Chapter 5, Problem 5.150P

Interpretation Introduction

Interpretation:

The number of steps needed to produce a sample of the enriched fuel used in nuclear reactors is to be calculated.

Concept introduction:

Effusion is explained as the movement of the gas molecule through a pinhole.

Diffusion can be explained as the mixing of one gas molecule with another gas molecule by random motion.

According to Graham’s law of effusion, the rate of effusion of a gas is inversely proportional to the square root of its molar mass.

The mathematical expression of Graham’s law of effusion is as follows:

$\frac{\text{Rate A}}{\text{Rate B}}=\frac{u_{rms\text{ of A}}}{u_{rms\text{ of B}}}=\frac{\sqrt{M_{\text{B}}}}{\sqrt{M_{\text{A}}}}=\frac{\text{time B}}{\text{time A}}=\frac{\text{Moles of A}}{\text{Moles of B}}$

Here, $M_{\text{B}}$ is the molar mass of gas $\text{B}$.

$M_{\text{A}}$ is the molar mass of gas $\text{A}$.

The ideal gas equation can be expressed as follows,

$PV=nRT$

Here, $P$ is the pressure, $V$ is the volume, $T$ is the temperature, $n$ is the mole of the gas and $R$ is the gas constant.

Here, $X_{\text{gas}}$ is the mole fraction of the gas.