Two intermetallic compounds, \(\mathrm{A}_{3} \mathrm{~B}\) and \(\mathrm{AB}_{3}\), exist for elements \(A\) and \(B\). If the compositions for \(\mathrm{A}_{3} \mathrm{~B}\) and \(\mathrm{AB}_{3}\) are \(91.0 \mathrm{wt} \% \mathrm{~A}-9.0 \mathrm{wt} \% \mathrm{~B}\) and \(53.0\) \(\mathrm{wt} \% \mathrm{~A}-47.0 \mathrm{wt} \% \mathrm{~B}\), respectively, and element \(\mathrm{A}\) is zirconium, identify element \(\mathrm{B}\).

When studying chemistry, the concept of atomic mass plays a crucial role. The atomic mass is a weighted average of the masses of all the naturally occurring isotopes of an element, measured in atomic mass units (amu). For accurate calculations, particularly when dealing with intermetallic compounds, understanding atomic mass is essential.

For example, when given two intermetallic compounds, such as \(\mathrm{A}_{3} \mathrm{~B}\) and \(\mathrm{AB}_{3}\), the atomic mass helps in establishing the stoichiometry of the compound. Knowing the atomic mass of one element, such as zirconium (Zr) with an approximate atomic mass of 91.22 amu, one can perform calculations to find the mass of another unknown element in the compound by setting up and solving algebraic equations based on the given weight percentages.

The chemical composition of a substance describes the proportion of elements present in that substance. In the case of intermetallic compounds, which are specific stoichiometric phases involving two or more metals, the chemical composition is defined in terms of weight percent (wt%).

Understanding the concept of weight percent allows us to relate the mass of an element within a compound to the overall mass of the compound. For example, in \(\mathrm{A}_{3} \mathrm{~B}\), if the composition is 91.0 wt% A and 9.0 wt% B, it implies that in a certain amount of the compound, 91.0% of the mass is due to element A and the remaining 9.0% is due to element B. With this information, one can use the atomic masses of the constituent elements to find out the identity of the second element, as showcased in the textual exercise.

The periodic table is an organized chart of elements, arranged by increasing atomic number, that helps predict the properties of elements and the compounds they can form. Each element on the periodic table has a unique atomic mass, which is invaluable when identifying unknown elements in a compound.

In our exercise, after determining the atomic mass of the unknown element (B), we consult the periodic table to match this value to an element. We find that Tin (Sn) has an atomic mass closest to the calculated mass. This use of the periodic table illustrates how crucial this tool is for not only learning about the individual elements but also for solving complex problems regarding the composition of compounds.