Note: I'll assume by the term "gram atom" you mean mole.
We're asked to find the number of moles of #"S"# in #48# #"g H"_2"SO"_4#.
We can solve this problems in a few steps:
-
Convert the given mass of #"H"_2"SO"_4# to moles (using its molar mass)
-
Convert the moles of #"H"_2"SO"_4# to moles of #"S"#)
Step 1.
We convert the given mass (#48# #"g H"_2"SO"_4#) to moles using the molar mass of #"H"_2"SO"_4#.
The molar mass is
#(2)overbrace((1.01color(white)(l)"g/mol"))^"hydrogen molar mass" + (1)overbrace((32.07color(white)(l)"g/mol"))^"sulfur molar mass" + (4)overbrace((16.00color(white)(l)"g/mol"))^"oxygen molar mass"#
#= color(red)(98.08# #color(red)("g/mol"#
Now converting grams to moles:
#48cancel("g H"_2"SO"_4)((1color(white)(l)"mol H"_2"SO"_4)/(98.08cancel("g H"_2"SO"_4))) = color(green)(0.489# #color(green)("mol H"_2"SO"_4#
Step 2.
Now we recognize that for every molecule of sulfuric acid, there is one atom of sulfur, so we end up with the same number:
#color(green)(0.489)cancel(color(green)("mol H"_2"SO"_4))((1color(white)(l)"mol S")/(1cancel("mol H"_2"SO"_4)))#
#= color(blue)(0.49# #color(blue)("mol S"#
rounded to #2# significant figures.
