# Question 268ae

Apr 11, 2016

$\text{1.89e23}$

#### Explanation:

The first thing to do here is use hydrazine's molar mass to determine how many moles you get in that $\text{10.08-g}$ sample.

Hydrazine has a molar mas of ${\text{32.045 g mol}}^{- 1}$, which means that one mole of this compound has a mass of $\text{32.045 g}$. 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 $6.022 \cdot {10}^{23}$ molecules.

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \text{1 mole" = 6.022 * 10^(23)"molecules} \textcolor{w h i t e}{\frac{a}{a}} |}}} \to$ 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)|)))#