# How do you convert 84.520 mg of "Ne" to atoms?

Aug 6, 2016

$2.5223 \cdot {10}^{22} \text{atoms of Ne}$

#### Explanation:

To convert your sample of neon to atoms of neon, you must

$\textcolor{red}{1.}$ Convert the mass of the sample from milligrams to grams

$\textcolor{b l u e}{2.}$ Convert the sample from grams to moles by using neon's molar mass

$\textcolor{\mathrm{da} r k g r e e n}{3.}$ Convert the number of moles to number of atoms by using Avogadro's numebr

So, let's start with the first step. To convert the mass of neon from milligrams to grams, use the fact that

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{1 g" = 10^3 "mg}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

You will have

84.520 color(red)(cancel(color(black)("mg"))) * "1 g"/(10^3color(red)(cancel(color(black)("mg")))) = "0.84520 g"

Next, use neon's molar mass to see how many moles of neon would be present in your sample.

color(blue)(|bar(ul(color(white)(a/a)color(black)(M_("M Ne") = "20.1797 g mol"^(-1))color(white)(a/a)|)))

Neon has a molar mass of ${\text{20.1797 g mol}}^{- 1}$, which means that one mole of neon has a mass of $\text{20.1797 g}$.

In your case, you will end up with

0.84520 color(blue)(cancel(color(black)("g"))) * "1 mole Ne"/(20.1797color(blue)(cancel(color(black)("g")))) = "0.041884 moles Ne"

Finally, use Avogadro's number to see how many atoms of neon would amount to that many moles.

$\textcolor{\mathrm{da} r k g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{1 mole" = 6.022 * 10^(23)"atoms}} \textcolor{w h i t e}{\frac{a}{a}} |}}} \to$ Avogadro's number

You will have

0.041884 color(darkgreen)(cancel(color(black)("moles Ne"))) * (6.022 * 10^(23)"atoms Ne")/(1color(darkgreen)(cancel(color(black)("mole Ne")))) = color(darkgreen)(|bar(ul(color(white)(a/a)color(black)(2.5223 * 10^(22)"atoms Ne")color(white)(a/a)|)))

The answer is rounded to five sig figs, the number of sig figs you have for the mass of neon.