Mix Examples of Solutions Questions in English

(A) Molar masses: $CH_3OH = 12 + 4(1) + 16 = 32 \text{ g mol}^{-1}$,$CCl_4 = 12 + 4(35.5) = 154 \text{ g mol}^{-1}$.
In a $30\%$ (w/w) solution,we have $30 \text{ g}$ of methanol and $70 \text{ g}$ of $CCl_4$.
Moles of methanol $(n_{CH_3OH})$ = $30 / 32 = 0.9375 \text{ mol}$.
Moles of $CCl_4$ $(n_{CCl_4})$ = $70 / 154 = 0.4545 \text{ mol}$.
Mole fraction of $CCl_4$ $(X_{CCl_4})$ = $n_{CCl_4} / (n_{CH_3OH} + n_{CCl_4}) = 0.4545 / (0.9375 + 0.4545) = 0.4545 / 1.392 = 0.3265 \approx 0.33$. Thus,Statement $I$ is true.
Methanol molecules exhibit strong intermolecular hydrogen bonding. When $CCl_4$ (a non-polar solvent) is added,it disrupts these hydrogen bonds,resulting in weaker solute-solvent interactions compared to solute-solute or solvent-solvent interactions. This leads to a positive deviation from Raoult's law. Thus,Statement $II$ is true.

(C) $1$. According to Raoult's Law for a dilute solution,the relative lowering of vapour pressure is given by: $\frac{P^0 - P_s}{P^0} = \frac{n_2}{n_1 + n_2} \approx \frac{n_2}{n_1}$.
$2$. Given: $P^0 = 760 \text{ mm Hg}$,$P_s = 750 \text{ mm Hg}$. So,$\frac{760 - 750}{760} = \frac{10}{760} = \frac{1}{76} = \frac{n_2}{n_1}$.
$3$. Boiling point elevation is given by: $\Delta T_b = K_b \times m$,where $m$ is molality.
$4$. $\Delta T_b = 320 - 319.5 = 0.5 \text{ K}$.
$5$. Molality $m = \frac{n_2}{w_1 \text{ (in kg)}} = \frac{n_2}{0.04 \text{ kg}}$.
$6$. Substituting values: $0.5 = 0.3 \times \frac{n_2}{0.04} \Rightarrow n_2 = \frac{0.5 \times 0.04}{0.3} = \frac{0.02}{0.3} = \frac{1}{15} \text{ mol}$.
$7$. Using the relation from step $2$: $\frac{n_2}{n_1} = \frac{1}{76} \Rightarrow n_1 = 76 \times n_2 = 76 \times \frac{1}{15} = 5.066 \text{ mol}$.
$8$. The nearest integer is $5$.

(A) Molality $(m)$ = $\frac{\text{moles of solute}}{\text{mass of solvent in kg}} = \frac{2.5 / 60}{75 / 1000} = \frac{0.04167}{0.075} \approx 0.556 \text{ m}$. Statement $(A)$ is correct.
$(B)$ Molarity $(M)$ = $\frac{\text{moles of solute}}{\text{volume of solution in L}} = \frac{5 / 40}{450 / 1000} = \frac{0.125}{0.45} \approx 0.278 \text{ M}$. Statement $(B)$ is correct.
$(C)$ According to Henry's law,the solubility of gases in liquids increases with a decrease in temperature. Thus,aquatic species are more comfortable in cold water. Statement $(C)$ is correct.
$(D)$ According to Henry's law,the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas. Thus,solubility increases with an increase in pressure. Statement $(D)$ is incorrect.
$(E)$ The mole fraction of component $B$ is defined as $x_{B} = \frac{n_{B}}{n_{A} + n_{B}}$. Statement $(E)$ is incorrect.
Therefore,statements $(A)$,$(B)$,and $(C)$ are correct.