Solutions Set-8

Q1. A binary ideal solution contains 1 mole of component A and 3 moles of component B at a temperature where the vapour pressures of the pure components are $p_A^{*}=400\ \mathrm{Torr}$ and $p_B^{*}=300\ \mathrm{Torr}$. Using Raoult's law $p=x_Ap_A^{*}+x_Bp_B^{*}$, the total vapour pressure of the solution is:

Q2. $11.1\ \mathrm{g}$ of $CaCl_2$ (molar mass $=111\ \mathrm{g\,mol^{-1}}$) is dissolved in $200\ \mathrm{g}$ of water. The observed freezing point depression is $\Delta T_f=2.50\ ^\circ\mathrm{C}$. Given $K_f(\text{water})=1.86\ ^\circ\mathrm{C\,kg\,mol^{-1}}$ and assuming $CaCl_2\rightleftharpoons Ca^{2+}+2Cl^{-}$, calculate the degree of dissociation $\alpha$ of $CaCl_2$ (use $\Delta T_f=iK_f m$ and $i=1+2\alpha$).

Q3. For an ideal binary solution at a temperature where $p_A^{*}=380\ \mathrm{Torr}$ and $p_B^{*}=220\ \mathrm{Torr}$, the liquid phase mole fraction of A is $x_A=0.40$. Using Raoult's law, the mole fraction of A in the vapour phase $y_A$ equals

Q4. A compound X (molar mass $=92.0\ \mathrm{g\,mol^{-1}}$) dissolves in benzene and partially associates to form dimers ($2M\rightleftharpoons M_2$). When $3.68\ \mathrm{g}$ of X is dissolved in $100\ \mathrm{g}$ benzene, the freezing point is depressed by $\Delta T_f=1.28\ ^\circ\mathrm{C}$. Given $K_f(\text{benzene})=5.12\ ^\circ\mathrm{C\,kg\,mol^{-1}}$ and using $i=1-\dfrac{\alpha}{2}$ for degree of association, the fraction $\alpha$ of molecules associated into dimers is:

Q5. Two solutions, each prepared in $1.00\ \mathrm{kg}$ of water, give the same freezing point depression. Solution I contains $34.2\ \mathrm{g}$ of sucrose (molar mass $=342\ \mathrm{g\,mol^{-1}}$; non‑electrolyte). Solution II contains $7.10\ \mathrm{g}$ of $Na_2SO_4$ (molar mass $=142\ \mathrm{g\,mol^{-1}}$) which dissociates partially as $Na_2SO_4\rightleftharpoons 2Na^{+}+SO_4^{2-}$. If the degree of dissociation of $Na_2SO_4$ is $\alpha$ and $i=1+2\alpha$ for the salt, the value of $\alpha$ is:

Q6. How many grams of NaCl must be dissolved in $1.00\ \mathrm{kg}$ of water to raise its boiling point by $1.02\ ^\circ\mathrm{C}$? Take $K_b=0.512\ \mathrm{K\,kg\,mol^{-1}}$, assume complete dissociation of NaCl ($i=2$) and $M_{\mathrm{NaCl}}=58.44\ \mathrm{g\,mol^{-1}}$. (Use $\Delta T_b = iK_b m$.)

Q7. $11.1\ \mathrm{g}$ of $\mathrm{CaCl_2}$ is dissolved in $100.0\ \mathrm{g}$ of water and the observed freezing point depression is $3.72\ \mathrm{K}$. Given $K_f=1.86\ \mathrm{K\,kg\,mol^{-1}}$ and $M_{\mathrm{CaCl_2}}=110.98\ \mathrm{g\,mol^{-1}}$, calculate the degree of dissociation $\alpha$ for $\mathrm{CaCl_2}\rightleftharpoons\mathrm{Ca^{2+}}+2\mathrm{Cl^-}$. (Use $\Delta T_f = iK_f m$ with $i=1+2\alpha$.)

Q8. A 0.50 g sample of a non-volatile polymer is dissolved in $500.0\ \mathrm{mL}$ of water at $298\ \mathrm{K}$ and the osmotic pressure is measured to be $0.025\ \mathrm{atm}$. Calculate the molar mass of the polymer. Use $\pi=\dfrac{n}{V}RT$, $R=0.0821\ \mathrm{L\,atm\,mol^{-1}\,K^{-1}}$ and assume no dissociation.

Q9. For a liquid mixture at a given temperature the activity coefficients are $\gamma_A=1.10$ and $\gamma_B=0.90$. The liquid composition is $x_A=0.20,\ x_B=0.80$ and the pure-component vapour pressures are $p_A^0=0.80\ \mathrm{atm}$ and $p_B^0=0.30\ \mathrm{atm}$. Using $p_i=x_i\gamma_i p_i^0$, calculate the mole fraction $y_A$ of A in the vapour phase.

Q10. Equal masses ($11.1\ \mathrm{g}$ each) of the following solutes are dissolved separately in $1.00\ \mathrm{kg}$ of water. Assuming complete dissociation for electrolytes, which solution will exhibit the largest boiling point elevation? ($\Delta T_b\propto i\cdot m$, where $m$ is moles of solute per kg solvent.)

Q11. 1.00 g of glucose ($C_6H_{12}O_6$) is dissolved in $100.0\ \mathrm{g}$ of water. Assuming an ideal dilute solution and $K_f(\text{water}) = 1.86\ \mathrm{K\,kg\,mol^{-1}}$, the freezing point of the solution is approximately:

Q12. An ideal binary solution at $25^\circ\mathrm{C}$ has vapour pressures of pure components $p_A^* = 200\ \mathrm{mmHg}$ and $p_B^* = 600\ \mathrm{mmHg}$. If the mole fraction of A in the liquid is $x_A = 0.40$, the mole fraction of A in the vapour phase $y_A$ is closest to:

Q13. $0.10\ \mathrm{mol}$ of an electrolyte AB (which dissociates as $AB \rightleftharpoons A^+ + B^-$) is dissolved in $1.00\ \mathrm{kg}$ of water. The observed freezing point depression is $\Delta T_f = 0.28\ \mathrm{K}$. Given $K_f(\text{water}) = 1.86\ \mathrm{K\,kg\,mol^{-1}}$, the degree of dissociation $\alpha$ of AB is approximately:

Q14. Assertion (A): For two dilute solutions of the same non-volatile solute at the same temperature and equal molality, the solution made with the solvent of higher density exhibits a larger osmotic pressure.
Reason (R): For dilute solutions molarity can be approximated by $M \approx m\,\rho$ (with $\rho$ the solution density), and since $\pi = MRT$, one gets $\pi \approx m\,\rho\,R\,T$, so at fixed $m$ and $T$ the osmotic pressure increases with $\rho$.

Q15. A sample of an organic compound dissolved in benzene ($K_f = 5.12\ \mathrm{K\,kg\,mol^{-1}}$) produced a freezing point depression $\Delta T_f = 0.64\ \mathrm{K}$. The experiment used $0.50\ \mathrm{g}$ of the compound dissolved in $25.0\ \mathrm{g}$ of benzene. If the compound exists predominantly as dimers in benzene, the molar mass of the monomeric unit is closest to: