# Question 1d274

May 19, 2017

The number of atoms of hydrogen in 6.5 g of water is $4.4 \times {10}^{23} \text{atoms H}$.

#### Explanation:

One mole of anything is $6.022 \times {10}^{23}$ particles, including atoms. Once you know the number of moles of H, you multiply that by $6.022 \times {10}^{23}$atoms/mol.

The ultimate goal is to determine the number of H atoms in a given mass of water. This requires several steps.

You need to first determine the percentage of hydrogen in water. Then multiply the percentage of hydrogen by the given mass of water. This will give the mass of hydrogen in a $6.5$ gram sample of water. Determine the moles H by multiplying its calculated mass by the inverse of its molar mass. Then multiply the moles by $6.022 \times {10}^{23}$ atoms/mol to get atoms of H.

color(blue)("Determine percentage of H in one mole of water".

$\text{Percent H"=("mass of H")/("mass of water")xx100}$

$\text{Percent H"=(2.016"g H")/(18.015"g H"_2"O")xx100="11.2% H}$

color(blue)("Determine the mass of H in 6.5 g of water".
Multiply the percent of H in decimal form by $6.5$g water.

(11.2%)/100=0.112

$0.112 \times 6.5 \text{g H"_2"O"="0.728 g H}$

color(blue)("Determine the number of moles of H".
Multiply the calculated mass of H by the inverse of its molar mass, which is its atomic weight on the periodic table in g/mol.

0.728color(red)cancel(color(black)("g H"))xx(1"mol H")/(1.008color(red)cancel(color(black)("g H")))="0.722 mol H"

color(blue)("Determine the number of atoms of H"
Multiply mol H by $6.022 \times {10}^{23}$ atoms/mol.

0.722color(red)cancel(color(black)("mol H"))xx(6.022xx10^23"atoms H")/(1color(red)cancel(color(black)("mol H")))=4.4xx10^23"atoms H"# (rounded to two decimal places due to $\text{6.5 g}$)