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Chapter 3: Problem 108

The atomic mass of \(\mathrm{Bi}\) is to be determined by converting the compound \(\mathrm{Bi}\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{3}\) to \(\mathrm{Bi}_{2} \mathrm{O}_{3} .\) If \(5.610 \mathrm{g}\) of \(\mathrm{Bi}\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{3}\) yields \(2.969 \mathrm{g} \mathrm{Bi}_{2} \mathrm{O}_{3},\) what is the atomic mass of Bi?

Short Answer

Expert verified
The atomic mass of Bi is calculated to be approximately 208.98 g/mol after following above steps and performing the calculations.

Step by step solution

01

Calculate Molar Mass of Bismuth Trioxide (Bi2O3)

Firstly, determine the molar mass of \( \mathrm{Bi}_{2}\mathrm{O}_{3} \). Since it is composed of 2 atoms of Bi and 3 atoms of O, the formula would be: \(Molar mass = 2 × (atomic mass of Bi) + 3 × (atomic mass of O)\). Here, we know that the atomic mass of O is 16 amu from the periodic table, but we do not know the atomic mass of Bi yet.
02

Establish Ratio of Bi in Bi(C6H5)3 to Bi in Bi2O3

The stoichiometry of the reaction indicates that each molecule of \( \mathrm{Bi}(\mathrm{C}_{6}\mathrm{H}_{5})_{3} \) generates half a molecule of \( \mathrm{Bi}_{2}\mathrm{O}_{3}\). Hence the ratio is 1:0.5.
03

Calculate the Mass of Bi

We have 2.969g of \( \mathrm{Bi}_{2}\mathrm{O}_{3}\), and this contains 2 atoms of Bi. Therefore, the mass of Bi that came from the 5.61 g of \( \mathrm{Bi}(\mathrm{C}_{6}\mathrm{H}_{5})_{3} \) is 2/3 of 2.969g since Bi contributes 2 out of the 3 parts (2 from Bi, 1 from O3) to \( \mathrm{Bi}_{2}\mathrm{O}_{3}\).
04

Calculate the Atomic Mass of Bi

From step 2, we know that the Bi in 5.61g of \( \mathrm{Bi}(\mathrm{C}_{6}\mathrm{H}_{5})_{3} \) is 2/3 of 2.969g. Hence, the atomic mass Bi can be obtained by diving this mass by the number of moles in 5.61g of \( \mathrm{Bi}(\mathrm{C}_{6}\mathrm{H}_{5})_{3} \). This gives the atomic mass in g/mol.

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Most popular questions from this chapter

An oxoacid with the formula \(\mathrm{H}_{x} \mathrm{E}_{y} \mathrm{O}_{z}\) has a formula mass of 178 u, has 13 atoms in its formula unit, contains \(34.80 \%\) by mass, and \(15.38 \%\) by number of atoms, of the element E. What is the element \(\mathrm{E}\), and what is the formula of this oxoacid?

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