Question

The mass of an empty density bottle is \[30g\] . It is \[75g\] when filled completely with water and \[65g\] when filled completely with a liquid. Find a) volume of density bottle b) density of liquid and c) relative density of the liquid.

Answer 1

Hint: Initially we need to find the volume of the density bottle through the mass of water that is filling it. Then we have to find the density of the liquid from its mass and mass of water. To obtain its relative density which is given by the mass of the liquid and water. Applying the respective formulae for each of them we obtain the results.

Complete answer:
First note down all the formulae,
The volume of density bottle = Mass of water in grams completely filling the bottle
 Density of liquid \[{\text{ }}\rho {\text{ }} = {\text{ }}\dfrac{{{\text{mass}}\,{\text{of}}\,{\text{liquid}}}}{{{\text{mass}}\,{\text{of}}\,{\text{water}}}}\]
The density of a substance is compared with the density of water to get a number which is called the relative density of that substance. To determine the relative density of the liquid, the relative density of the bottle is used.
Relative Density = $\operatorname{R} = \dfrac{{{\text{Mass}}\,{\text{of}}\,{\text{given}}\,{\text{volume}}\,{\text{of}}\,{\text{liquid}}}}{{{\text{Mass}}\,{\text{of}}\,{\text{same}}\,{\text{volume}}\,{\text{of}}\,{\text{water}}}}$
Mass of empty density bottle, ${M_1} = 30\,grams$
Mass of bottle and water, ${M_2} = 75\,grams$
Mass of liquid$(x)$${M_3} = 65\,grams$
Mass of water = $M = {M_2} - {M_1} = 45\,grams$
Hence we apply the above formulae
a) Volume of density bottle = Mass of water $ = 45\,grams$
b) Density of liquid \[{\text{ }}\rho {\text{ }} = {\text{ }}\dfrac{{{\text{mass}}\,{\text{of}}\,{\text{liquid}}}}{{{\text{mass}}\,{\text{of}}\,{\text{water}}}}\]
Taking Mass of liquid $(x)$= \[{M_3}{\text{ }}-{\text{ }}{M_1}{\text{ }} = {\text{ }}65{\text{ }}-{\text{ }}30 = \,\,35\,grams\]
Therefore $\rho = \dfrac{{35}}{{45}} = {\mathbf{0}}.{\mathbf{77}}\,grams\,c{m^{ - 3}}$
c) Mass of water in the density bottle \[ = {\text{ }}75{\text{ }}-{\text{ }}30{\text{ }} = {\text{ }}45\,grams\]
Therefore, the volume of water in density bottle \[ = 45\]
Mass of the liquid whose volume is equal to the density bottle = \[65{\text{ }}-{\text{ }}30{\text{ }} = {\text{ }}35\,\,grams\]
Therefore, the relative density of the liquid = $\dfrac{{{\text{mass}}\,{\text{of}}\,45{\text{cc}}\,{\text{of}}\,{\text{liquid}}}}{{{\text{mass}}\,{\text{of}}\,45{\text{cc}}\,{\text{of}}\,{\text{water}}}} = \dfrac{{35}}{{45}} = \dfrac{7}{9} = 0.77$

Note: Different substances will be having different densities, which means for the same volume different substances weigh differently, as they weigh differently heavier substances have a tendency to settle at the bottom. Hence by applying the relevant formulae given above for the density, volume, and mass of either water or other liquids we can obtain its relative density. Here we are considering water as a reference liquid.