Question

Calculate the relative density of the liquid from the following information:
Mass of empty bottle = 24.5g
Mass of bottle filled with water = 56.2g
Mass of bottle filled with liquid = 51.2g

Answer 1

Hint: Relative density of a substance is the ratio of its density to the density of a standard liquid. The standard liquid often used is water. Since bottles used for observing mass of liquid and water used are the same, their volume is also the same. Use the given data to find densities of water and liquid individually and then calculate relative density from the results obtained.

Complete step-by-step answer:
We know that the density of any liquid is the ratio of its mass to its volume. Here, the liquid and water are filled in the same bottle and then, the mass of the filled bottle is observed. We can note here that the volume of the liquid and water is the same and equal to the volume of the bottle.
If ${{m}_{w}}$ and ${{m}_{l}}$ are the masses of water and liquid respectively and $V$ is the volume of the bottle then their respective densities are ${{\rho }_{w}}=\dfrac{{{m}_{w}}}{V}$ and ${{\rho }_{l}}=\dfrac{{{m}_{l}}}{V}$.
Therefore, relative density of the liquid can be written as
${{k}_{l}}=\dfrac{{{\rho }_{l}}}{{{\rho }_{w}}}=\dfrac{\dfrac{{{m}_{l}}}{V}}{\dfrac{{{m}_{w}}}{V}}=\dfrac{{{m}_{l}}}{{{m}_{w}}}$
We are provided that, Mass of empty bottle = 24.5g, a Mass of bottle filled with water = 56.2g and a Mass of bottle filled with liquid = 51.2g.
We can write, mass of liquid as difference of mass of bottle filled with liquid and mass of empty bottle ${{m}_{l}}=51.2-24.5=26.7g$; and mass of water as difference of mass of bottle filled with water and mass of empty bottle. That is, ${{m}_{w}}=56.2-24.5=31.7g$.
Substituting these values, we get relative density of the liquid as
${{k}_{l}}=\dfrac{{{m}_{l}}}{{{m}_{w}}}=\dfrac{26.7}{31.7}$
Solving this, we have
${{k}_{l}}=0.84$
The relative density of the liquid is 0.84

Note: Avoid any calculation mistakes and also note the units of the quantities carefully. Before doing any calculations, the units of the quantities must be changed in the same system.
Relative density of a liquid is often calculated with respect to water. Relative density is a unitless quantity.