Question

We separate U-235 from U-238 by fluorinating a sample of 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 238UF6 and 235UF6. The atomic mass of U-235 is 235.054 amu and that of U-238 is 238.051 amu.

Answer 1

Answer:

The ratio of effusion rates for $^{238}UF_6$ and $^{235}UF_6$ is 0.995734.

Explanation:

Effusion rate of the $^{235}UF_6$gas = $R$

Effusion rate of the $^{238}UF_6$gas = $r$

Molar mass of $^{235}UF_6=235.054+6\times 19.00 amu=349.054 amu$

Molar mass of $^{238}UF_6=238.051+6\times 19.00 amu=352.051 amu$

Graham's law states that the rate of effusion or diffusion of gas is inversely proportional to the square root of the molar mass of the gas. The equation given by this law follows the equation:

$\text{Rate of diffusion}\propto \frac{1}{\sqrt{\text{Molar mass of the gas}}}$

$\frac{r}{R}=\sqrt{\frac{349.054 amu}{352.051 amu}}=0.995734$

The ratio of effusion rates for $^{238}UF_6$ and $^{235}UF_6$ is 0.995734.