Chapter 2, Problem 2.CCP

Interpretation Introduction

Interpretation:

The data for three compounds and their percent by mass of the elements $\text{Ex}\text{Ey}\text{and}\text{Ez}$ in each compound.

  $\begin{array}{l}\text{Compound}\text{\%Ex}\text{\%Ey}\text{\%Ez}\\ \text{A}\text{37}\text{.485}\text{12}\text{.583}\text{49}\text{.931}\\ \text{B}\text{40}\text{.002}\text{6}\text{.7142}\text{53}\text{.284}\\ \text{C}\text{40}\text{.685}\text{5}\text{.1216}\text{54}\text{.193}\end{array}$.

The possible thing to know about the empirical formulas for these three compounds has to be determined.

Explanation of Solution

The three compounds have different formulas.  The first of these has a larger number of $\text{Ey}$ atoms in the formula, due to its larger % mass; the third has the least $\text{Ey}$.

$\text{100}\text{.0g}$ of compound B has $\text{40}\text{.002g}$ $\text{Ex}$, $\text{6}\text{.7142}\text{g}$ $\text{Ey}$ and $\text{53}\text{.284}\text{g}$ $\text{Ez}$.  Scaling the sample A by a factor of $\text{1}\text{.0671}$ shows that $\text{106}\text{.71}\text{g}$ of A has $\text{40}\text{.002g}$ $\text{Ex}$, $\text{13}\text{.472}\text{g}$ $\text{Ey}$ and $\text{53}\text{.284}\text{g}$ $\text{Ez}$.  Scaling the sample C by a factor 0.983212 shows that $\text{98}\text{.3212g}$ of compound C has $\text{40}\text{.002g}$ $\text{Ex}$, $\text{5}\text{.0356}\text{g}$ $\text{Ey}$ and $\text{53}\text{.284}\text{g}$ $\text{Ez}$.

Masses shows that these three compounds have the same proportion of $\text{Ex}$ to $\text{Ez}$.  So the ratio of $\text{Ex}$ atoms to $\text{Ey}$ atoms in each of these formulas is the same.  The ratio of $\text{Ey}$ in each of them is $\text{A/B}\text{=}\text{2/1}\text{and}\text{B/C}\text{=}\text{1}\text{.333}\text{=}\text{4/3}$   By comparing the information, it is possible to determine the $\text{Ey}$ ratio in the three compounds is $\text{A:B:C}\text{=}\text{8:4:3}$.