Solutions Set-3

Q1. A student wants to lower the freezing point of $200\ \mathrm{g}$ of water by $1.86\ \mathrm{K}$. How many grams of glucose ($C_6H_{12}O_6$, $M=180\ \mathrm{g\,mol^{-1}}$) must be dissolved? (Use $\Delta T_f = K_f\,m$ and $K_f(\text{water})=1.86\ \mathrm{K\,kg\,mol^{-1}}$.)

Q2. 46 g of methanol ($M=32\ \mathrm{g\,mol^{-1}}$) and 156 g of ethanol ($M=46\ \mathrm{g\,mol^{-1}}$) are mixed to form an ideal solution at 298 K. Vapor pressures of pure methanol and ethanol are $P^\circ_{\text{meth}}=120\ \text{torr}$ and $P^\circ_{\text{eth}}=60\ \text{torr}$. Using $p_i=x_iP_i^\circ$ and $y_{\text{meth}}=\dfrac{p_{\text{meth}}}{p_{\text{total}}}$, the mole fraction of methanol in the vapor phase $y_{\text{meth}}$ is approximately:

Q3. A $0.10$ molal aqueous solution of $\mathrm{CaCl_2}$ causes a freezing point depression of $0.372\ \mathrm{K}$. ($K_f(\text{water})=1.86\ \mathrm{K\,kg\,mol^{-1}}$.) Using $\Delta T_f = iK_f m$ and $i=1+2\alpha$ for $\mathrm{CaCl_2}$, the degree of dissociation $\alpha$ is:

Q4. At $298\ \mathrm{K}$ a binary solution contains component A at $x_A=0.01$ (very dilute) and component B at $x_B=0.99$. A obeys Henry's law $p_A=k_A x_A$ with $k_A=5000\ \text{torr}$, while B obeys Raoult's law $p_B=x_B P_B^\circ$ with $P_B^\circ=200\ \text{torr}$. The mole fraction of A in the vapour $y_A=\dfrac{p_A}{p_A+p_B}$ is closest to:

Q5. A student dissolves a fixed mass $w$ of an unknown solute in $100\ \mathrm{g}$ of water and measures the freezing point depression $\Delta T_f$ and the osmotic pressure $\pi$ at the same temperature. Using $\Delta T_f = iK_f m$ and $\pi = i c R T$ (taking solution volume ≈ $0.100\ \mathrm{L}$), which statement is correct about determining the molar mass $M$ and degree of dissociation $i$?

Q6. Pure benzene has vapour pressure $0.12\ \text{atm}$ at $298\ \text{K}$. When a non-volatile solute is dissolved in $1.00\ \text{mol}$ of benzene the vapour pressure of benzene above the solution at $298\ \text{K}$ becomes $0.10\ \text{atm}$. The number of moles of solute added is:

Q7. $0.100\ \text{mol}$ of a salt of type $AB_2$ is dissolved in $1.00\ \text{kg}$ of water. The boiling point of the solution is found to increase by $0.123\ \text{K}$. (Take $K_b(\text{water})=0.512\ \text{K kg mol}^{-1}$.) The degree of dissociation $\alpha$ of the salt is closest to:

Q8. An ideal binary solution of volatile liquids A and B at $298\ \text{K}$ has liquid mole fractions $x_A=0.40$ and $x_B=0.60$. The vapour pressures of pure A and B at $298\ \text{K}$ are $P_A^0=250\ \text{torr}$ and $P_B^0=150\ \text{torr}$ respectively. The mole fraction of A in the vapour phase $y_A$ is:

Q9. When $0.100\ \text{mol}$ of acetic acid (HA) is dissolved in $1.00\ \text{kg}$ of benzene the freezing point is depressed by $0.320\ \text{K}$. ($K_f$ of benzene $=5.12\ \text{K kg mol}^{-1}$.) Acetic acid dimerizes in benzene: $2\mathrm{HA}\rightleftharpoons(\mathrm{HA})_2$. If $\alpha$ is the fraction of acid molecules that dimerize, the value of $\alpha$ is closest to:

Q10. A binary ideal solution at $298\ \text{K}$ has liquid composition $x_A=0.20$. The total vapour pressure above the solution is $0.600\ \text{atm}$ and the mole fraction of A in the vapour phase is $y_A=0.55$. Using Raoult's and Dalton's laws, the vapour pressures of pure A and pure B at $298\ \text{K}$, $P_A^0$ and $P_B^0$, are approximately: