Assertion (A) When methyl alcohol is added to water, boiling point of water increases.
Reason (R) When a volatile solute is added to a volatile solvent elevation in boiling point is observed.
Assertion (A) When NaCl is added to water a depression in freezing point is observed.
Reason (R) The lowering of vapour pressure of a solution causes depression in the freezing point.
Assertion (A) When a solution is separated from the pure solvent by a semipermeable membrane, the solvent molecules pass through it from pure solvent side to the solution side.
Reason (R) Diffusion of solvent occurs from a region of high concentration solution to a region of low concentration solution.
Define the following modes of expressing the concentration of a solution? Which of these modes are independent of temperature and why?
(a) w/w (mass percentage)
(b) V/V (volume percentage)
(c) $w / V$ (mass by volume percentage)
(d) ppm (parts per million)
(e) $\chi$ (mole fraction)
(f) M (molarity)
(g) m (molality)
(a) $\boldsymbol{w} / \boldsymbol{w}$ (mass percentage) Mass percentage of a component of a solution can be expressed as
$$\text { Mass } \% \text { of component }=\frac{\text { mass of component in the solution }}{\text { total mass of solution }} \times 100$$
Thus, the percentage by mass means the mass of the solute in grams present in 100 g of the solution.
(b) $V / V$ (volume percentage) is defined as
$$\text { Volume percentage }=\frac{\text { volume of the component }}{\text { total volume of solution }} \times 100$$
Thus, volume percentage means the volume of the liquid solute in $\mathrm{cm}^3$ present in $100 \mathrm{~cm}^3$ of the solution.
(c) $\boldsymbol{w} / \boldsymbol{V}$ (mass by volume percentage) = mass of solute dissolved in 100 mL of solution.
(d) ppm (parts per million) This parametre is used to express the concentration of very dilute solution.
$$\begin{aligned} & \text { ppm }=\frac{\text { number of parts of component }}{\begin{array}{c} \text { total number of parts of all component } \\ \text { of solution } \end{array}} \times 10^6 \\ & \hline \end{aligned}$$
(e) $\chi$ (mole fraction) Mole fraction is an unitless quantity used to determine extent of any particular component present in total solution.
$$\chi=\frac{\text { number of moles of the component }}{\text { total number of moles of all components }}$$
(f) $\boldsymbol{M}$ (molarity) Number of moles of solute dissolved in per litre of solution is known as molarity.
$$M=\frac{\text { number of moles of solute }}{\text { volume of solution in litre }}$$
(g) $m$ (Molality) Molality of any solution can be defined as number of moles of solute dissolved in per kg of solvent.
$$m=\frac{\text { number of moles of solute }}{\text { mass of solvent in } \mathrm{kg}}$$
Using Raoult's law explain how the total vapour pressure over the solution is related to mole fraction of components in the following solutions.
(a) $\mathrm{CHCl}_3(l)$ and $\mathrm{CH}_2 \mathrm{Cl}_2(l)$
(b) $\mathrm{NaCl}(\mathrm{s})$ and $\mathrm{H}_2 \mathrm{O}(l)$
According to Raoult's law for any solution the partial vapour pressure of each volatile component in the solution is directly proportional to its mole fraction.
$$p_1=p_1^o x_1$$
(a) $\mathrm{CHCl}_3(l)$ and $\mathrm{CH}_2 \mathrm{Cl}_2(l)$ both are volatile components.
Hence, for a binary solution in which both components are volatile liquids, the total pressure will be
$$\begin{aligned} p & =p_1+p_2=x_1 p_1^{\circ}+x_2 p_2^{\circ} \\ & =x_1 p_1^{\circ}+\left(1-x_1\right) p_2^{\circ}=\left(p_1^o-p_2^{\circ}\right) x_1+p_2^o \end{aligned}$$
where, $\quad p=$ total vapour pressure $p_1=$ partial vapour pressure of component 1
$p_2=$ partial vapour pressure of component 2
(b) $\mathrm{NaCl}(s)$ and $\mathrm{H}_2 \mathrm{O}(l)$ both are non-volatile components.
Hence, for a solution containing non-volatile solute, the Raoult's law is applicable only to vaporisable component and total vapour pressure can be written as
$$p=p_1=x_1 p_1^{\circ}$$