# How much gallons of deionized water contains 2,000,000 hydrogen atoms?? Please solve. Thanks a lot.

Sep 16, 2017

Not that many gallons, and first we specify $\text{1 US gallon} \equiv 3785.4 \cdot m L$...........

#### Explanation:

And I use $\text{US gallon}$ because even here in the UK we have moved away (thankfully) from the gallon as a unit of volume......(NB $\text{1 Imperial Gallon} \equiv 4546 \cdot m L$). Maybe now that we are leaving the EU, there will be a move to reinstate pounds, shillings, and pence, and tons, and pounds, and gallons, and pints and gills, as the units of measure.

And if there are $2 \times {10}^{6} \cdot \text{hydrogen atoms}$, there are $1 \times {10}^{6}$ individual water molecules.....

And thus there are........

$\left(1 \times {10}^{6} \cdot \text{water molecules")/(6.022xx10^23*"water molecules} \cdot m o {l}^{-} 1\right) \times 18.01 \cdot g \cdot m o {l}^{-} 1 =$

$3.00 \times {10}^{-} 17 \cdot g \equiv 3.00 \times {10}^{-} 17 \cdot m L \equiv 7.90 \times {10}^{-} 21 \cdot \text{US gallons.}$

This measurement is almost meaningless, and it is really only an exercise.