# The density of bismuth metal is 9.8 g/cm^3. What is the mass of a sample of bismuth that displaces 65.8 mL of water?

Aug 16, 2016

$\text{645 g}$

#### Explanation:

Don't be confused by the phrase

... the mass of a sample of bismuth that displaces $\text{65.8 mL}$ of water

that's just a fancy way of saying that you're dealing with a sample of bismuth metal that has a volume of $\text{65.8 mL}$.

The idea is that when you add a solid to a sample of water, the volume of the solid will be equal to the volume of the water it displaces.

Now, the problem provides you with the density of bismuth metal, which is said to be equal to ${\text{9.8 g cm}}^{- 3}$.

This tells you that for every cubic centimeter of bismuth, you get a mass of $\text{9.8 g}$.

${\text{9.8 g cm"^(-3) = "9.8 g"/"1 cm}}^{3}$

Use the density of the metal as a conversion factor to calculate the mass of your sample

65.8 color(red)(cancel(color(black)("cm"^3))) * "9.8 g"/(1color(red)(cancel(color(black)("cm"^3)))) = "645 g"

I'll leave the answer rounded to three sig figs.