Question #5956f

1 Answer
Apr 17, 2016

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.