# Question eb525

Jun 30, 2016

$2.6 \cdot {10}^{24} \text{atoms}$

#### Explanation:

I assume that you're interested in finding out how may atoms of sodium, $\text{Na}$, you have in your $\text{0.1 kg}$ sample.

The first thing to do here is convert the mass of sodium from kilograms to grams

0.1 color(red)(cancel(color(black)("kg"))) * (10^3"g")/(1color(red)(cancel(color(black)("kg")))) = "100 g"

From this point on, you will have to use two conversion factors

• grams to moles $\to$ use the molar mass of sodium $\text{ } \textcolor{b l u e}{\left(1\right)}$
• moles to number of atoms $\to$ use Avogadro's number $\text{ } \textcolor{\mathrm{da} r k g r e e n}{\left(2\right)}$

$\textcolor{b l u e}{\left(1\right)} \text{ }$Grams to moles

The molar mass of an element essentially tells you the mass of one mole of said element. In this case, sodium has a molar mass of ${\text{23.0 g mol}}^{- 1}$, which means that one mole of sodium has a mass of $\text{23.0 g}$.

In your case, $\text{100 g}$ of sodium will be equivalent to

100color(blue)(cancel(color(black)("g"))) * "1 mole Na"/(23.0color(blue)(cancel(color(black)("g")))) = "4.35 moles Na"

$\textcolor{\mathrm{da} r k g r e e n}{\left(2\right)} \text{ }$ Moles to number of atoms

A mole is simply a very, very large collection of atoms. In order to have one mole of a given element, you need to have $6.022 \cdot {10}^{23}$ atoms of said element.

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

In your case, $4.35$ moles of sodium will contain

4.35 color(darkgreen)(cancel(color(black)("moles Na"))) * (6.022 * 10^(23)"atoms of Na")/(1color(darkgreen)(cancel(color(black)("moles Na")))) = color(green)(|bar(ul(color(white)(a/a)color(black)(2.6 * 10^(24)"atoms Na")color(white)(a/a)|)))#

I'll leave the answer rounded to two sig figs, but keep in mind that you only have one sig fig for the mass of sodium.