Chapter 5, Problem 5.153P

(a)

Interpretation Introduction

Interpretation:

The different molecular masses obtained for ${\text{PCl}}_{\text{3}}$ is to be determined.

Concept introduction:

The isotopes can be defined as the atom of the same element with same number different number of neutrons.

The molar mass is defined as the mass of the all the atoms are present in the molecules in grams per mole.

(b)

Interpretation Introduction

Interpretation:

Among the different combination of ${\text{PCl}}_{\text{3}}$ molecules the most abundant molecule is to be determined.

Concept introduction:

The expression to calculate the fraction abundance of each isotope is as follows:

  $\text{fractional abundance of the isotope}=\left(\frac{\text{Percent abundance of isotope}\left(\%\right)}{100\text{ \%}}\right)$

(c)

Interpretation Introduction

Interpretation:

The ratio of effusion rates of the heaviest and lightest ${\text{PCl}}_{\text{3}}$ molecule 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:

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

Here,

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

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