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There are #1.40 × 10^25 color(white)(l)"H atoms"#.
The formula of ammonium sulfide is #("NH"_4)_2"S"#.
We see that 1 formula unit of #("NH"_4)_2"S"# contains 2 #"NH"_4# units, and each #"NH"_4# unit contains 4 #"H"# atoms.
Thus,
1 formula unit of #("NH"_4)_2"S"# contains 8 #"H"# atoms
and
1 mol of #("NH"_4)_2"S"# contains 8 mol of #"H"# atoms.
#"H atoms" = 2.90 color(red)(cancel(color(black)("mol" color(white)(l)("NH"_4)_2"S"))) × (8 color(red)(cancel(color(black)("mol H atoms"))))/(1 color(red)(cancel(color(black)("mol" color(white)(l)("NH"_4)_2"S")))) × (6.022 × 10^23color(white)(l) "H atoms")/(1 color(red)(cancel(color(black)("mol H atoms")))) = 1.40 × 10^25 color(white)(l)"H atoms"#