# Question #5956f

##### 1 Answer

#### Explanation:

The first thing to do here is figure out how much *pure gold* you have in your **carat** gold.

The *carat* is simply a measure of the **purity** of a given *metal alloy* based on **fractions** of **for every**

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

So, if

#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 *mass* to *moles* by using the element's **molar mass**.

Gold has a molar mass of **one mole** of gold will have a mass of

#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

#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**.