Note: I'll assume by the term "gram atom" you mean mole.
We're asked to find the number of moles of "S"S in 4848 "g H"_2"SO"_4g H2SO4.
We can solve this problems in a few steps:
-
Convert the given mass of "H"_2"SO"_4H2SO4 to moles (using its molar mass)
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Convert the moles of "H"_2"SO"_4H2SO4 to moles of "S"S)
Step 1.
We convert the given mass (4848 "g H"_2"SO"_4g H2SO4) to moles using the molar mass of "H"_2"SO"_4H2SO4.
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.
