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

Nov 5, 2017

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 ${\text{7.1 g cm}}^{- 3}$, which means that ${\text{1 cm}}^{3}$ of zinc will have a mass of $\text{7.1 g}$.

$\text{7.1 g cm"^(-3) " " implies " " "1 cm"^3color(white)(.)"of zinc has a mass of 7.1 g}$

Now, you know that your sample has a volume of ${\text{22.31 cm}}^{3}$. Since you know for a fact that you get $\text{7.1 g}$ of zinc for every ${\text{1 cm}}^{3}$, you can say that your sample will have a mass of $x$ $\text{g}$, which you can find by doing

$\left(x \textcolor{w h i t e}{.} \textcolor{red}{\cancel{\textcolor{b l a c k}{{\text{g"))))/(22.31 color(red)(cancel(color(black)("cm"^3)))) = (7.1 color(red)(cancel(color(black)("g"))))/(1 color(red)(cancel(color(black)("cm}}^{3}}}}\right)$

This will get you

$x = 22.31 \cdot 7.1 = 158.4$

You can thus say that your sample will have a mass of

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{mass = 158.4 g}}}}$

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.