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

May 9, 2018

$\textcolor{red}{2016.912 \text{ grams P}}$

#### Explanation:

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

Start with your $3.92 \cdot {10}^{25}$ 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 $30.974 \text{g"/"mol}$

You can set it up like this:

$\left(3.92 \cdot {10}^{25} \text{atoms P" )/"" * (1 " mol")/(6.02*10^23 "atoms P")*(30.974 " g")/(1 " mol}\right)$

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

$\left(3.92 \cdot {10}^{25} \textcolor{red}{\cancel{\text{atoms P")) )/"" * (1 color(red)(cancel(" mol")))/(6.02*10^23color(red)(cancel("atoms P")) )*(30.974 " g")/(1 color(red)(cancel(" mol}}}\right)$

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:

$\frac{3.92 \cdot {10}^{25} \left(30.974 \text{ g}\right)}{6.02 \cdot {10}^{23}}$

Simplify the top row to get this:

$\frac{1.2142 \cdot {10}^{27} \text{ g}}{6.02 \cdot {10}^{23}}$

And finally, divide to get:

$\textcolor{red}{2016.912 \text{ grams P}}$

May 9, 2018

$\text{2016 g}$

#### Explanation:

$\text{1 mol of atoms = 6.022 × 10"^23\ "atoms}$

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 $\text{30.97 g/mol}$

Then, mass of phosphorus in given sample

$65.09 \cancel{\text{mol" × 30.97 "g"/cancel"mol" ≈ "2016 g}}$