As discussed in the “Chemistry Put to Work” box in Section 10.8, ...

Question

As discussed in the “Chemistry Put to Work” box in Section 10.8, enriched uranium can be produced by effusion of gaseous UF6 across a porous membrane. Suppose a process were developed to allow effusion of gaseous uranium atoms, U(g). Calculate the ratio of effusion rates for 235U and 238U, and compare it to the ratio for UF6 given in the essay.

Accepted Answer

Identify the formula for the effusion rate ratio using Graham's law: $ \frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}} $, where $ r_1 $ and $ r_2 $ are the effusion rates of two gases, and $ M_1 $ and $ M_2 $ are their molar masses.. Determine the molar masses of the isotopes: $ M_{235U} = 235 \text{ g/mol} $ and $ M_{238U} = 238 \text{ g/mol} $.. Substitute the molar masses of $ 235U $ and $ 238U $ into Graham's law to find the effusion rate ratio: $ \frac{r_{235U}}{r_{238U}} = \sqrt{\frac{238}{235}} $.. Calculate the molar mass of $ UF_6 $ for both isotopes: $ M_{235UF_6} = 235 + 6(19) $ and $ M_{238UF_6} = 238 + 6(19) $.. Substitute the molar masses of $ UF_6 $ into Graham's law to find the effusion rate ratio for $ UF_6 $: $ \frac{r_{235UF_6}}{r_{238UF_6}} = \sqrt{\frac{M_{238UF_6}}{M_{235UF_6}}} $.