9 questions
An aqueous solution is prepared by dissolving \( 0.1 \) mol of an ionic salt in \( 1.8 \) kg of water at \( 35^\circ \text{C} \). The salt remains \( 90\% \) dissociated in the solution. The vapour pressure of the solution is \( 59.724 \, \text{mm of Hg} \). Vapor pressure of water at \( 35^\circ \text{C} \) is \( 60.000 \, \text{mm of Hg} \). The number of ions present per formula unit of the ionic salt is _______.
Two volatile liquids \( A \) and \( B \) form an ideal solution. Consider a \( 5 \, \text{molal} \) solution of \( B \) in \( A \) inside a closed container having a total vapour pressure of \( 100 \, \text{mm Hg} \) at \( 300 \, \text{K} \). The vapour pressure of pure \( A \) at \( 300 \, \text{K} \) is \( 105 \, \text{mm Hg} \). Assume that \( A \) and \( B \) behave as ideal gases in the vapour phase.
Given:
The gas constant \( R = 0.08 \, \text{L atm K}^{-1} \text{ mol}^{-1} \)
Molar mass of \( A \) is \( 50 \, \text{g mol}^{-1} \)
Molar mass of \( B \) is \( 57 \, \text{g mol}^{-1} \)
Density of liquid \( B \) at \( 300 \, \text{K} \) is \( 0.5 \, \text{g/mL} \)
\( 1 \, \text{atm} = 760 \, \text{mm Hg} \)
The mole fraction of \( B \) in vapour phase which is in equilibrium with this solution is ________.
At \( 300 \, \text{K} \), an ideal dilute solution of a macromolecule exerts osmotic pressure that is expressed in terms of the height (\( h \)) of the solution (density \( = 1.00 \, g \, \text{cm}^{-3} \)) where \( h \) is equal to \( 2.00 \, \text{cm} \). If the concentration of the dilute solution of the macromolecule is \( 2.00 \, g \, \text{dm}^{-3} \), the molar mass of the macromolecule is calculated to be \( X \times 10^{4} \, g \, \text{mol}^{-1} \). The value of \( X \) is __________.
Use: Universal gas constant (\( R \)) \( = 8.3 \, J \, K^{-1} \, \text{mol}^{-1} \) and acceleration due to gravity (\( g \)) \( = 10 \, \text{m} \, \text{s}^{-2} \).
Two volatile liquids \( A \) and \( B \) form an ideal solution. Consider a \( 5 \) molal solution of \( B \) in \( A \) inside a closed container having a total vapour pressure of \( 100 \, \text{mm Hg} \) at \( 300 \, \text{K} \). The vapour pressure of pure \( A \) at \( 300 \, \text{K} \) is \( 105 \, \text{mm Hg} \). Assume that \( A \) and \( B \) behave as ideal gases in the vapour phase.
Given:
The gas constant \( R = 0.08 \, \text{L atm K}^{-1} \text{ mol}^{-1} \)
Molar mass of \( A \) is \( 50 \, \text{g mol}^{-1} \)
Molar mass of \( B \) is \( 57 \, \text{g mol}^{-1} \)
Density of liquid \( B \) at \( 300 \, \text{K} \) is \( 0.5 \, \text{g/mL} \)
\( 1 \, \text{atm} = 760 \, \text{mm Hg} \)
At \( 300 \, \text{K} \), the ratio of the molar volume of pure \( B \) in vapour phase to its molar volume in liquid phase is ________.
Vessel-1 contains \( W_2 \) \( \mathrm{g} \) of a non-volatile solute X dissolved in \( W_1 \) \( \mathrm{g} \) of water. Vessel-2 contains \( W_2 \) \( \mathrm{g} \) of another non-volatile solute Y dissolved in \( W_1 \) \( \mathrm{g} \) of water. Both the vessels are at the same temperature and pressure. The molar mass of X is \( 80\% \) of that of Y. The van’t Hoff factor for X is \( 1.2 \) times of that of Y for their respective concentrations. The elevation of boiling point for solution in Vessel-1 is _______\( \% \) of the solution in Vessel-2.
The boiling point of water in a \( 0.1 \) molal silver nitrate solution (solution \( A \)) is \( x^\circ \mathrm{C} \). To this solution \( A \), an equal volume of \( 0.1 \) molal aqueous barium chloride solution is added to make a new solution \( B \). The difference in the boiling points of water in the two solutions \( A \) and \( B \) is \( y \times 10^{-2} \, ^\circ \mathrm{C} \). (Assume: Densities of the solutions \( A \) and \( B \) are the same as that of water and the soluble salts dissociate completely. Use: Molal elevation constant (Ebullioscopic Constant), \( K_b = 0.5 \, \text{K kg mol}^{-1} \); Boiling point of pure water as \( 100^\circ \mathrm{C} \).)
The value of \( x \) is ______.
The boiling point of water in a \( 0.1 \) molal silver nitrate solution (solution A) is \( x^\circ \, \text{C} \). To this solution A, an equal volume of \( 0.1 \) molal aqueous barium chloride solution is added to make a new solution B. The difference in the boiling points of water in the two solutions A and B is \( y \times 10^{-2} \, ^\circ \text{C} \).
(Assume : Densities of the solutions A and B are the same as that of water and the soluble salts dissociate completely. Use : Molal elevation constant (Ebullioscopic Constant), \( K_b = 0.5 \, \text{K kg mol}^{-1} \); Boiling point of pure water as \( 100^\circ \text{C} \).)
The value of \( |y| \) is ______.
In a solvent \( S \), a compound \( B \) is partially dissociated into \( C \) and \( D \) as given below:
\( B \rightleftharpoons 2C + 2D \)
\( B, C \) and \( D \) are non-volatile in nature. The molar mass of \( B \) is \( 10 \) times the molar mass of \( S \). The standard boiling point and the standard enthalpy of vaporization of \( S \) are \( 400 \, \text{K} \) and \( 10R \, \text{J mol}^{-1} \), respectively \( (R \) is the gas constant in \( \text{J K}^{-1} \text{ mol}^{-1}) \). A solution of \( B \) in \( S \) with an initial concentration of \( B \) as \( 0.25\% \) (mass/mass) has a boiling point of \( 408 \, \text{K} \) at \( 1 \) bar pressure. In this solution, the mole percent of \( B \) that has been dissociated is ________.
\( 50 \, \text{mL} \) of \( 0.2 \) molal urea solution (density \( = 1.012 \, \text{g mL}^{-1} \) at \( 300 \, \text{K} \)) is mixed with \( 250 \, \text{mL} \) of a solution containing \( 0.06 \, \text{g} \) of urea. Both the solutions were prepared in the same solvent. The osmotic pressure (in Torr) of the resulting solution at \( 300 \, \text{K} \) is ________.
[Use : Molar mass of urea \( = 60 \, \text{g mol}^{-1} \); gas constant, \( R = 62 \, \text{L Torr K}^{-1} \text{ mol}^{-1} \); Assume \( \Delta_{\text{mix}} H = 0 \), \( \Delta_{\text{mix}} V = 0 \)]
