Solutions Set-6

Q1. A 0.500 g sample of a non-electrolyte solute is dissolved in 10.00 g of water. The freezing point of the solution is lowered by $0.93^\circ\mathrm{C}$. Given $K_f(\text{water})=1.86\ \mathrm{K\ kg\ mol^{-1}}$ and $\Delta T_f = K_f \, m$ where $m$ is molality, the molar mass of the solute is:

Q2. Two volatile liquids A and B form an ideal solution at $298\ \mathrm{K}$. Vapour pressures of the pure components are $P_A^*=400\ \mathrm{Torr}$ and $P_B^*=600\ \mathrm{Torr}$. A solution contains $1$ mol A and $4$ mol B. Using Raoult's law $P_i = x_i P_i^*$ and $y_A=\dfrac{P_A}{P_A+P_B}$, the mole fraction of A in the vapour phase is:

Q3. A sample of NaCl of mass $2.925\ \mathrm{g}$ is dissolved in $100.0\ \mathrm{g}$ of water. The observed freezing point depression is $1.395^\circ\mathrm{C}$. Given $K_f(\text{water})=1.86\ \mathrm{K\ kg\ mol^{-1}}$ and for NaCl $i=1+\alpha$ (where $\alpha$ is degree of dissociation) and $\Delta T_f = K_f m i$, the value of $\alpha$ is:

Q4. An ideal binary mixture contains volatile liquids A and B with $P_A^*=200\ \mathrm{mmHg}$ and $P_B^*=600\ \mathrm{mmHg}$. Initially there are $3$ moles of A and $1$ mole of B. At equilibrium the vapour in contact with the liquid is formed and $1$ mole of that vapour (with the equilibrium vapour composition) is removed. After removal, the remaining liquid has mole fractions $x_A$ and $x_B$. The mole fraction $x_A$ of A in the remaining liquid is:

Q5. Acetic acid in benzene dimerizes: $2\,\mathrm{HA} \rightleftharpoons \mathrm{(HA)_2}$. A solution prepared by dissolving $2.00\ \mathrm{g}$ of acetic acid (molar mass $60.0\ \mathrm{g\ mol^{-1}}$) in $100.0\ \mathrm{g}$ benzene shows a freezing point depression of $1.02^\circ\mathrm{C}$. Given $K_f(\text{benzene})=5.12\ \mathrm{K\ kg\ mol^{-1}}$ and for dimerization the van't Hoff factor $i=1-\dfrac{\alpha}{2}$, the degree of association $\alpha$ is approximately:

Q6. A solution is prepared by dissolving $5.00\ \mathrm{g}$ of a non-volatile solute in $100.0\ \mathrm{g}$ of benzene. The freezing point of benzene is lowered by $2.56\ \mathrm{K}$. Given $K_f(\text{benzene})=5.12\ \mathrm{K\,kg^{-1}mol^{-1}}$ and using $\Delta T_f = K_f\cdot m$, the molar mass of the solute (in $\mathrm{g\,mol^{-1}}$) is closest to:

Q7. A binary ideal liquid mixture contains $60.0\ \mathrm{g}$ of A ($M_A=46.0\ \mathrm{g\,mol^{-1}}$) and $40.0\ \mathrm{g}$ of B ($M_B=92.0\ \mathrm{g\,mol^{-1}}$). At the temperature of interest the vapour pressures of pure components are $p_A^0=400\ \mathrm{mmHg}$ and $p_B^0=160\ \mathrm{mmHg}$. Assuming ideal behaviour (Raoult's law), the mole fraction of A in the vapour phase $y_A$ is:

Q8. $11.0\ \mathrm{g}$ of $\mathrm{CaCl_2}$ (molar mass $M_{\mathrm{CaCl_2}}=110.98\ \mathrm{g\,mol^{-1}}$) is dissolved in $100.0\ \mathrm{g}$ of water. The observed freezing point depression is $\Delta T_f=4.50\ \mathrm{K}$. Given $K_f(\text{water})=1.86\ \mathrm{K\,kg^{-1}mol^{-1}}$ and assuming $\mathrm{CaCl_2}$ dissociates as $\mathrm{CaCl_2}\rightarrow \mathrm{Ca^{2+}}+2\mathrm{Cl^-}$ with degree of dissociation $\alpha$ (so $i=1+2\alpha$), the value of $\alpha$ (approx) is:

Q9. Assertion (A): For a binary ideal solution at equilibrium, the component with the higher pure-component vapour pressure will always have a larger mole fraction in the vapour phase than the other component.
Reason (R): Raoult's law gives $p_i = x_i p_i^0$ and the vapour-phase mole fraction is $y_i=\dfrac{x_i p_i^0}{x_A p_A^0 + x_B p_B^0}$.
Which of the following is correct?

Q10. $6.00\ \mathrm{g}$ of acetic acid (molar mass $60.0\ \mathrm{g\,mol^{-1}}$) is dissolved in $100.0\ \mathrm{g}$ of benzene; the observed freezing-point depression is $\Delta T_f=3.072\ \mathrm{K}$. Given $K_f(\text{benzene})=5.12\ \mathrm{K\,kg^{-1}mol^{-1}}$ and that acetic acid associates as $2A\rightleftharpoons A_2$, the fraction $\alpha$ of acetic acid molecules present as dimers is closest to:

Q11. A $10.0\ \mathrm{g}$ sample of a non-volatile, non‑electrolyte solute (molar mass $60.0\ \mathrm{g\ mol^{-1}}$) is dissolved in $500.0\ \mathrm{g}$ of water. Using $\Delta T_b = K_b\,m$ and $K_b(\text{water})=0.512\ \mathrm{K\ kg\ mol^{-1}}$, the boiling point of the solution (assume ideal behaviour) is closest to:

Q12. A $2.00\ \mathrm{g}$ sample of a non‑volatile solute is dissolved in $98.00\ \mathrm{g}$ of water at $25^\circ\mathrm{C}$. The vapour pressure of pure water at $25^\circ\mathrm{C}$ is $23.76\ \mathrm{mmHg}$ and that of the solution is $23.57\ \mathrm{mmHg}$. Assuming ideal behaviour and no dissociation, the molar mass of the solute (use $M_{H_2O}=18.0\ \mathrm{g\ mol^{-1}}$) is approximately:

Q13. An ideal binary solution at $25^\circ\mathrm{C}$ has mole fractions $x_A=0.40$ and $x_B=0.60$. The vapour pressures of pure components are $P_A^\circ=200\ \mathrm{mmHg}$ and $P_B^\circ=100\ \mathrm{mmHg}$. Using Raoult's law, the mole fraction of A in the vapour phase $y_A$ above the solution is:

Q14. Assertion (A): For $0.10\ \mathrm{m}$ solutions in benzene at $25^\circ\mathrm{C}$, acetic acid causes a larger freezing point depression than $n$‑hexane.
Reason (R): Acetic acid dimerizes in benzene, reducing the effective number of solute particles.

Q15. A student measures the freezing point depression $\Delta T_f$ and the osmotic pressure $\pi$ of a dilute aqueous solution of an electrolyte at temperature $T$ and attempts to determine both the molar mass $M$ of the solute and its degree of dissociation $\alpha$ from these two measurements alone. Which statement is correct?