# Question b9611

Sep 3, 2015

That depends on how many grams of 20-carat gold you have.

#### Explanation:

Now, since you didn't provide an actual mass of 20-carat gold, I'll use $x$ grams.

Now, the first thing that you need to do is figure out how much gold you have in $x$ grams of 20-carat gold. As you know, the purity of gold varies depending on what it's used for.

As you can see, 20-carat gold contains 83.33% gold by weight. This means that a 100-g sample of 20-carat gold will contain 83.33 g of pure gold.

In your case, $x$ grams will contain

xcolor(red)(cancel(color(black)("g 20-carat"))) * "83.33 g gold"/(100color(red)(cancel(color(black)("g 20-carat")))) = (0.833 * x) " grams of gold"

Use gold's molar mass, which tells you what the mass of 1 mole of gold is, to determine how many moles of gold you'd get in that mass

(0.833 * x)color(red)(cancel(color(black)("g gold"))) * "1 mole Au"/(196.97color(red)(cancel(color(black)("g gold")))) = (0.00423 * x)" moles Au"

To get how many atoms of gold you'd get in that many moles, use the fact that 1 mole of any element contains exactly $6.022 \cdot {10}^{23}$ atoms of that element - this is known as Avogadro's number.

In your case, that many moles would contain

(0.00423 * x)color(red)(cancel(color(black)("moles Au"))) * (6.022 * 10^(23)"atoms of Au")/(1color(red)(cancel(color(black)("mole Au")))) = (2.55 * x) * 10^(21)"atoms of Au"#

To get the actual answer, simply replace $x$ with the mass of 20-carat gold given to you in the problem.

$2.55 \cdot 20 \cdot {10}^{21} = 5.1 \cdot {10}^{22} \text{atoms of Au}$