Final answer:
To calculate the mass of iron(III) oxide that contains a billion oxygen atoms, first determine the empirical formula of the compound. From the given information of the percentage composition of iron and oxygen, the empirical formula is Fe2O3. The molar mass of Fe2O3 is 159.69 g/mol. Using Avogadro's number, set up a proportion to find the mass of Fe2O3 containing a billion oxygen atoms.
Step-by-step explanation:
To calculate the mass of iron(III) oxide that contains a billion oxygen atoms, we need to determine the empirical formula of iron(III) oxide. From the given information, the compound contains 69.94% iron and 30.06% oxygen. We can assume a 100 gram sample, which would give us 69.94 grams of iron and 30.06 grams of oxygen. From the molar mass of iron (55.85 g/mol) and oxygen (16.00 g/mol), we can calculate the number of moles of iron and oxygen in the sample.
The molar ratio of iron to oxygen can be calculated by dividing the moles of iron by the moles of oxygen. In this case, we get a ratio of 1:1.5, which can be multiplied by 2 to get whole number subscripts while maintaining the correct ratio. Therefore, the empirical formula of iron(III) oxide is Fe2O3.
Now, the molar mass of Fe2O3 is 159.69 g/mol (2 x 55.85 g/mol + 3 x 16.00 g/mol). To find the mass of iron(III) oxide that contains a billion oxygen atoms, we can use the mole concept. The Avogadro's number states that 1 mole of any substance contains 6.022 x 10^23 particles (atoms, molecules, ions, etc.). Therefore, a mole of oxygen atoms is equal to 6.022 x 10^23 oxygen atoms.
We can set up a proportion to find the mass of iron(III) oxide containing a billion oxygen atoms:
- 1 mole Fe2O3 = 159.69 g
- 6.022 x 1023 moles O = 1 billion O atoms
- x grams Fe2O3 = mass containing 1 billion O atoms
Solving for x, we can cross-multiply and calculate the mass of iron(III) oxide that contains a billion oxygen atoms.