Question

A piece of tin has a mass of `"16.52 g"` and a volume of `"2.26 cm"^3`. What is the density of tin?

Answer 1

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

Explanation:

Your goal when trying to find the density of a given substance is to determine the mass of one unit of volume of that substance.

In this case, the volume of a piece of tin is given in cubic centimeters, which means that one unit of volume will be `"1 cm"^3`.

To find the mass of `"1 cm"^3` of tin, use the fact that mass is distributed uniformly in the given volume of tin. In other words, you can use the known composition to find

`1 color(red)(cancel(color(black)("cm"^3))) * "16.52 g"/(2.26color(red)(cancel(color(black)("cm"^3))) ) = "7.31 g"`

Now, the density of a given substance is defined as the mass that corresponds to one unit of volume of that substance. In this case, every `"1 cm"^3` has a mass of `"7.31 g"`, which is why tin is said to have a density of

`color(green)(bar(ul(|color(white)(a/a)color(black)("7.31 g cm"^(-3))color(white)(a/a)|))) -> 7.31` grams per cubic centimer

The answer is rounded to three sig figs, the number of sig figs you have for the volume of the piece of tin.