Azeotropic mixtures and Raoult's Law

Question

So I find this everywhere:
"Mixtures showing large deviations from Rault's law form azetropic mixtures at specific compositions"

My questions are:
(a)Why is it so?Why deviation from Raoult's law is needed at all.
Wikipedia simply skips over the answer stating its a mathematical consequence. (Quoting wikipedia: When the deviation is great enough to cause a maximum or minimum in the vapor pressure versus composition function, it is a mathematical consequence that at that point, the vapor will have the same composition as the liquid, resulting in an azeotrope.)

(b) why can't ideal mixtures form azeotropes?

P.S: (a)A more intuitive answer would be appreciated although maths may be included if necessary.
(b)I did my research but nowhere the reason was to be found. It's presented as a very obvious consequence everywhere.

Answer 1

To understand why non - ideal mixtures form azeotropes, we need to understand what is ideal mixture. If you have a liquid mixture of two components A and B, ideal mixture is a mixture in which heterogeneous interactions (A - B) are the same as the average homogeneous (A - A and B - B). This means when you mix components A and B, they don't "feel" like their enviroment has changed at all and thus no component has higher nor lower tendency to escape the liquid phase and go into vapor phase. When interactions are largely different, in most cases heterogeneous interactions are less favourable than homogeneous (molecules of A in most cases like to be around molecules of A rather than B) than component will have higher tendency to escape from liquid phase to vapor since in vapor interactions are much less pronounced due to much bigger average distance of the molecules. If this scenario happens you got yourself a lower boiling azeotrope since due to higher tendency of molecules to escape liquid phase, vapor pressure is higher than in ideal case (Raoult's Law). In some cases heterogeneous interactions can be very favourable and this is usually due to some specific interactions which mostly originate from hydrogen bonding, if so molecules will tend to stay in liquid and you got yourself higher boiling azeotrope. Example of such azeotrope is HNO3 and water. If you have any questions, fire.

Answer 2

In his answer Dario Miric has explained the basis of azeotropes clearly, this is a small addition to his answer. Raoult determined experimentally that the partial vapour pressure over some liquid mixtures is directly proportional to the mole fraction $x$ of each component, and thus the total pressure is

$$P=x_1p_1^\text{o}+x_2p_2^\text{o}=x_1p_1^\text{o}+(1-x_1)p_2^\text{o}$$

where $p^\text{o}$ is the vapour pressure of the pure liquid. An ideal solution can be defined as one that obeys Raoult's law at all temperatures. Solutions obeying Raoult's law are, for example, dichloroethane - benzene or ethylene bromide - propylene bromide. As the pressure is the sum of the partial pressures the two species cannot interact to any great extent that would cause their vapour pressures to differ from that expected from the pure solution. Of course this is only true in a few cases.

If the two types of molecule interact with one another then the potential energy of the mixture has an additional term describing this interaction. The result of this interaction is that the total pressure becomes

$$P=x_1p_1^\text{o}e^{\alpha}+(1-x_1)p_2^\text{o}e^{\beta}$$

where $\alpha =(1-x_1)^2)\Delta U/RT$ and $\beta =x_1^2\Delta U/RT$ and $\Delta U$ is a measure of the average difference in interaction energy. When $\Delta U$ is small vs $RT$ only a slight deviation from Raoult's law (pressure $p_{1,2}/p_{1,2}^\text{o}$,vs. $x$) is evident and instead of being a straight line is slightly bent, convex of concave, for example methanol in water. If the plot of total pressure vs mole fraction passes through a maximum or minimum then this is the Azeotrope and the vapour has the same composition as the mixture. Additionally as $dP/dx=0$ at the azeotrope and as the mole fraction is known an estimate of $\Delta U$ can be obtained. Example of azeotropes are dichloromethane - acetone, carbon disulphide - dimethoxymethane and CS$_2$-CHCl$_3$