Question

If $60\,{\text{g}}$ of sucrose and ${\text{90}}\,{\text{g}}$ of glucose are dissolved in $1000\,{\text{mL}}$ of solution (aqueous). The specific gravity of the resulting solution is $1.1\,{\text{g/mL}}$. The percentage of moles of sucrose present in the solution will be:
(Assume volume of solution does not change by addition of solutes)
A. $0.328$
B.$0.258$
C.$0.469$
D. $0.152$

Answer 1

Hint: We can determine the percentage of moles per sucrose by using the mole fraction formula. For this, we will determine the moles of each solute of the mixture by using a mole formula. Mass of solvent is determined by density formula.

Formula used:
${\text{mole fraction}}\,{\text{ = }}\,\dfrac{{{\text{Moles}}\,{\text{of}}\,{\text{a component}}}}{{{\text{total moles of the mixture}}}}$
${\text{density}}\,{\text{ = }}\,\dfrac{{{\text{Mass}}}}{{{\text{Volume}}}}$
${\text{Mole}}\,{\text{ = }}\,\dfrac{{{\text{Mass}}}}{{{\text{Molar}}\,{\text{mass}}}}$

Complete step by step answer:
Determine the mole of glucose as follows:
${\text{Mole}}\,{\text{ = }}\,\dfrac{{{\text{Mass}}}}{{{\text{Molar}}\,{\text{mass}}}}$
Molar mass of the glucose is $180\,{\text{g/mol}}$ .
Substitute $180\,{\text{g/mol}}$for molar mass and ${\text{90}}\,{\text{g}}$ for mass.
\[\Rightarrow {\text{Mole}}\,{\text{ = }}\,\dfrac{{90\,{\text{g}}}}{{180\,{\text{g/mol}}}}\]
\[\Rightarrow {\text{Mole}}\,{\text{ = }}\,0.5\,{\text{mol}}\]
Determine the mole of sucrose as follows:
Molar mass of the sucrose is $342\,{\text{g/mol}}$ .
Substitute $180\,{\text{g/mol}}$ for molar mass and ${\text{60}}\,{\text{g}}$ for mass.
\[\Rightarrow {\text{Mole}}\,{\text{ = }}\,\dfrac{{60\,{\text{g}}}}{{342\,{\text{g/mol}}}}\]
\[\Rightarrow {\text{Mole}}\,{\text{ = }}\,0.175\,{\text{mol}}\]
Determine the mass of solution as follows:
${\text{density}}\,{\text{ = }}\,\dfrac{{{\text{Mass}}}}{{{\text{Volume}}}}$
Substitute $1000\,{\text{mL}}$ for volume and $1.1\,{\text{g/mL}}$ for density.
$\Rightarrow 1.1\,{\text{g/mL}}\,{\text{ = }}\,\dfrac{{{\text{Mass}}}}{{1000\,{\text{mL}}}}$
$\Rightarrow {\text{Mass}}\,{\text{of}}\,{\text{solution}}\,\,{\text{ = }}\,\,{\text{1}}{\text{.1}}\,{\text{g/mL}}\, \times \,{\text{1000}}\,{\text{mL}}\,$
$\Rightarrow{\text{Mass}}\,{\text{of}}\,{\text{solution}}\,\,{\text{ = }}\,\,{\text{1100}}\,{\text{g}}$
Subtract the mass of sucrose and glucose from the mass of solution to determine the mass of water.
$\Rightarrow{\text{g}}\,$$1100\,{\text{g}} - 90\,{\text{g}} - 60\,{\text{g}}\,{\text{ = }}\,{\text{950}}\,{\text{g}}$
Determine the mole of water as follows:
Molar mass of the water is$18\,{\text{g/mol}}$ .
Substitute $18\,{\text{g/mol}}$ for molar mass and ${\text{950}}\,{\text{g}}$ for mass.
\[\Rightarrow {\text{Mole}}\,{\text{ = }}\,\dfrac{{950\,{\text{g}}}}{{18\,{\text{g/mol}}}}\]
\[\Rightarrow {\text{Mole}}\,{\text{ = }}\,52.8\,{\text{mol}}\]
Use the mole fraction formula to determine the mole fraction of sucrose as follows:
$\Rightarrow {\text{mole fraction}}\,{\text{ = }}\,\dfrac{{{\text{Moles}}\,{\text{of}}\,{\text{sucrose}}}}{{{\text{Moles}}\,{\text{of}}\,{\text{sucrose}} + {\text{Moles}}\,{\text{of}}\,{\text{glucose}} + {\text{Moles}}\,{\text{of}}\,{\text{water}}}}$
$\Rightarrow {\text{mole fraction}}\,{\text{ = }}\,\dfrac{{{\text{0}}{\text{.175}}\,{\text{mol}}}}{{{\text{0}}{\text{.175}}\,{\text{mol}} + {\text{0}}{\text{.5}}\,{\text{mol}} + {\text{52}}{\text{.8 mol}}}}$
$\Rightarrow {\text{mole fraction}}\,{\text{ = }}\,3.28\, \times \,{10^{ - 3}}$
Multiply the mole fraction of sucrose with $100$ to determine the percentage of moles of sucrose.
$\,{\text{ = }}\,3.28\, \times \,{10^{ - 3}}\, \times 100$
$\,{\text{ = }}\,0.328$
So, the percentage of moles of sucrose present in the solution will be $0.328$.

Therefore, option (A) $0.328$ is correct.

Note:
Specific gravity represents the density. Similarly, the mole fraction of other components can also be determined. The sum of the mole fraction of all components of a mixture is considered as $1$. In the case of three components, after calculating the mole fraction of two components the third can be calculated by subtracting the values of two components from $1$.