Question

If the density of a sample is 14 g/mL, and its mass is 56 grams, what would its volume be?

Answer 1

`"4.0 mL"`

Explanation:

The idea here is that the density of a substance can be thought of as being a conversion factor between the mass of a sample of this substance and the volume it occupies.

In your case, the sample is said to have a density of `"14 g mL"^(-1)`. This means that `"1 mL"` of this substance will have a mass of `"14 g"`.

In other words, for every milliliter of that substance that you have in your sample, you get a mass of `"14 g"`.

The problem tells you that the mass of the sample is equal to `"56 g"`. Since this is more than the mass of `"1 mL"`, you can say for a fact that this sample will occupy more than `"1 mL"`.

How much more?

Use the given density to find out!

`56 color(red)(cancel(color(black)("g"))) * overbrace("1 mL"/(14color(red)(cancel(color(black)("g")))))^(color(purple)("density as a conversion factor")) = color(green)(|bar(ul(color(white)(a/a)"4.0 mL"color(white)(a/a)|)))`