Question

How do you calculate the density of a 6.75 g solid with a volume of 5.35 cm3?

Answer 1

`"1.26 g cm"^(-3)`

Explanation:

Your goal when trying to calculate the density of a substance when given its mass and the volume it occupies is to use the given info to find the mass of one unit of volume of that substance.

As you know, the density of a substance is defined as the mass of exactly one unit of volume of that substance. In your case, the volume of the sample is expressed in cubic centimeters, `"cm"^3`, which means that one unit of volume will be `"1 cm"^3`.

So, you must find the mass of `"1 cm"^3` of this unknown solid. To do that, use the fact that the mass of the solid is uniformly distributed in the volume it occupies.

This means that you will have

`1 color(red)(cancel(color(black)("cm"^3))) * "6.75 g"/(5.35color(red)(cancel(color(black)("cm"^3)))) = "1.26 g"`

You can now say that because `"1 cm"^3` of this solid has a mass of `"1.26 g"`, the density of the solid, `rho_"solid"`, is

`color(green)(|bar(ul(color(white)(a/a)color(black)(rho_"solid" = "1.26 g cm"^(-3))color(white)(a/a)|)))`

The answer is rounded to three sig figs.