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Chapter 2: Problem 44

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 \(\mathrm{In}_{2} \mathrm{O}_{3}\) 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
For the formula InO, the atomic mass of indium is approximately \(76.54\,\text{g/mol}\), while for the formula In2O3, it is approximately \(114.81\,\text{g/mol}\).

Step by step solution

01

Calculate the molar mass ratio of indium to oxygen for the formula InO

The given formula for indium oxide is InO, which means there is one atom of indium for one atom of oxygen. Since the atomic mass of oxygen is given as 16.00 g/mol, we can write the molar mass ratio of indium to oxygen for InO as x : 16.00.
02

Calculate the molar mass ratio of indium to oxygen for the formula In2O3

The given formula for indium oxide is In2O3, which means there are two atoms of indium for every three atoms of oxygen. Since the atomic mass of oxygen is given as 16.00 g/mol, we can write the molar mass ratio of indium to oxygen for the formula In₂O₃ as 2x : 3(16.00), where x is the atomic mass of indium.
03

Compare the molar mass ratios to the given mass ratio

The mass ratio of indium to oxygen given is 4.784 g of indium to 1.000 g of oxygen. We can use these values to find the atomic mass of indium for each possible formula. By cross-multiplying, we can set up equations for each formula based on the molar mass ratios: InO: x = (4.784 g / 1.000 g) * 16.00 g/mol In2O3: 2x = (4.784 g / 1.000 g) * 3 * 16.00 g/mol
04

Solve for the atomic mass of indium for each formula

For the formula InO, we have: x = (4.784 g / 1.000 g) * 16.00 g/mol x = 76.54 g/mol For the formula In2O3, we have: 2x = (4.784 g / 1.000 g) * 3 * 16.00 g/mol 2x = 229.61 g/mol x = 114.81 g/mol The atomic mass of indium obtained for the formula InO is approximately 76.54 g/mol, and for the formula In2O3 is approximately 114.81 g/mol.

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