Question

Question #5956f

Answer 1

`2.3 * 10^(22)"atoms"`

Explanation:

The first thing to do here is figure out how much pure gold you have in your `"10-g"` sample of `18` carat gold.

The carat is simply a measure of the purity of a given metal alloy based on fractions of `24`. In your case, `18` carat gold will contain `18` parts gold for every `24` parts of alloy by mass, which means that it has a percent purity of

`"% gold" = (18 color(red)(cancel(color(black)("parts gold"))))/(24color(red)(cancel(color(black)("parts alloy")))) xx 100 = "75% Au"`

So, if `18` carat gold has a purity of `75%`, it follows that your sample will contain

`10 color(red)(cancel(color(black)("g 18 carat gold"))) * overbrace("75 g pure gold"/(100color(red)(cancel(color(black)("g 18 carat gold")))))^(color(purple)("= 75% Au")) = "7.5 g pure gold"`

In order to determine how many atoms you have in `"7.5 g"` of pure gold, convert the mass to moles by using the element's molar mass.

Gold has a molar mass of `"197 g mol"^(-1)`, which means that one mole of gold will have a mass of `"197 g"`. This means that your sample will contain

`7.5 color(red)(cancel(color(black)("g"))) * overbrace("1 mole Au"/(197color(red)(cancel(color(black)("g")))))^(color(green)("the molar mass of Au")) = "0.0381 moles Au"`

Now that you know how many moles of gold you have, use Avogadro's number to convert them to atoms of gold

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

So, if one mole of gold contains `6.022 * 10^(23)` atoms, it follows that `0.0381` moles will contain

`0.0381color(red)(cancel(color(black)("moles Au"))) * (6.022 * 10^(23)"atoms")/(1color(red)(cancel(color(black)("mole Au")))) = color(green)(|bar(ul(color(white)(a/a)2.3 * 10^(22)"atoms"color(white)(a/a)|)))`

I'll leave the answer rounded to two sig figs.