Question

Calculator the mass of iron (III) oxide ( Fe2O3) that contains a billion (1.0x10^9) oxygen atoms. Be sure your answer has a unit symbol if necessary, and round it to 2 significant digits

Answer 1

The mass of iron (III) oxide
`(Fe_2O_3)`that contains a billion
`(1.0x10^9)` oxygen atoms is
`8.8x10^-^1^3 g.`

To solve this problem

The number of moles of oxygen atoms can be calculated using the following formula:

moles of solute = number of atoms / Avogadro's number

moles of oxygen atoms =
`(1.0x10^9 atoms) / (6.022x10^2^3 atoms/mol)`

moles of oxygen atoms =
`1.66x10^-^1^5 mol`

Now, Since there are 3 oxygen atoms in one molecule of
`Fe_2O_3`, the number of moles of
`Fe_2O_3` can be calculated using the following formula:

moles of
`Fe_2O_3` = moles of oxygen atoms / 3

moles of
`Fe_2O_3` =
`(1.66x10^-^1^5 mol) / 3`

moles of
`Fe_2O_3` =
`5.53x10^-^1^6 mol`

Now, The mass of
`Fe_2O_3`can be calculated using the following formula:

mass of solute = moles of solute * molar mass of solute

molar mass of
`Fe_2O_3`= 159.69 g/mol

mass of
`Fe_2O_3` =
`(5.53x10^-^1^6 mol) * (159.69 g/mol)`

mass of
`Fe__2O_3`=
`8.84x10^-^1^3 g`

Rounding
`8.84x10^-^1^3`g to two significant digits gives:

mass of
`Fe_2O_3`=
`8.8x10^-^1^3 g`

So, the mass of iron (III) oxide
`(Fe_2O_3)` that contains a billion
`(1.0x10^9)`oxygen atoms is
`8.8x10^-^1^3 g.`

Answer 2

1)First, let's use the chemical formula of iron (III) oxide (Fe₂O₃) to find the number of molecules of Fe₂O₃.

So one molecule of iron oxide contains 2 atom of Fe and 3 atom of Oxygen.

So you might find that:

1 molecule of Fe₂O₃ ------ 3 atoms of Oxygen

x molecule of Fe₂O₃ ------ 1.0×10⁹ atoms of Oxygen

x = 1.0×10⁹/3

x = 3.3 × 10⁸ molecules of Fe₂O₃

2) Now you use the Avogrado's constant to transform molecules into moles.

6.022 × 10²³ molecules ----- 1 mol

3.3 × 10⁸ molecules of Fe₂O₃ ----- x mol

x = 3.3 × 10⁸/6.022 × 10²³

x = 5.5 × 10⁻¹⁶ moles of Fe₂O₃

3) Finally, let's use the molar mass of Fe₂O₃ to find out the mass.

Molar mass of Fe₂O₃: (2x55.9) + (3x16) = 159.8

159.8 g ----- 1 mol

x g ----- 5.5 × 10⁻¹⁶ moles of Fe₂O₃

x = 8.8 x 10^-14 grams

Answer: The mass of iron (III) oxide ( Fe2O3) that contains a billion (1.0x10^9) oxygen atoms is 8.8 x 10^-14 grams