Question

Calculate the mass of 3.920 × 10 to the power of 25 atoms of phosphorus?

Answer 1

`color(red)(2016.912 " grams P")`

Explanation:

You can use dimensional analysis to convert units easily for this problem.

Start with your `3.92*10^25` atoms P. You need to convert this number to moles, which requires you use Avogadro's number, which is the number of atoms of an element. in a mole.

You also need to use the molar mass of Phosphorus, which is `30.974 "g"/"mol"`

You can set it up like this:

`(3.92*10^25 "atoms P" )/"" * (1 " mol")/(6.02*10^23 "atoms P")*(30.974 " g")/(1 " mol")`

You can go ahead and cancel out units that appear on both the top and the bottom of the fraction:

`(3.92*10^25 color(red)(cancel("atoms P")) )/"" * (1 color(red)(cancel(" mol")))/(6.02*10^23color(red)(cancel("atoms P")) )*(30.974 " g")/(1 color(red)(cancel(" mol")))`

You can see that the unit will be grams, which makes sense as the question asks for mass.

You can multiply across to make your expression look like this:

`(3.92*10^25(30.974 " g"))/(6.02*10^23)`

Simplify the top row to get this:

`(1.2142*10^27 " g")/(6.02*10^23)`

And finally, divide to get:

`color(red)(2016.912 " grams P")`

Answer 2

`"2016 g"`

Explanation:

`"1 mol of atoms = 6.022 × 10"^23\ "atoms"`

Number of moles of phosphorus atoms given is

`3.920 × 10^25 cancel"atoms" × "1 mol"/(6.022 × 10^23\ cancel"atoms") = "65.09 mol"`

Molar mass of phosphorus is `"30.97 g/mol"`

Then, mass of phosphorus in given sample

`65.09 cancel"mol" × 30.97 "g"/cancel"mol" ≈ "2016 g"`