Question

Question #59469

Answer 1

`"68 g"`

Explanation:

The thing to remember about density is that it always tells you the mass of exactly one unit of volume of a given substance.

In this case, the density of mercury is said to be equal to `"13.6 g cm"^(-3)`, so one unit of volume is equal to `"1 cm"^3`. This means that the mass of `"1 cm"^3` of mercury is equal to `"13.6 g"`.

`"13.6 g cm"^(-3) implies "1 cm"^3 "Hg" stackrel(color(white)(acolor(red)("has a mass of")aaaa))(->) "13.6 g"`

You know that the sample of mercury has a volume of `"5.0 mL"`, so use the density of mercury as a conversion factor to find the mass of the sample.

Start by converting the volume of the sample to cubic centimeters

`5.0 color(red)(cancel(color(black)("mL"))) * "1 cm"^3/(1color(red)(cancel(color(black)("mL")))) = "5.0 cm"^3`

You will thus have

`5.0 color(red)(cancel(color(black)("cm"^3))) * overbrace("13.6 g"/(1color(red)(cancel(color(black)("cm"^3)))))^(color(blue)("the density of Hg")) = color(darkgreen)(ul(color(black)("68 g")))`

The answer is rounded to two sig figs.