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?
1 Answer
Explanation:
Don't be confused by the phrase
... the mass of a sample of bismuth that displaces
#"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
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
This tells you that for every cubic centimeter of bismuth, you get a mass of
#"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.
