Chapter 10, Problem 87QP

Interpretation Introduction

Interpretation:

To identify an unknown gas formed by the fermentation of glucose and calculate its molar mass.

Concept introduction:

From Maxwell’s Speed Distribution Curve, the molecular speed of two gas samples can be compared using the relation as follows:

$u_{rms}\left(1\right)=\sqrt{\frac{3RT}{{\mu }_1}}$

and,

$u_{rms}\left(2\right)=\sqrt{\frac{3RT}{{\mu }_2}}$

Now,

$\begin{array}{c}\frac{u_{rms}\left(1\right)}{u_{rms}\left(2\right)}=\frac{\sqrt{\frac{3RT}{{\mu }_1}}}{\sqrt{\frac{3RT}{{\mu }_2}}}\\ =\sqrt{\frac{{\mu }_2}{{\mu }_1}}\end{array}$ …… (1)

Here, $u_{rms}\left(1\right)$ and $u_{rms}\left(2\right)$ is the root mean square speed of each gas compound, respectively, $R$ is the gas constant, $T$ is the absolute temperature, and ${\mu }_1\text{ and }{\mu }_2$ is the molar mass of each gas compound, respectively.