Question

The relative density of mercury is $13.6$. What does this statement mean?

Answer 1

Relative density of a substance is defined to be the ratio of the density of that substance to the density of water. The relative viscosity is the proportion of the viscosity of a solution for the viscosity of the solvent utilized, here since both of the amounts are viscosities, their units get dropped off. Henceforth delivering no unit. This is the situation of relative density also. That is, it has no unit.

Formulas used:
$\text{Relative density of mercury} = \dfrac{\text{Density of mercury}}{\text{Density of water}}$
$\text{Density}= \dfrac{\text{Mass}}{\text{Volume}}$

Complete step by step answer:
We know that,
$\text{Relative density of mercury} = \,\dfrac{\text{Density of mercury}}{\text{Density of water}} = 13.6$
This expression when simplified means,
$\text{Density of mercury} = 13.6 \times \text{Density of water}$
We also know that density is the ratio of mass and volume of a substance. So, if we consider
$\text{Density of mercury} = \dfrac{\text{Mass of mercury}}{\text{Volume of mercury}}$
And, $\text{Density of water} = \dfrac{\text{Mass of water}}{\text{Volume of water}}$

We replace the values above instead of density of water and density of mercury, we have,
Relative density of mercury= $\dfrac{\text{Mass of mercury}}{\text{Volume of mercury}} \times \dfrac{\text{Volume of water}}{\text{Mass of water}}$
Let us assume that we take equal volume of mercy and water. This assumption cancels the volume part of the above equation, leaving only the mass part.
$\dfrac{\text{Mass of mercury}}{\text{Mass of water}} = 13.6$
Equating and bringing the denominator part to the other side, we get to the conclusion that, mass of mercury will be $13.6 \, \times$ the mass of water

In conclusion, the relative density of mercury is $13.6$ means that mercury is $13.6\,times$ as heavy as an equivalent volume of water.

Note: Relative density does not have a unit. Some relative quantities are ratios of the same quantities but for different substances. For instance, the relative viscosity is the ratio of the viscosity of a solution to the viscosity of the solvent used, here since both of the quantities are viscosities, their units get cancelled off. Hence producing no unit. Likewise, is the case of relative density as well.