Question

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

Answer 1

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

`"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

`"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

`"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"`