Question #5956f

1 Answer
Apr 17, 2016

Answer:

#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.