Question

Mercury, which is often used in thermometers, has a density of 13.534 g/mL at room temperature. What volume of mercury contains 10.0 g?

Answer 1

`"0.739 mL"`

Explanation:

A substance's density basically tells you how much mass of said substance occupies one unit of volume.

In your case, the density of mercury is given in Grams per milliliter, `"g mL"^(-1)`, which means that it expresses the mass of mercury in `"1 mL"` of mercury.

So, mercury is said to have a density of `"13.534 g mL"^(-1)`, which means that `"1 mL"` of mercury has a mass of `"13.534 g"`.

You want to know the volume of mercury that will contain `"10.0 g"` of the element. Since your sample is lighter than the mass associated with `"1 mL"`, you can expect its volume to be smaller than `"1 mL"`.

You can use dimensional analysis using the density of mercury as a conversion factor

`10.0color(red)(cancel(color(black)("g"))) * overbrace("1 mL"/(13.534color(red)(cancel(color(black)("g")))))^(color(purple)("given density")) = color(green)(|bar(ul("0.739 mL"))|)`

The answer is rounded to three **sig figs, the number of sig figs you have for the mass of your sample.