First, convert #"50 g H"_2"SO"_4"# to moles using the molar mass of #"H"_2"SO"_4"#.
The molar mass of #"H"_2"SO"_4"# is equivalent to the molar mass of two atoms of #"H"#, one atom of #"S"#, and four atoms of #"O"#. The molar masses for all atoms can be found on the Periodic Table of Elements.
#(2 xx 1.008) + 32.06 + (4 xx 15.999) = 98.07#
There are #"98.07 g H"_2"SO"_4"# in #"1 mol"# of it. Therefore, in #"50 g H"_2"SO"_4"#, we have
#"50" cancel("g H"_2"SO"_4) xx ("1 mol H"_2"SO"_4)/("98.07" cancel("g H"_2"SO"_4)) = "0.5 mol H"_2"SO"_4 #
We know there are #6.022 xx 10^23# objects in #"1 mol"# of anything, so there are #6.022 xx 10^23# molecules of #"H"_2"SO"_4 # in #"1 mol"# of sulfuric acid.
Thus,
#"0.5" cancel("mol H"_2"SO"_4) xx (6.022 xx 10^23 " molecules H"_2"SO"_4)/(1 cancel("mol H"_2"SO"_4)) = 3 xx 10^23# #"molecules H"_2"SO"_4"#
This is rounded to one significant figure.
Additionally, in #"1 mol H"_2"SO"_4#, we know there are #"2 mol"# hydrogen atoms, #"1 mol"# sulfur atoms, and #"4 mol"# oxygen atoms. Since we have approximately #"0.5 mol H"_2"SO"_4#, we take half of each value: there are #"1 mol H"#, #"0.5 mol S"#, and #"2 mol O"#. If you want to find the number of atoms in each, just multiply each value by #6.022 xx 10^23#.
