Chapter 5, Problem 5.98P

(a)

Interpretation Introduction

Interpretation:

The following equation should be derived.

  $u_{rms}=\sqrt{\frac{3RT}{M}}$

Concept Introduction:

The energy which is linked with the motion of a body is known as kinetic energy. According to kinetic theory of gases, the average kinetic energy of a gas is calculated by following expression:

  $E_k=\frac{1}{2}m{u}^2$

Where, $E_k$ = average kinetic energy

m = molecular mass and u = average velocity

Another expression of average kinetic energy is:

  $E_K=\frac{3R}{2N_A}T$

Where, R = universal gas constant and N_A = Avogadro number

Average kinetic energy depends upon the temperature.

(b)

Interpretation Introduction

Interpretation:

The following equation should be derived.

  $\frac{Rat{e}_{Ar}}{Rat{e}_{Kr}}=\sqrt{\frac{M_{Kr}}{M_{Ar}}}or\frac{Rat{e}_A}{Rat{e}_B}=\sqrt{\frac{M_B}{M_A}}$

Concept Introduction:

The expression of root mean square velocity is:

  $u=\sqrt{\frac{3RT}{M}}$

From above expression, the relationship between molar mass and average velocity of gas is:

  $u\propto \sqrt{\frac{1}{M}}$

Average velocity is inversely proportional to the square root of molar mass.