Solutions Set-4

Q1. A solution is prepared by dissolving 18.0 g of glucose (C6H12O6, $M = 180\ \text{g mol}^{-1}$) in 162.0 g of water at $25^\circ\text{C}$. Vapour pressure of pure water at $25^\circ\text{C}$ is $p^\circ_{\text{water}} = 23.8\ \text{mmHg}$. Assuming glucose is non-volatile and the solution is ideal, calculate the vapour pressure of water above the solution. (Use Raoult's law $p_{\text{water}} = x_{\text{water}}\,p^\circ_{\text{water}}$.)

Q2. A binary ideal mixture of volatile liquids A and B at a given temperature has vapour pressures of pure components $p_A^\circ = 300\ \text{Torr}$ and $p_B^\circ = 100\ \text{Torr}$. If the mole fraction of A in the liquid is $x_A = 0.40$, calculate the mole fraction of A in the vapour phase $y_A$. (Use $p_A = x_A p_A^\circ,\ p_B = x_B p_B^\circ$ and $y_A = \dfrac{p_A}{p_A+p_B}$.)

Q3. A $1.50\ \text{g}$ sample of an ionic compound AB$_2$ (molar mass $=150\ \text{g mol}^{-1}$) is dissolved in water and diluted to a total volume of $250\ \text{mL}$. At $298\ \text{K}$ the solution exerts an osmotic pressure $\pi = 1.00\ \text{atm}$. If AB$_2$ partially dissociates as AB$_2 \rightleftharpoons A^+ + 2B^-$ with degree of dissociation $\alpha$, calculate $\alpha$. (Use $\pi = i C R T$ with $i = 1 + 2\alpha$ and $R = 0.08206\ \text{L atm mol}^{-1}\text{K}^{-1}$.)

Q4. Assertion (A): A binary solution that shows positive deviation from Raoult's law will always exhibit a minimum‑boiling azeotrope (a composition whose boiling point is lower than both pure components).
Reason (R): Positive deviation indicates weaker A–B interactions than A–A and B–B, so mixing is endothermic ($\Delta H_{\text{mix}} > 0$) and the total vapour pressure may show a maximum at some composition, producing a minimum‑boiling azeotrope.

Q5. At $298\ \text{K}$ pure liquids A and B have vapour pressures $p_A^\circ = 300\ \text{Torr}$ and $p_B^\circ = 100\ \text{Torr}$. For a binary solution with liquid mole fractions $x_A = x_B = 0.50$, the measured total vapour pressure is $230\ \text{Torr}$ and the vapour‑phase mole fraction of A is $y_A = 0.696$. Using the relation $p_i = x_i \gamma_i p_i^\circ$ (with Dalton's law $p_{\text{total}} = p_A + p_B$), calculate the activity coefficients $\gamma_A$ and $\gamma_B$.

Q6. 2.00 g of an unknown non-volatile solute is dissolved in 50.0 g of benzene. The freezing point of benzene is lowered by $1.28\ \mathrm{K}$. Given $K_f(\text{benzene}) = 5.12\ \mathrm{K\,kg\,mol^{-1}}$, calculate the molar mass of the solute. (Use $\Delta T_f = K_f\,m$ and $m=\dfrac{\text{moles solute}}{\text{kg solvent}}$.)

Q7. At a given temperature two volatile liquids A and B form an ideal solution. Vapor pressures of pure components are $p^\circ_A = 400\ \mathrm{mmHg}$ and $p^\circ_B = 200\ \mathrm{mmHg}$. For a liquid mixture with mole fraction $x_A = 0.40$, calculate the total vapour pressure and the mole fraction of A in the vapour phase. (Use Raoult's law $p = x_A p^\circ_A + x_B p^\circ_B$ and $y_A = \dfrac{x_A p^\circ_A}{p}$.)

Q8. A sample of an electrolyte AB (partially dissociating) is dissolved: $0.250\ \mathrm{g}$ of the salt is dissolved in $100.0\ \mathrm{mL}$ of solution at $25^\circ\mathrm{C}$ and exerts an osmotic pressure of $0.500\ \mathrm{atm}$. If the degree of dissociation is $\alpha = 0.60$, calculate the molar mass of AB. (Use $\Pi=\dfrac{n_{\text{particles}}}{V}RT$ and $i=1+\alpha$.)

Q9. An ideal binary solution of A and B at a certain temperature has $p^\circ_A = 400\ \text{mmHg}$ and $p^\circ_B = 200\ \text{mmHg}$. Starting from $1.00\ \text{mol}$ total of liquid mixture with $x_A = 0.50$, a fraction $0.25$ (i.e. $0.25\ \text{mol}$) of the mixture is vaporised and removed as distillate (assume instantaneous equilibrium; vapour composition is $y_A=\dfrac{x_A p^\circ_A}{x_A p^\circ_A + x_B p^\circ_B}$). What is the mole fraction of A remaining in the liquid after removal?

Q10. How many grams of NaCl (molar mass $M = 58.44\ \mathrm{g\,mol^{-1}}$) must be dissolved in $500.0\ \mathrm{g}$ of water to raise its boiling point by $1.00\ ^\circ\mathrm{C}$? Assume $K_b(\mathrm{H_2O}) = 0.512\ \mathrm{K\,kg\,mol^{-1}}$ and that due to ion pairing the effective van't Hoff factor is $i = 1.80$. (Use $\Delta T_b = K_b\,m\,i$.)

Q11. A 0.50 m aqueous solution of glucose (non-electrolyte) is prepared. Using the cryoscopic constant of water $K_f = 1.86\ \text{K kg mol}^{-1}$ and the relation $\Delta T_f = K_f \, m$, calculate the freezing point of the solution in kelvin (pure water freezes at $T_f^\circ = 273.15\ \text{K}$).

Q12. At $350\ \text{K}$ the vapour pressures of pure liquids A and B are $p_A^* = 400\ \text{Torr}$ and $p_B^* = 200\ \text{Torr}$ respectively. An ideal solution contains 1 mole of A and 3 moles of B. Using Raoult's law $p_i = x_i p_i^*$, calculate (i) the total vapour pressure of the solution and (ii) the mole fraction of A in the vapour phase.

Q13. A solution of $\mathrm{Na_2SO_4}$ in water gives a van't Hoff factor $i = 2.6$ from osmotic pressure measurements. For $\mathrm{Na_2SO_4}$, which ideally yields $v=3$ ions, calculate the degree of dissociation $\alpha$ using $i = 1 + (v-1)\alpha$.

Q14. 1.00 g of an electrolyte of type MX (1:1) is dissolved in 100.0 g of water. The degree of dissociation is $\alpha = 0.60$ (from conductivity). The observed freezing point depression is $\Delta T_f = 0.372\ \mathrm{K}$. Using $\Delta T_f = i K_f m$ with $K_f(\text{water}) = 1.86\ \text{K kg mol}^{-1}$ and $i = 1+\alpha$ for a 1:1 electrolyte, estimate the molar mass of MX (in g mol$^{-1}$).

Q15. Pure vapour pressures of liquids A and B at a given temperature are $p_A^* = 600\ \text{Torr}$ and $p_B^* = 300\ \text{Torr}$. For $x_A = 0.50$ Raoult's law predicts $p_{\text{tot}} = 450\ \text{Torr}$, but the experimentally measured $p_{\text{tot}} = 490\ \text{Torr}$. Which one of the following conclusions is correct about the solution behaviour?