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Chapter 1: Problem 36

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
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 by step solution

01

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.
02

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) = \(4.784 * 3 = 14.352 g\)
03

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.
04

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: \(7.176 g/mol\)

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