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
Aug 16, 2016

Answer:

#"645 g"#

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 #"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.

https://sciencelanguagegallery.wikispaces.com/Measuring+volume+by+Displacement

Now, the problem provides you with the density of bismuth metal, which is said to be equal to #"9.8 g cm"^(-3)#.

This tells you that for every cubic centimeter of bismuth, you get a mass of #"9.8 g"#.

#"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.