# 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?

Sep 5, 2016

${\text{7.31 g cm}}^{- 3}$

#### 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 ${\text{1 cm}}^{3}$.

To find the mass of ${\text{1 cm}}^{3}$ 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 ${\text{1 cm}}^{3}$ has a mass of $\text{7.31 g}$, which is why tin is said to have a density of

$\textcolor{g r e e n}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{\text{7.31 g cm}}^{- 3}} \textcolor{w h i t e}{\frac{a}{a}} |}}} \to 7.31$ 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.