Problem 36 - Chemistry An Atoms First Approach

Question

Indium oxide contains \(4.784 \mathrm{g}\) of indium for every \(1.000 \mathrm{g}\) of oxygen. In \(1869,\) when Mendeleev first presented his version of the periodic table, he proposed the formula \(\operatorname{In}_{2} \mathrm{O}_{3}\) for indium oxide. Before that time it was thought that the formula was InO. What values for the atomic mass of indium are obtained using these two formulas? Assume that oxygen has an atomic mass of \(16.00 .\)

Step-by-Step Solution

Answer

The values for the atomic mass of indium for the two proposed formulas are: For InO: \(4.784 g/mol\) For In2O3: \(7.176 g/mol\)

Step 1: Find Mass of Oxygen in 1 Mole of Each Formulation

For each potential formula of indium oxide, we need to find the corresponding mass of oxygen. For InO, there is only 1 mole of oxygen (O) present. For In2O3, there are 3 moles of oxygen (O) present.

Step 2: Calculate Mass of Indium for 1 Mole of Oxygen

We are given the ratio of indium to oxygen in indium oxide, i.e., \(4.784 g\) of indium for every \(1.000 g\) of oxygen. Mass of Indium for InO (1 mole of oxygen) = \(4.784 * 1 = 4.784 g\) Mass of Indium for In2O3 (3 moles of oxygen) = \(4.784 * 3 = 14.352 g\)

Step 3: Find Number of Moles of Indium for Each Formulation

For each potential formula of indium oxide, we need to find the number of moles of indium (In). For InO, there is only 1 mole of indium (In) present. For In2O3, there are 2 moles of indium (In) present.

Step 4: Calculate the Atomic Mass of Indium for Each Formulation

Now that we have the mass and the number of moles for indium in each formulation, we can calculate the atomic mass of indium for each formulation using the formula: Atomic mass of Indium = Mass of Indium in the Compound / Number of moles of Indium in the Compound Atomic mass of Indium for InO = \(4.784 g / 1 mole = 4.784 g/mol\) Atomic mass of Indium for In2O3 = \(14.352 g / 2 moles = 7.176 g/mol\) Thus, the values for the atomic mass of indium for the two proposed formulas are: For InO: \(4.784 g/mol\) For In2O3: \(7.176 g/mol\)

Key Concepts

Indium Oxide Formula

The formula of indium oxide has evolved over time based on advancements in chemical knowledge. Originally, scientists thought the formula was simply InO, meaning each molecule consisted of one atom of indium and one atom of oxygen. This changed when Mendeleev, a pioneering chemist, suggested a new formula:

• InO: One atom of indium and one atom of oxygen.
• In₂O₃: Two atoms of indium and three atoms of oxygen.

Based on chemical ratios given in the problem, for every 1 gram of oxygen, there are 4.784 grams of indium. This allows us to calculate the hypothetical atomic masses used in these formulas.
As our understanding of chemistry improved, In₂O₃ became widely accepted because it accounts for the stoichiometry that correctly matches with the periodic table's later developments.

Mendeleev's Periodic Table

Mendeleev's periodic table was a groundbreaking advancement in chemistry, offering a systematic way to organize elements based on their atomic weights and properties. Back in 1869, Dmitri Mendeleev's version did not just categorize elements but also predicted the existence and properties of undiscovered elements.
This periodic arrangement helped him correctly propose formulas like In₂O₃ for indium oxide. However, the significant contribution of Mendeleev's table lies in its ability to order elements logically by properties and predict chemical behaviors.
For indium oxide, Mendeleev's foresight into the compound's structure illustrated the power of his periodic table in influencing the atomic mass calculations that follow from accurate molecular formulas.

Chemical Stoichiometry

Chemical stoichiometry is the pillar of understanding how compounds form and how their constituent parts relate to each other. It involves calculating the ratios of elements in compounds to predict the outcomes of chemical reactions.

• When calculating the atomic mass of elements in a compound, stoichiometry is crucial.
• It explains how 4.784g of indium combines with 1.000g of oxygen to form indium oxide correctly.
• This ratio is essential to determine which formula - either InO or In₂O₃ - accurately represents the compound.

Thus, stoichiometry not only guides these calculations but ensures that the atomic mass of indium is interpreted correctly based on the number of atoms present as suggested by the stoichiometric coefficients in a balanced equation.

Molecular Formulas

Molecular formulas provide insight into the exact number of each type of atom in a molecule, which directly affects calculating atomic masses. They are key to understanding the composition and properties of chemical compounds.
Considering the formulas in this example, InO and In₂O₃ suggest different compositions:

• InO indicates a simpler, potentially less accurate representation based on earlier assumptions.
• In₂O₃ gives a more complex and accurate depiction of the bond structure and masses involved.

With the correct molecular formulas, we achieve precise calculations of atomic masses, which then allow scientists to accurately understand and predict chemical reactions and compound formation involving elements like indium.