In a series of experiments, a chemist prepared three different compounds that contain only iodine and fluorine and determined the mass of each element in each compound: $$ \begin{array}{lcc} \hline \text { Compound } & \text { Mass of Iodine (g) } & \text { Mass of Fluorine (g) } \\ \hline 1 & 4.75 & 3.56 \\ 2 & 7.64 & 3.43 \\ 3 & 9.41 & 9.86 \\ \hline \end{array} $$ (a) Calculate the mass of fluorine per gram of iodine in each compound. (b) How do the numbers in part (a) support the atomic theory?

To calculate the mass ratio of fluorine per gram of iodine in each compound, divide the mass of fluorine given in the problem by the mass of iodine. For Compound 1: $$ \text{Mass ratio} = \frac{\text{Mass of Fluorine}}{\text{Mass of Iodine}} = \frac{3.56\,\text{g}}{4.75\,\text{g}} \approx 0.749\,\text{g/g} $$ For Compound 2: $$ \text{Mass ratio} = \frac{\text{Mass of Fluorine}}{\text{Mass of Iodine}} = \frac{3.43\,\text{g}}{7.64\,\text{g}} \approx 0.449\,\text{g/g} $$ For Compound 3: $$ \text{Mass ratio} = \frac{\text{Mass of Fluorine}}{\text{Mass of Iodine}} = \frac{9.86\,\text{g}}{9.41\,\text{g}} \approx 1.048\,\text{g/g} $$

The numbers calculated in part (a) show the relationship between the masses of fluorine and iodine in each compound formed. The compounds were formed by combining the individual atoms of iodine and fluorine together in different whole number ratios. This supports the atomic theory by showcasing the law of multiple proportions, which states that when two elements combine to form more than one compound, the masses of one element that combines with a fixed mass of the other element are in a ratio of small whole numbers. Here, we observe that the mass ratios of fluorine to iodine are in ratios close to either whole numbers or simple fractions (e.g., \(\frac{3}{4}\), \(\frac{1}{2}\), and 1). This indicates that elements combine in fixed whole number ratios, as the atomic theory suggests. In conclusion, the calculated mass ratios of fluorine to iodine in each compound demonstrate the law of multiple proportions, which serves as an important foundation for the atomic theory.