Question

What is the mass of $ 15{\text{ ml}} $ sample of mercury, if the density of mercury $ (liquid){\text{ = 13}}{\text{.55 g c}}{{\text{m}}^{ - 3}} $ .
 $ (i){\text{ 209}} $
 $ (ii){\text{ 203}} $
 $ (iii){\text{ 208}} $
 $ (iv){\text{ 231}} $

Answer 1

Hint: Density is the ratio of mass of a sample to the volume of sample used. Density is affected by the change in temperature of the solvent. For finding the density of a given sample we are required with the mass of the sample and the volume of the sample in $ ml $ .
 $ Density{\text{ = }}\dfrac{{mass}}{{volume}} $

Complete answer:
The density of a substance is the ratio of the mass of the substance to its volume. Thus we can say that density is the mass per unit volume of the substance. It is denoted by the symbol $ \rho $ . Mass is represented by symbol $ M $ and volume is denoted by symbol $ V $ . Therefore we can derive the formula for density as:
 $ Density{\text{ = }}\dfrac{{mass}}{{volume}} $
It can be represented symbolically as:
 $ \rho {\text{ = }}\dfrac{M}{V} $
The mass of substance must be in grams and the volume of substance must be in millimeters or cubic-centimetre. Thus the units of density will be $ g{\text{ m}}{{\text{l}}^{ - 1}} $ or $ g{\text{ c}}{{\text{m}}^{ - 3}} $ . Here we are given a sample of mercury whose volume is $ 15{\text{ ml}} $ . The density of the liquid mercury given is $ 13.55{\text{ g c}}{{\text{m}}^{ - 3}} $ . We have to find the mass of this sample. Since we know the formulae for density as,
 $ Density{\text{ = }}\dfrac{{mass}}{{volume}} $
For finding mass it can be deduced as,
 $ {\text{ Mass = Density }} \times {\text{ Volume}} $
On substituting the values we get,
 $ {\text{ Mass = }}\left( {{\text{13}}{\text{.55 }} \times {\text{ 15}}} \right){\text{ g}} $
 $ {\text{ Mass = 203}}{\text{.25 g}} $
Thus we can say that the mass of a given sample of mercury is approximately $ {\text{ 203 g}} $ approximately.

Note:
The given quantities must have units in the same standard either in $ c.g.s $ system or in $ m.k.s $ system. If it is not so then firstly change all units to the same standard. The value of density may vary according to temperature, thus the value of mass also varies according to density.