# How many atoms are in "0.390 g P"_2"O"?

Feb 27, 2017

$\text{0.390 g P"_2"O}$ contains $9.04 \times {10}^{21} \textcolor{w h i t e}{.} \text{atoms}$.

#### Explanation:

The process for determining the number atoms in $\text{0.390 g P"_2"O}$ involves the following steps:

$\text{molar mass}$$\rightarrow$$\text{moles of molecules}$$\rightarrow$$\text{number of molecules}$$\rightarrow$$\text{number of atoms}$

Determine molar mass of $\text{P"_2"O}$.

Determine the molar mass of $\text{P"_2"O}$. I looked it up online and found it to be $\text{77.947 g/mol}$ (rounded to five significant figures).
http://www.webqc.org/molecular-weight-of-P2O.html

Determine moles of molecules $\text{P"_2"O}$
In order to determine moles of $\text{P"_2"O}$, we divide the given mass in the question by the molar mass.

(0.390color(red)cancel(color(black)("g")))/(77.947color(red)cancel(color(black)("g"))/"mol")="0.0050034 mol P"_2"O"

I am leaving some extra digits in the number of moles to reduce rounding errors. I will round the final answer to three significant figures.

Determine number of molecules.

Multiply the moles of $\text{P"_2"O}$ by $6.022 \times {10}^{23}$ molecules.

0.0050034color(red)(cancel(color(black)("mol")))xx(6.022xx10^23"molecules")/color(red)(cancel(color(black)("mol")))=3.0130xx10^21"molecules"

Determine number of atoms of $\text{P"_2"O}$.

Since every molecule of $\text{P"_2"O}$ consists of three atoms, multiply $3.0130 \times {20}^{21} \text{molecules}$ by $\text{3 atoms/molecule}$.

3.0130xx10^21 color(red)cancel(color(black)("molecules"))xx(3color(white)(.)"atoms")/color(red)(cancel(color(black)("molecule")))=9.04 xx10^21color(white)(.)"atoms" (rounded to three significant figures)