# If the EPA allowable limit is 30 micrograms per liter how many atoms of uranium are present in 1 L?

May 3, 2018

$7.6 \cdot {10}^{19}$ uranium atoms.

#### Explanation:

The relative atomic mass of uranium is $238.0 \textcolor{w h i t e}{l} \text{u}$ , such that every mole of the atom has a mass of $238.0 \textcolor{w h i t e}{l} \text{g}$.

30color(white)(l)color(blue)("mg")=30*color(blue)(10^(-3)color(white)(l)"g")=3.0*10^(-2)color(white)(l)"g"

Hence the number of moles of Uranium atoms in a $30 \textcolor{w h i t e}{l} \text{mg}$ sample would be

3.0*10^(-2)color(white)(l)color(red)(cancel(color(black)("g")))*(1color(white)(l)"mol")/(238.0color(white)(l)color(red)(cancel(color(black)("g"))))=1.26*10^(-4)color(white)(l)"mol"

Each mole of any substance contains $6.023 \cdot {10}^{23}$ particles. Therefore $30 \textcolor{w h i t e}{l} \text{g}$ of uranium would contain

1.26*10^(-4)color(white)(l)color(red)(cancel(color(black)("mol")))*6.023*10^(23)color(white)(l)"atoms"*color(red)(cancel(color(black)("mol")))^(-1)=7.6*10^(19)color(white)(l) "atoms"