Question

If ethanol has a density of $ {\text{0}}{\text{.785 gm m}}{{\text{L}}^{ - 1}} $ , what is the volume of $ 83.3{\text{ gm}} $ of ethanol?

Answer 1

Hint: The density of substance is defined as the ratio of the mass of substance and the volume of substance. Thus we can say that density of substance is equal to mass of substance when volume of substance is unity. We will use the relation between density, mass and volume of substance to find the volume of ethanol.
 $ Density = \dfrac{{Mass}}{{Volume}} $

Complete answer:
The ratio of mass of substance and the volume of substance is known as density of the substance. We are given the density of ethanol as $ {\text{0}}{\text{.785 gm m}}{{\text{L}}^{ - 1}} $ . It can be represented as;
 $ Density = \dfrac{{0.785{\text{ gm}}}}{{1{\text{ }}mL}} $
Thus by assuming the volume of ethanol as $ 1{\text{ mL}} $ we can say that the $ 1{\text{ mL}} $ of ethanol weight $ {\text{0}}{\text{.785 gm}} $ . Hence we can find the volume of the $ 83.3{\text{ gm}} $ ethanol as:
 $ Density = \dfrac{{Mass}}{{Volume}} $
 $ \Rightarrow Volume = \dfrac{{Mass}}{{Density}} $
 $ \Rightarrow Volume = \dfrac{{83.3}}{{0.785}} $
 $ \Rightarrow Volume = 106.11{\text{ mL}} $
It can be round off as:
 $ \Rightarrow Volume = 106{\text{ mL}} $
Therefore the volume of $ 83.3{\text{ gm}} $ of ethanol having density $ {\text{0}}{\text{.785 gm m}}{{\text{L}}^{ - 1}} $ is $ {\text{106 mL}} $ . The units of density is $ {\text{gm m}}{{\text{L}}^{ - 1}} $ , therefore the volume is in milliliters . We can also say $ {\text{106 mL}} $ of ethanol of density $ {\text{0}}{\text{.785 gm m}}{{\text{L}}^{ - 1}} $ will weight $ 83.3{\text{ gm}} $ . The volume can be converted into litres by dividing by a factor of thousand and it will be $ {\text{0}}{\text{.106 L}} $ .

Note:
There is no need to convert the milliliter into litre as the density has unit in $ {\text{gm m}}{{\text{L}}^{ - 1}} $ and the volume of ethanol will be come in milliliters. If we are asked the volume in litre then we can do the conversion. We can also find the volume of ethanol by substituting. The answer would be the same in both cases. It must be noted that $ 1{\text{ mL}} $ of ethanol has weight equal to $ {\text{0}}{\text{.785 gm}} $ .