Question

The density of sulphuric acid is $ 1.84{\text{ g m}}{{\text{l}}^{ - 1}} $ . What volume of this acid will weigh $ 171{\text{ g}} $ ?

Answer 1

Hint: The density of a solution is defined at the ratio of mass of solute to the mass of solution. We will use this relation to find the volume of sulphuric acid whose density is given as $ 1.84{\text{ g m}}{{\text{l}}^{ - 1}} $ and it weigh $ 171{\text{ g}} $ . Since the units of density are in $ {\text{ g m}}{{\text{l}}^{ - 1}} $ hence the volume of solution will be in millilitres.
 $ Density{\text{ = }}\dfrac{{Mass}}{{Volume}} $ .

Complete Step By Step Answer:
Since we know that the density of a substance is the ratio of mass of substance and the volume of substance. Therefore we can write this ratio as:
 $ Density{\text{ = }}\dfrac{{Mass}}{{Volume}} $
According to the question , the density of sulphuric acid is given as $ 1.84{\text{ g m}}{{\text{l}}^{ - 1}} $ . The volume of this sulphuric which will weigh $ 171{\text{ g}} $ can be calculated as:
 $ \Rightarrow {\text{ }}Density{\text{ = }}\dfrac{{Mass}}{{Volume}} $
 $ \Rightarrow {\text{ }}1.84{\text{ g m}}{{\text{l}}^{ - 1}}{\text{ = }}\dfrac{{171{\text{ g}}}}{{Volume}} $
On cross-multiplying the above equation we get the volume of sulphuric acid as:
 $ \Rightarrow {\text{ }}Volume{\text{ = }}\dfrac{{171{\text{ g}}}}{{1.84{\text{ g m}}{{\text{l}}^{ - 1}}}} $
On solving the above expression we the volume as:
 $ \Rightarrow {\text{ }}Volume{\text{ = 92}}{\text{.93 ml}} $
Hence $ {\text{54}}{\text{.34 ml}} $ of sulphuric acid having density $ 1.84{\text{ g m}}{{\text{l}}^{ - 1}} $ will weigh equal to $ 171{\text{ g}} $ . The volume comes in milliliters and it can be converted into litres by dividing by a $ 1000 $ . Therefore the volume of sulphuric acid in litres will be $ 0.0929{\text{ L}} $ .

Note:
Since the units of density are $ {\text{ g m}}{{\text{l}}^{ - 1}} $ , therefore there is no need to convert any units. The volume of sulphuric acid we get is also millilitre. All the units of given parameters are in c.g.s standard. We can also find the volume of sulphuric by unitary method. The answer would be the same in both cases. There is no need to convert gram into kilo-gram and millilitre to litre. The molecular formula of sulphuric acid is $ {H_2}S{O_4} $ .