A mass of mercury occupies 0.95 L. What volume would an equal mass of ethanol occupy? The density of mercury is 13.546 g/mL and the density of ethanol is .789 g/mL?

##”16 L”##

For a given substance, its tells you the mass occupied by one unit of volume of that substance.

In essence, is a measure of how well the molecules of a substance are packed in a unit of volume. In your case, the densities of the two substances are expressed in grams per milliliter, which means that a unit of volume will be ##”1 mL”##.

So, mercury has a density of ##”13.546 g/mL”##, which means that ##”1 mL”## of mercury will have a mass of ##”13.546 g”##. On the other hand, ##”1 mL”## of ethanol will have a mass of ##”0.789 g”##.

Your strategy here will be to use the density of mercury to find the mass that occupies ##”0.95 L”##, then use the density of ethanol to find the volume that would have an equal mass.

So, you will have – don’t forget to convert the volume from liters to milliliters

0.95 color(red)(cancel(color(black)(“L”))) * (10^3color(red)(cancel(color(black)(“mL”))))/(1color(red)(cancel(color(black)(“L”)))) * overbrace(“13.546 g”/(1color(red)(cancel(color(black)(“mL”)))))^(color(purple)(“density of mercury”)) = “12,868.7 g”##

The volume of ethanol that will have an equal mass is

##”12,868.7″ color(red)(cancel(color(black)(“g”))) * overbrace(“1 mL”/(0.789color(red)(cancel(color(black)(“g”)))))^(color(purple)(“density of ethanol”)) = “16,310.1 mL”##

Rounded to two and expressed in liters, the answer will be

##”16,310.1″color(red)(cancel(color(black)(“mL”))) * “1 L”/(10^3color(red)(cancel(color(black)(“mL”)))) = color(green)(“16 L”)##

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