Solutions · Chemistry · JEE Advanced
Numerical
In a solvent $\mathbf{S}$, a compound $\mathbf{B}$ is partially dissociated into $\mathbf{C}$ and $\mathbf{D}$ as given below :
$$ \mathbf{B} \rightleftharpoons 2 \mathbf{C}+2 \mathbf{D} $$
$\mathbf{B}, \mathbf{C}$ and $\mathbf{D}$ are non-volatile in nature. The molar mass of $\mathbf{B}$ is 10 times the molar mass of $\mathbf{S}$. The standard boiling point and the standard enthalpy of vaporization of $\mathbf{S}$ are 400 K and $10 R \mathrm{~J} \mathrm{~mol}^{-1}$, respectively ( $R$ is the gas constant in $\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$ ). A solution of $\mathbf{B}$ in $\mathbf{S}$ with an initial concentration of $\mathbf{B}$ as $0.25 \%$ (mass/mass) has a boiling point of 408 K at 1 bar pressure. In this solution, the mole percent of $\mathbf{B}$ that has been dissociated is $\_\_\_\_$ .
Two volatile liquids $\mathbf{A}$ and $\mathbf{B}$ form an ideal solution. Consider a 5 molal solution of $\mathbf{B}$ in $\mathbf{A}$ inside a closed container having a total vapour pressure of 100 mm Hg at 300 K . The vapour pressure of pure $\mathbf{A}$ at 300 K is 105 mm Hg . Assume that $\mathbf{A}$ and $\mathbf{B}$ behave as ideal gases in the vapour phase.
Given :
The gas constant $R=0.08 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$
Molar mass of $\mathbf{A}$ is $50 \mathrm{~g} \mathrm{~mol}^{-1}$
Molar mass of $\mathbf{B}$ is $57 \mathrm{~g} \mathrm{~mol}^{-1}$
Density of liquid $\mathbf{B}$ at 300 K is $0.5 \mathrm{~g} / \mathrm{mL}$
$1 \mathrm{~atm}=760 \mathrm{~mm} \mathrm{Hg}$
At 300 K , the ratio of the molar volume of pure $\mathbf{B}$ in vapour phase to its molar volume in liquid phase is $\_\_\_\_$ .
Two volatile liquids $\mathbf{A}$ and $\mathbf{B}$ form an ideal solution. Consider a 5 molal solution of $\mathbf{B}$ in $\mathbf{A}$ inside a closed container having a total vapour pressure of 100 mm Hg at 300 K . The vapour pressure of pure $\mathbf{A}$ at 300 K is 105 mm Hg . Assume that $\mathbf{A}$ and $\mathbf{B}$ behave as ideal gases in the vapour phase.
Given :
The gas constant $R=0.08 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$
Molar mass of $\mathbf{A}$ is $50 \mathrm{~g} \mathrm{~mol}^{-1}$
Molar mass of $\mathbf{B}$ is $57 \mathrm{~g} \mathrm{~mol}^{-1}$
Density of liquid $\mathbf{B}$ at 300 K is $0.5 \mathrm{~g} / \mathrm{mL}$
$1 \mathrm{~atm}=760 \mathrm{~mm} \mathrm{Hg}$
The mole fraction of $\mathbf{B}$ in vapour phase which is in equilibrium with this solution is $\_\_\_\_$ .
At 300 K , an ideal dilute solution of a macromolecule exerts osmotic pressure that is expressed in terms of the height $(h)$ of the solution (density $=1.00 \mathrm{~g} \mathrm{~cm}^{-3}$ ) where $h$ is equal to 2.00 cm . If the concentration of the dilute solution of the macromolecule is $2.00 \mathrm{~g} \mathrm{dm}^{-3}$, the molar mass of the macromolecule is calculated to be $\boldsymbol{X} \times 10^4 \mathrm{~g} \mathrm{~mol}^{-1}$. The value of $\boldsymbol{X}$ is __________.
Use: Universal gas constant $(R)=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ and acceleration due to gravity $(g)=10 \mathrm{~m} \mathrm{~s}^{-2}$
The elevation of boiling point for solution in Vessel-1 is ________ $\%$ of the solution in Vessel-2.
[Use: Molar mass of urea $=60 \mathrm{~g} \mathrm{~mol}^{-1}$; gas constant, $\mathrm{R}=62$ L Torr $\mathrm{K}^{-1} \mathrm{~mol}^{-1}$;
Assume, $\Delta_{\text {mix }} \mathrm{H}=0, \Delta_{\text {mix }} \mathrm{V}=0$ ]
(Given data: Molar mass and the molal freezing point depression constant of benzene are 78 g mol-1 and 5.12 K kg mol-1, respectively).
On addition of equal number of moles of a non-volatile solute $$S$$ in equal amount (in $$kg$$) of these solvents, the elevation of boiling point of solvent $$X$$ is three times that of solvent $$Y$$. Solute $$S$$ is known to undergo dimerization in these solvents. If the degree of dimerization is $$0.7$$ in solvent $$Y$$, the degree of dimerization in solvent $$X$$ is ___________.
(given that the vapor pressure of pure liquid $$A$$ is $$20$$ $$Torr$$ at temperature $$T$$)
MCQ (Single Correct Answer)
The qualitative sketches I, II and III given below show the variation of surface tension with molar concentration of three different aqueous solutions of KCl, CH3OH and CH3(CH2)11 OSO$$_3^ - $$ Na+ at room temperature. The correct assignment of the sketches is
The Henry's law constant for the solubility of N$$_2$$ gas in water at 298 K is 1.0 $$\times$$ 10$$^5$$ atm. The mole fraction of N$$_2$$ in air is 0.8. The number of moles of N$$_2$$ from air dissolved in 10 moles of water at 298 K and 5 atm pressure is
The freezing point of the solution M is :
The vapour pressure of the solution M is :
Water is added to the solution M such that the fraction of water in the solution becomes 0.9 mole. The boiling point of this solution is:
When 20 g of naphthoic acid (C$$_{11}$$H$$_{8}$$O$$_{2}$$) is dissolved in 50 g of benzene in 50 g of benzene (K$$_f$$ = 1.72 K kg mol$$^{-1}$$), a freezing point depression of 2 K is observed. The van't Hoff factor (i) is :
MCQ (More than One Correct Answer)
