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Chapter 2: Problem 48

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 .

Short Answer

Expert verified
Using the formulas InO and In₂O₃ and the given mass ratio, the calculated values for the atomic mass of Indium are 76.544 g per atom for InO and 114.816 g per atom for In₂O₃.

Step by step solution

01

Determine the mass of Oxygen in both formulas

In the InO formula, there is one Oxygen atom, so the mass of Oxygen will be its atomic mass (16.00g). In the In₂O₃ formula, there are three Oxygen atoms, so the mass of Oxygen will be three times its atomic mass (48.00 g).
02

Calculate the mass of Indium in both formulas using the mass ratio.

Using the given mass ratio, we will determine the mass of Indium in both formulas. In the InO formula: For 1g of Oxygen, there are 4.784g of Indium; For 16g of Oxygen (equal to one Oxygen atom), there will be: \( 16 \times 4.784 \) = \( 76.544 g \) of Indium (one Indium atom). In the In₂O₃ formula: For 1g of Oxygen, there are 4.784g of Indium; For 48g of Oxygen (equal to three Oxygen atoms), there will be: \( 48 \times 4.784 \) = \( 229.632 g \) of Indium (two Indium atoms).
03

Determine the atomic mass of Indium for each formula.

For the InO formula: There is one Indium atom, so the atomic mass of Indium is equal to the total mass of Indium in the InO formula, which is 76.544 g per atom. For the In₂O₃ formula: There are two Indium atoms, so we need to divide the total mass of Indium in the In₂O₃ formula by 2 to find the atomic mass of Indium. \( \frac{229.632}{2} \) = \( 114.816 g \) per atom. So, the values for atomic mass of Indium that are obtained using the formulas are: InO: 76.544 g per atom In₂O₃: 114.816 g per atom

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