuses 1.0043 times faster than ²³⁸UF₆

Explanation:

The rate of effusion of two gases A and B can be expressed by Graham's law:

[tex]\frac{EffusionRateA}{EffusionRateB}=\sqrt{\frac{M_{B}}{M_{A}} }[/tex]

Where M is the molar mass, and in this case A is ²³⁵UF₆ while B is ²³⁸UF₆.

So now we calculate the molar mass of each mass:

²³⁵UF₆ ⇒235 + 6*19 = 349 g/mol

²³⁸UF₆ ⇒238 + 6*19 = 352 g/mol

Putting the data in Graham's law:

[tex]\frac{Rate^{235}UF_{6}}{Rate^{238}UF_{6}}=\sqrt{\frac{352}{349} }[/tex] = 1.0043

So ²³⁵UF₆ effuses 1.0043 times faster than ²³⁸UF₆.