# How many atoms of hydrogen are in a 10 gram sample of water?

May 29, 2016

$6.7 \cdot {10}^{23} \text{atoms of H}$

#### Explanation:

In order to be able to determine how many atoms of hydrogen you get in $\text{10 g}$ of water, you must use the following conversions

$\text{grams" stackrel(color(red)(1)color(white)(aa))(->) "moles" stackrel(color(blue)(2)color(white)(aa))(->) "no. of molecules" stackrel(color(green)(3)color(white)(aa))(->) "no. of atoms}$

So, let's take these steps in order

$\textcolor{w h i t e}{}$

$\textcolor{red}{1} \to$ Grams of water to moles of water

In order to determine how many moles you have in a given mass of a compound, you must use said compound's molar mass. In water's case, you will have

10 color(red)(cancel(color(black)("g"))) * ("1 moleH"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "0.5551 moles H"_2"O"

$\textcolor{w h i t e}{}$

$\textcolor{b l u e}{2} \to$ Moles of water to number of molecules of water

Your conversion factor here will be Avogadro's number, which tells you how many molecules are needed in order to have exactly one mole of a substance.

More specifically, you have

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{1 mole" = 6.022 * 10^(23)"molecules}} \textcolor{w h i t e}{\frac{a}{a}} |}}} \to$ Avogadro's number

In your case, you will have

0.5551color(blue)(cancel(color(black)("moles H"_2"O"))) * (6.022 * 10^(23)"molec H"_2"O")/(1color(blue)(cancel(color(black)("mole H"_2"O")))) = 3.343 * 10^(23)"molec. H"_2"O"

$\textcolor{w h i t e}{}$

$\textcolor{g r e e n}{3} \to$ Molecules of water to atoms of hydrogen

Now, in order to find the number of atoms of hydrogen you have in your sample, you must use the fact that one water molecule is made up of $1$ atom of oxygen and $2$ atoms of hydrogen

This means that your sample will contain

3.343 * 10^(23)color(green)(cancel(color(black)("molec. H"_2"O"))) * "2 atoms of H"/(1color(green)(cancel(color(black)("molec. H"_2"O")))) = 6.7 * 10^(23)"atoms of H"

I'll leave the answer rounded to two sig figs.