Question #268ae

The first thing to do here is use hydrazine's molar mass to determine how many moles you get in that `"10.08-g"` sample.

Hydrazine has a molar mas of `"32.045 g mol"^(-1)`, which means that one mole of this compound has a mass of `"32.045 g"`. This means that your sample will contain

`10.08 color(red)(cancel(color(black)("g"))) * ("1 mole N"_2"H"_4)/(32.045color(red)(cancel(color(black)("g")))) = "0.3146 moles N"_2"H"_4`

To convert the number of moles of hydrazine to molecules, use the fact that one mole of any compound contains `6.022 * 10^(23)` molecules.

`color(blue)(|bar(ul(color(white)(a/a)"1 mole" = 6.022 * 10^(23)"molecules"color(white)(a/a)|))) ->` Avogadro's number

In your case, `0.3146` moles of hydrazine will contain

`0.3146 color(red)(cancel(color(black)("moles N"_2"H"_4))) * overbrace((6.022 * 10^(23)"molec.")/(1color(red)(cancel(color(black)("mole N"_2"H"_4)))))^(color(purple)("Avogadro's number")) = 1.8945 * 10^(23)"molec."`

Rounded to three sig figs, the answer will be

`"no. of atoms of N"_2"H"_4 = color(green)(|bar(ul(color(white)(a/a)"1.89e23"color(white)(a/a)|)))`