We're asked to find the number of atoms in #1.6# #"g CH"_4#.
To do this, we can first find the number of moles of #"CH"_4# present, using the molar mass of methane (#16.04# #"g/mol"#):
#1.6cancel("g")((1color(white)(l)"mol CH"_4)/(16.04cancel("g CH"_4))) = 0.0997# #"mol CH"_4#
Now, we can use Avogadro's number to find the number of molecules of #"CH"_4# present:
#0.0997cancel("mol CH"_4)((6.022xx10^23color(white)(l)"molecules CH"_4)/(1cancel("mol CH"_4)))#
#= 6.01xx10^22# #"molecules CH"_4#
Now, we ask ourselves, "How many atoms are in one molecule of methane?"
Well, there is #1# #"C"# and #4# #"H"# , which totals to #color(red)(5#. We can use this relationship to find the number of atoms:
#6.01xx10^22cancel("molecules CH"_4)((5color(white)(l)"atoms")/(1cancel("molecule"))) = color(blue)(3.0xx10^23# #color(blue)("atoms"#
rounded to #2# significant figures.
