The process for determining the number atoms in #"0.390 g P"_2"O"# involves the following steps:

**#"molar mass"##rarr##"moles of molecules"##rarr##"number of molecules"##rarr##"number of atoms"#**

**Determine molar mass of #"P"_2"O"#.**

Determine the molar mass of #"P"_2"O"#. I looked it up online and found it to be #"77.947 g/mol"# (rounded to five significant figures).

http://www.webqc.org/molecular-weight-of-P2O.html

**Determine moles of molecules #"P"_2"O"#**

In order to determine moles of #"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 #"P"_2"O"# by #6.022xx10^23# 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 #"P"_2"O"#.**

Since every molecule of #"P"_2"O"# consists of three atoms, multiply #3.0130xx20^21"molecules"# by #"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)