Natasha's mother gave her a solid gold necklace. She determines the chain has a mass of #7.6# #g#. The density of pure gold is #19.3# #g##/##cm^3#. About how much gold was used to make her necklace?

1 Answer
Stefan V.
Aug 8, 2016

#"0.39 cm"^3#

Explanation:

Assuming that the neckless is made from #"24K"#, #24# karat gold, i. e. gold that is #99.9%# pure, you can solve this problem by using the mass of the neckless and the density of pure gold.

You know that gold has a density of #"19.3 g cm"^(-3)#. This tells you that every milliliter of gold has a mass of #"19.3 g"#. In your case, the mass of gold is said to be equal to #"7.6 g"#.

This means that in order to get this mass of gold, you must use

#7.6 color(red)(cancel(color(black)("g"))) * overbrace("1 cm"^3/(19.3 color(red)(cancel(color(black)("g")))))^(color(blue)("the density of gold")) = color(green)(|bar(ul(color(white)(a/a)color(black)("0.39 cm"^3)color(white)(a/a)|)))#

The answer is rounded to two sig figs, the number of sig figs you have for the mass of the neckless.

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