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Chapter 5: Problem 64

Bauxite, the principal ore used in the production of aluminum, has a molecular formula of \(\mathrm{Al}_{2} \mathrm{O}_{3} \cdot 2 \mathrm{H}_{2} \mathrm{O} .\) The \(\cdot \mathrm{H}_{2} \mathrm{O}\) in the formula are called waters of hydration. Each formula unit of the compound contains two water molecules. a. What is the molar mass of bauxite? b. What is the mass of aluminum in 0.58 mole of bauxite? c. How many atoms of aluminum are in 0.58 mole of bauxite? d. What is the mass of \(2.1 \times 10^{24}\) formula units of bauxite?

Short Answer

Expert verified
The molar mass of bauxite is 106.00 g/mol. The mass of aluminum in 0.58 mole of bauxite is 31.72 g, and there are 6.98 × 10^23 aluminum atoms in this amount of bauxite. The mass of 2.1 × 10^24 formula units of bauxite is 369.28 g.

Step by step solution

01

1. Determine the molar mass of each element in the formula

Using the periodic table, find the molar mass for each element in the formula: Aluminum (Al): 26.98 g/mol Oxygen (O): 16.00 g/mol Hydrogen (H): 1.01 g/mol
02

2. Calculate the molar mass of bauxite

Using the molar masses of the elements and their respective numbers in the formula, we can find the molar mass of bauxite: Molar mass of bauxite = (2 × 26.98 g/mol) + (3 × 16.00 g/mol) + (4 × 1.01 g/mol) = 53.96 g/mol + 48.00 g/mol + 4.04 g/mol = 106.00 g/mol The molar mass of bauxite is 106.00 g/mol. b. Mass of Aluminum in 0.58 mole of bauxite
03

1. Calculate the mass of 0.58 mole of bauxite

Using the calculated molar mass of bauxite: Mass of bauxite = (0.58 mol) × (106.00 g/mol) = 61.48 g
04

2. Calculate the mass of aluminum in bauxite

Bauxite has a molar mass of 106.00 g/mol, out of which aluminum has a mass of 2 × 26.98 g/mol = 53.96 g/mol. Thus, the mass of aluminum in 1 mole of bauxite is: 53.96 ÷ 106.00 So, the mass of aluminum in 0.58 mole of bauxite is: Mass of aluminum = (61.48 g) × (53.96 ÷ 106.00) = 31.72 g The mass of aluminum in 0.58 mole of bauxite is 31.72 g. c. Number of atoms of aluminum in 0.58 mole of bauxite
05

1. Calculate the number of moles of aluminum in bauxite

In one mole of bauxite, there are two moles of aluminum as in the molecular formula \(\mathrm{Al}_{2} \mathrm{O}_{3} \cdot 2 \mathrm{H}_{2} \mathrm{O}\). So, in 0.58 mole of bauxite, there are: Aluminum moles = 0.58 mole × 2 = 1.16 moles
06

2. Calculate the number of aluminum atoms

Number of atoms can be determined by using Avogadro's number (6.022 × 10^23 atoms/mol). So, the number of aluminum atoms in 1.16 moles of aluminum is: Number of atoms = (1.16 mol) × (6.022 × 10^23 atoms/mol) = 6.98 × 10^23 atoms There are 6.98 × 10^23 aluminum atoms in 0.58 mole of bauxite. d. Mass of 2.1 × 10^24 formula units of bauxite
07

1. Calculate the number of moles of bauxite

Using Avogadro's number to convert formula units to moles: 2.1 × 10^24 formula units × (1 mol / 6.022 × 10^23 formula units) = 3.48 moles
08

2. Calculate the mass of bauxite

Using the molar mass of bauxite (106.00 g/mol) to find the mass: Mass of bauxite = (3.48 mol) × (106.00 g/mol) = 369.28 g The mass of 2.1 × 10^24 formula units of bauxite is 369.28 g.

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Most popular questions from this chapter

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