Question

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

Answer 1

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.