We're asked to find the volume occupied by #1# #"molecule"# of #"H"_2"O"#.
We can find this through a few steps:
-
Convert molecules to moles via Avogadro's number
-
Convert moles to grams via molar mass
-
Convert grams to cubic centimeters (milliliters) via density
Step 1:
We'll first convert the one molecule of water to moles, using Avogadro's number:
#1cancel("molecule H"_2"O")((1color(white)(l)"mol H"_2"O")/(6.022xx10^23cancel("molecules H"_2"O")))#
#= color(red)(1.66 xx 10^-24# #color(red)("mol H"_2"O"#
Step 2:
Now, using the molar mass of water (#18.02# #"g/mol"#), we'll calculate the number of grams:
#color(red)(1.66xx10^-24)cancel(color(red)("mol H"_2"O"))((18.02color(white)(l)"g H"_2"O")/(1cancel("mol H"_2"O")))#
#= color(green)(2.99xx10^-23# #color(green)("g H"_2"O"#
Step 3:
Finally, knowing that #1# #"g"# water occupies a volume of #1# #"cm"^3# (or #1# #"mL"#, which is more conventional for liquids), we can calculate the volume occupied by one molecules of water:
#color(green)(2.99xx10^-23)cancel(color(green)("g H"_2"O"))((1color(white)(l)"mL")/(1cancel("g H"_2"O")))#
#= color(blue)(2.99xx10^-23# #color(blue)("mL H"_2"O"#
