Question

Question #eb525

Answer 1

`2.6 * 10^(24)"atoms"`

Explanation:

I assume that you're interested in finding out how may atoms of sodium, `"Na"`, you have in your `"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 `->` use the molar mass of sodium `" "color(blue)((1))`
• moles to number of atoms `->` use Avogadro's number `" "color(darkgreen)((2))`

`color(blue)((1))" "`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 `"23.0 g mol"^(-1)`, which means that one mole of sodium has a mass of `"23.0 g"`.

In your case, `"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"`

`color(darkgreen)((2))" "` 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 * 10^(23)` atoms of said element.

`color(blue)(|bar(ul(color(white)(a/a)"1 mole" = 6.022 * 10^(23)"atoms"color(white)(a/a)|))) ->` 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.