What is the mass of #"22.31 cm"^3# of zinc if the density of this metal is #"7.1 g/cm"^3# ?

1 Answer
Nov 5, 2017

Answer:

Here's what I got.

Explanation:

The thing to remember about a substance's density is that it tells you the mass of exactly #1# unit of volume that substance occupies.

In this case, you know that the density of zinc is equal to #"7.1 g cm"^(-3)#, which means that #"1 cm"^3# of zinc will have a mass of #"7.1 g"#.

#"7.1 g cm"^(-3) " " implies " " "1 cm"^3color(white)(.)"of zinc has a mass of 7.1 g"#

Now, you know that your sample has a volume of #"22.31 cm"^3#. Since you know for a fact that you get #"7.1 g"# of zinc for every #"1 cm"^3#, you can say that your sample will have a mass of #x# #"g"#, which you can find by doing

#(xcolor(white)(.)color(red)(cancel(color(black)("g"))))/(22.31 color(red)(cancel(color(black)("cm"^3)))) = (7.1 color(red)(cancel(color(black)("g"))))/(1 color(red)(cancel(color(black)("cm"^3))))#

This will get you

#x = 22.31 * 7.1 = 158.4#

You can thus say that your sample will have a mass of

#color(darkgreen)(ul(color(black)("mass = 158.4 g")))#

I'll leave the answer rounded to four sig figs, but keep in mind that you have two sig figs for the density of zinc.