Question

The weight of source (formula weight $ = 342{\text{ g mo}}{{\text{l}}^{ - 1}}$) in an aqueous solution is $3.42$. The density of the solution is $1{\text{ g m}}{{\text{L}}^{ - 1}}$, the concentration of sucrose in the solution in ${\text{mol }}{{\text{L}}^{ - 1}}$ is :
(A). $0.01$
(B). $0.1$
(C). $1.0$
(D). $10$

Answer 1

Hint:Density is defined as mass per volume; its units are $Kg{L^{ - 1}}$.
${\text{Density = }}\dfrac{{{\text{Mass}}}}{{{\text{Volume}}}} = \dfrac{{{\text{Kg}}}}{{\text{L}}} = {\text{Kg}}{{\text{L}}^{ - 1}}\;{\text{or gm}}{{\text{l}}^{ - 1}}.$
Concentration of a substance is defined as the amount of that substance dissolved in another substance.

Complete step by step answer:Given, Weight present of sucrose in aqueous solution $ = 3.42$
$ \bullet $ Formula weight of sucrose $ = 342{\text{ gmo}}{{\text{l}}^{ - 1}}$
$ \bullet $ Density of solution $ = 1\;{\text{gmo}}{{\text{l}}^{ - 1}}$
$ \bullet $ Concentration of sucrose in the solution = number of moles of sucrose per litre solution
Mass of $1\;L$ solution of sucrose,
${\text{Density = }}\dfrac{{{\text{mass}}}}{{{\text{volume}}}}$
${\text{mass = Density }} \times {\text{ volume}}{\text{.}}$
${\text{mass = 1g/mL }} \times {\text{ 1000 mL}}$
$ = 1000g$
$ \bullet $ Mass of sucrose in $1000{\text{ g}}$ solution
$ = {\text{ mass percent }} \times {\text{ mass of sucrose}}$
$ = \dfrac{{3.42}}{{100}} \times 1000{\text{g}}$
$ = 34.2{\text{g}}$
$ \bullet $ number of moles of sucrose,
${\text{n = }}\dfrac{{{\text{m (given}}\;{\text{mass)}}}}{{{\text{M }}\left( {{\text{Moles}}\;{\text{mass}}} \right)}}$
$ = \dfrac{{34.2g}}{{342{\text{g}}}}$
$ = 0.1\;{\text{mole}}{\text{.}}$
$ \bullet $ The concentration of sucrose in the
${\text{Solution = }}\dfrac{{{\text{number of moles}}}}{{{\text{volume of solution}}\left( L \right)}}$
$ = \dfrac{{0.1}}{1} = 0.1{\text{ M}}$
Therefore, concentration of sucrose in the solution is $0.1\;{\text{M}}$.
Hence, the correct option is (B) $0.1$.

Additional information :-
Table sugar is also known as sucrose. Sucrose is composed of monomers of glucose and fructose. It is obtained from sugar cane or beet root. The chemical formula of sucrose is ${C_{12}}{H_{22}}{O_{11}}.$

Note:The concentration of sucrose or its molarity can also be calculated by using another direct formula, this is :-
${\text{Molarity = }}\dfrac{{{\text{no}}{\text{. of moles}}}}{{{\text{volume of solution }}}} \times 1000$
For using this formula, we must prioritize knowing the number of moles and volume of sucrose solution.