# How I can calculate the number of hydrogen atoms in one gallon deionized water? thank you so much.

Sep 16, 2017

There are 3.04 × 10^26color(white)(l) "atoms of H" in 1 gal of water.

#### Explanation:

Step 1. Convert gallons of water to litres

$\text{Volume" = 1 color(red)(cancel(color(black)("gal"))) × "4.55 L"/(1 color(red)(cancel(color(black)("gal")))) = "4.55 L}$

Step 2. Convert litres of water to grams of water

$\text{Grams of water" = 4.55 color(red)(cancel(color(black)("L"))) × (1000 color(red)(cancel(color(black)("mL"))))/(1 color(red)(cancel(color(black)("L")))) × "0.9982 g"/(1 color(red)(cancel(color(black)("L")))) = "4542 g}$

Step 3. Convert grams of water to moles of water

$\text{Moles of water" = 4542 color(red)(cancel(color(black)("g"))) × "1 mol"/(18.02 color(red)(cancel(color(black)("g")))) = "252.0 mol}$

Step 4. Convert moles of water to molecules of water

"Molecules of water" = 252.0 color(red)(cancel(color(black)("mol"))) × (6.022 × 10^23 "molecules")/(1 color(red)(cancel(color(black)("mol"))))

= 1.518 × 10^26color(white)(l) "molecules"

Step 5. Convert molecules of water to atoms of hydrogen

"Atoms of H" = 1.518 × 10^26color(red)(cancel(color(black)("molecules H"_2"O"))) × "2 atoms H"/(1 color(red)(cancel(color(black)("molecule H"_2"O"))))

= 3.04 × 10^26color(white)(l) "atoms H"