(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.

$$m=\frac{\text { number of moles of solute }}{\text { mass of solvent in } \mathrm{kg}}$$

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

$$p=p_1=x_1 p_1^{\circ}$$

The solutions which obey Raoult's law over the entire range of concentration are known as ideal solutions. For an ideal solution $\Delta V_{\text {mix }}=O$ and $\Delta V_{\text {mix }}=O$. The ideal behaviour of the solutions can be explained by considering two components $A$ and $B$.

In pure components, the intermolecular attractive interactions will be of $A-A$ type and $B-B$ type, whereas in the binary solutions in addition to these two, $A-B$ type of interaction will also be present. If $A-A$ and $B-B$ intermolecular forces are nearly equal to those between $A-B$, this leads to the formation of ideal solution e.g., solution of $n$-hexane and $n$-heptane. When a solution does not obey-Raoult's law over the entire range of concentration, then it is called non-ideal solution. The vapour pressure of such a solution is either higher or lower, than that predicted by Raoult's law.

If it is higher, the solution exhibits positive deviation and if it is lower it exhibits negative deviation from Raoult's law. In case of positive deviation, $A-B$ interactions are weaker than those between $A-A$ or $B$ - B. i.e., the attractive forces between solute solvent molecules are weaker than those between solute-solute and solvent-solvent molecules e.g., mixture of ethanol and acetone.

For such solutions $\quad \Delta H_{\text {mixing }}=+$ ve and $\Delta V_{\text {mixing }}=+$ ve

On the other hand, in case of negative deviation the intermolecular attractive forces between $A-A$ and $B-B$ are weaker than those between $A-B$ molecules. Thus, the escaping tendency of $A$ and $B$ types of molecules from the solution becomes less than from the pure liquids i.e., mixture of chloroform and acetone.

For such solution $$\quad \Delta H_{\text {mix }}=-\mathrm{ve} \text { and } \Delta V_{\text {mix }}=-\mathrm{ve}$$

The solution or mixture having same composition in liquid as well as in vapour phase and boils at a constant temperature is known as azeotropes. Due to constant composition it can't be separated by fractional distillation. There are two types of azeotropes

(i) Minimum boiling azeotropes Solutions which show large positive deviation from Raoult's law form minimum boiling azeotropes at a specific composition. e.g., ethanol -water mixture

(ii) Maximum boiling azeotropes Solutions which show large negative deviation from Raoult's law form maximum boiling azeotropes. e.g., solution having composition 68$\%$ $\mathrm{HNO}_3$ and $32 \%$ water by mass.

This phenomenon is called endo osmosis, i.e., movement of water inside the raisin and shown with the help of diagram as

The process of osmosis is of immense biological as well as industrial important. It is evident from the following examples.

(i) Movement of water from soil into plant roots and subsequently into upper portion of the plant is partly due to osmosis.

(ii) Preservation of meat against bacterial action by addition of salt.

(iii) Preservation of fruits against bacterial action by adding sugar. Bacterium in canned fruit loses water through the process of osmosis and become inactive.

(iv) Reverse-osmosis is used in desalination of water.