# Dimensional analysis - 2 | Chemistry and the Scientific Method

Mercury is a metal with a very low melting point (-38.8°C) and therefore thermometers were made with mercury. The volume of mercury changes slightly with temperature; the small change in volume indicates the temperature. But it is important to know the density of mercury.

At 25°C, 1.667 mL of mercury has a mass of 22.55 grams. What is the density of mercury in g.mL^{-1} and kg.m^{-3}?

density = $\frac{\mathrm{mass}}{\mathrm{volume}}$

density (in g.mL^{-1}) = $\frac{\mathrm{mass}(\mathrm{in}\mathrm{g})}{\mathrm{volume}(\mathrm{in}\mathrm{mL})}$ = $\frac{22.55}{1.667}$ = 13.53 g.mL^{-1}

13.53 g.mL^{-1} = $\frac{13.53\mathrm{g}}{1\mathrm{mL}}$ x $\frac{1\mathrm{kg}}{1000\mathrm{g}}$ x $\frac{1000\mathrm{mL}}{1\mathrm{L}}$ x $\frac{1\mathrm{L}}{1{\mathrm{dm}}^{3}}$ x $\frac{1000{\mathrm{dm}}^{3}}{1{\mathrm{m}}^{3}}$ = 13.53 x 10^{3} kg.m^{-3}

density (in kg.m^{-3}) = 13.53 x 10^{3} kg.m^{-3}