Question

The density of solid fe is 7.87 g/cm3. how many atoms are present per cubic centimeter of fe?

Answer 1

Answer: The number of iron atoms in given amount is
`8.49* 10^(22)`

Step-by-step explanation:

Density of a substance is defined as the ratio of its mass and volume. The chemical equation representing density of a substance is:

`\text{Density of substance}=\frac{\text{Mass of substance}}{\text{Volume of substance}}`

We are given:

Density of iron =
`7.87g/cm^3`

Volume of iron =
`1cm^3`

Putting values in above equation, we get:

`7.87g/cm^3=\frac{\text{Mass of iron}}{1g/cm^3}\\\\\text{Mass of iron}=(7.87g/cm^3* 1cm^3)=7.87g`

To calculate the number of moles, we use the equation:

`\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}`

Given mass of iron = 7.87 g

Molar mass of iron = 55.65 g/mol

Putting values in above equation, we get:

`\text{Moles of iron}=(7.87g)/(55.65g/mol)=0.141mol`

According to mole concept:

1 mole of an element contains
`6.022* 10^(23)` number of atoms.

So, 0.141 moles of iron will contain =
`0.141* 6.022* 10^(23)=8.49* 10^(22)` number of atoms.

Hence, the number of iron atoms in given amount is
`8.49* 10^(22)`

Answer 2

The average that reflect the typical ratio of natural abundance of iron isotope is the atomic weight of the iron. Iron has four stable isotope that is iron 54 ,56, 57, 58. its atomic weight by mass is 9.27 x10^-22 grams
therefore number of atoms in cm^3 is
(7.87g/cm^3)/(9.27x10^-22)=8.49x10^21atoms/cm^3