**Introduction to the Liquid State**

**Difference between solid, liquid and gas**

**Solids**

**• Closely packed ordered arrangement ****of particles (atoms, molecules, ions)**

**• Intermolecular forces of attraction are very strong.**

**• Definite shape**** (because molecules in solid are strongly held and cannot move)**

**• Definite Volume**

**• Low K.E. i.e., only vibrate about their mean position.**

**• Long range order**** (i.e., the definite and ordered arrangement of the constituents of solids extends over a large distance.)**

**Liquids**

**• Molecules in liquids are not far apart from each other i.e., ****molecules are in contact with each other. ****But ****no regular arrangement. **

**• Fairly strong intermolecular forces**** but less than solids.**

**• Molecules move past one another but this movement is restricted as compared to molecules in gases. Hence liquids have ****definite volume ****but ****no definite shape****(takes shape of container)****.**

**• Particles of liquid have High kinetic energy, i.e., they slide over each other.**

**• Random motion or irregular motion of particles.**

**• Liquids exhibit ****short range order.**

**Gases**

**• Molecules are in ****constant random motion.**

**• No regular pattern.**

**• There are ****large spaces in between them.**** Therefore, ****very weak ****(negligible)**** intermolecular forces**** of attraction .**

**• Molecules have random motion therefore it has ****neither definite shape****(takes shape of container)**** nor definite volume.**

**• Show ****no order**** at all.**

**Some Important Orders****:-**

**Intermolecular Force****➤ Solid> Liquid> Gas**

**• The forces of attraction or repulsion which act between neighboring particles is called as Intermolecular force.**

**compressibility****➤ Solid < Liquid < Gas**

**• Solids can not be compressed. **

**• Liquids are slightly compressible. **

**• While gases are ****highly compressible.**

**Kinetic Energy**** ➤Solid< Liquid< Gas**

**• More is the distance between the particles, less will be the inter particle force of attraction. Hence, particles would be free to move with higher kinetic energy.**

**order of expansion on heating****➤ Solid< Liquid< Gas**

**• In solids, molecules are tightly packed as compared to liquids and gases.**

**• similarly, molecules of a liquid are bound more as compared to gases. **

**• Hence, on heating, solids expand less as compared to liquids and liquids expand less as compared to gases. **

**• In case of gases, the molecules are not bound at all. Thus they expand maximum upon heating.**

**The nature and magnitude of intermolecular forces is the key concept in describing the physical properties of liquids.**

**Different types of Intermolecular forces **

**Intermolecular forces are the****attractive or repulsive forces****between****the molecules.**

**Intermolecular forces****exists between polar molecules as well as non-polar molecules.**

**Intermolecular forces as a whole are usually called as****Van der Walls forces.**

**These are****electrostatic in nature.**

**Intermolecular forces only exists in non-metals.**

**There are different types of Intermolecular Forces/interactions :-**

**1. Dipole-Dipole forces**

**2. Dipole-Induced dipole forces**

**3. Induced dipole – Induced dipole forces**

**4. Hydrogen bonding**

**1. ****Dipole-Dipole forces**

**As polar molecule have permanent dipole moment.**

**A polar molecule exists as dipole having a positive pole and a negative pole.**

**The positive pole of one molecule is attracted by the negative pole of other molecule.**

**The van der Walls force****due to electrical interaction between the dipoles****of two molecules is known as****dipole-dipole interaction****or****dipole-dipole force.**

**It exists only in polar covalent compounds e.g. NH**_{3}, HCl, SO_{2}etc. As all these gases have permanent dipoles which results in appreciable dipole-dipole interactions between the dipoles of these molecules.

**Some Important Points****–**

**As a polarized molecule have****two poles****, partial positive and partial negative pole.**

**The electron cloud lies****near more electronegative element****which results in the dipole-dipole interactions.**

**It exists only in polar covalent compounds e.g. HCl, SO**_{2}etc.

**It is****not****a chemical bond. It is an intermolecular force.**

**Dipole-Dipole forces****doesn’t exist in non-polar covalent compounds****like O**_{2}, Cl_{2}etc. because the electron cloud lies**in between****them and hence no interactions between the compounds.**

**Magnitude of dipole-dipole interactions **

**The magnitude of dipole dipole forces depends upon the dipole moment of the polar molecule.**

**More is the value of dipole moment, more will be the dipole-dipole interaction.****e.g.1**

**$$\mu_{{NH}_3}=1.49\,D$$**

**$$\mu_{HCl}=1.03\,D$$**

**$$\mu_{{NH}_3}>\mu_{HCl}$$**

**\(\implies\) the dipole-dipole forces are stronger in NH _{3}**

**\(\implies\) NH**

_{3}is more easily liquefiable than HCl gas.**e.g. 2**

**$$\mu_{{NH}_3}=1.49\,D$$**

**$$\mu_{{H}_2 O}=1.85\,D$$**

**$$\mu_{H_2 O}>\mu_{{NH}_3}$$**

**\(\implies\) intermolecular forces of attraction are stronger in case of \({H}_2 O\) than in \(NH_3\)**

**\(\implies meling\,\, point➤ {H}_2 O > NH_3\)**

**Average Potential Energy of Dipole-Dipole Forces **

**Consider two polar molecules having dipole moments \(\mu_1\) & \(\mu_2\) respectively.**

**The average interaction energy between them is given by the expression :**

**Interaction energy,$$V=\frac{C}{r^6}$$**

**where \(C=\frac{-2}{3kT}×\mu_1^2\, \mu_2^2\)**

**\(\therefore\) \(V=-\frac{2}{3kT}\mu_1^2\, \mu_2^2 ×\frac{1}{r^6} \) …….(1)**

**where r= distance between polar molecules **

** k= Boltzmann constant **

** T= Absolute temperature **

**The above equation (1) carries -ve sign because dipole-dipole interaction is an attractive force.**

**Equation (1) shows that: **

**the force of attraction between dipoles depends on \(\frac{1}{r^6}\).****dipole-dipole attractions vary inversely with temperature.****As the intermolecular distance ‘r’ is very large under normal conditions of temperature and pressure;**

**\(\implies\)dipole-dipole interactions among gas molecules are very small.****When P \(\uparrow\) or T \(\downarrow\)**

**then the distance ‘r’ between the molecules decreases.****\(\implies\) magnitude of attractive forces increases and the gas changes into liquid or solid under these conditions.**

**2. ****Dipole-induced dipole forces**

**When a non-polar molecule lies in neighbourhood of a polar molecule then it may sometimes polarized by the polar molecule.**

**In this way, the polar molecule having dipole moment \(\mu_1\) can induce a dipole \(\mu_2\) in the polarisable molecule.**

**Thus, the non-polar molecule behaves as an Induced dipole.**

**This Induced dipole then interacts with the permanent dipole moment of polar molecule, and hence the two molecules are attracted together as shown in fig.**

**Note:-**

**The magnitude of this interaction depends upon the polarisability of the non-polar molecule and the dipole moment of the polar molecule .**

**In 1920, Debye showed that a non-polar molecule is polarized by a polar molecule in its vicinity.**

**The average kinetic energy of attraction of dipole-induced dipole interaction is given by:**

**\(V=-\frac{C}{r^6}\) ; where \(C=2 \alpha \mu_1^2 \)**

**\(\therefore V=-2 \alpha \mu_1^2 × \frac{1}{r^6}\)**

**where \(\mu_1\) = permanent dipole moment of polar molecule **

**\(\alpha\) = polarisability of non-polar(polarisable) molecule.**

**r= distance between the molecules.**

**Above equation shows that the dipole-induced dipole interaction energy depends upon \(\frac{1}{r^6}\) and is independent of temperature.**

**Note:-**

**Dipole-induced dipole interaction varies with distance in the same way as dipole-dipole interaction. But its magnitude is much smaller.**

**3. ****Induced dipole-induced dipole forces**

** ****or London/dispersion Forces**

**In 1930, the existance of forces of attraction between the non-polar molecules was explained by Fritz London. **

**Due to temporary distortion of electron cloud of the non-polar molecule, it produces a momentary dipole.**

**This momentary dipole induces again a momentary dipole in the neighbouring molecule.**

**These two dipoles attract each other and the force of attraction between these two dipoles ( induced dipole and original dipole) are known as London/dispersion forces.**

**Some Important Facts:-**

**London forces arises due to motion of electrons, therefore, also exists in polar molecules.**

**Vanderwaals attraction in non-polar molecules is only due to London forces.**

**Van der Walls forces is a general term that includes the forces of attraction between polar as well as non-polar molecules. Hence, the London forces are reffered to as Van der Walls forces.**

**Energy of Interaction of London Forces**

**The energy of interaction of London forces is given by London formula as :**

**Interaction Energy, \(V=-\frac{C}{r^6}\)**

**where, \(C=\frac{3}{2} \alpha_1 \alpha_2 (\frac{I_1 I_2}{I_1 + I_2}) \)**

**where \(\alpha_1 \, and \, \alpha_2\) = polarisabilities of molecule 1 and 2 respectively.**

**\(I_1\) and \(I_2\) = ionisation energies of two molecules.**

**\(\therefore\) \(V=-\frac{3}{2} \alpha_1 \alpha_2 \frac{I_1 I_2}{I_1 + I_2} × \frac{1}{r^6}\)**

**Magnitude of London Forces **

**Magnitude of London Forces \(\propto\) size of molecule**

**Magnitude of London Forces \(\propto\) Surface area of the molecule.**

** **

**i.e., magnitude of London forces increase with increase in size and surface area of the molecule.**

**Because the extent of polarisation increase with the increase in the surface area which results in increasing amount of attractive forces.**

**For example : n-pentane & neo-pentane **

**molecular formula of both are same = \(C_5 H_{14}\)**

**n-pentane ➤ linear shape ➠ Large surface area **

**neo-pentane➤nearly spherical shape➠ Less surface area**

**\(\implies\) Intermolecular force of attraction is more in n-pentane.**

**\(\implies\) Boiling point of n-pentane is more**

**\({B.P.}_{n-pentane} = 36.4° \)**

**\({B.P.}_{neo-pentane} = 9.7° \)**

**Note:-**

**The magnitude of London forces increase with increase in molecular mass.**

**\(\Rightarrow\) The extent of polarisability increase with increase in molecular size. Due to which, the London forces of attraction also increase.**

**4. ****Hydrogen Bond**

**It is a unique type of dipole-dipole interaction and exists in the molecules in which a hydrogen atom is covalently bonded to the highly electronegative atom (e.g. F, O, N)**

**As electronegativity of hydrogen is very less than F, O and N.**

**Due to this large electronegativity difference, the shared pair of electron between them lies far away from hydrogen atom, i.e., the shared pair of electron displaced towards more electronegative atom and more electronegative atom acquires partial negative charge (δ-).**

**As a result, hydrogen atom becomes highly electropositive w.r.t. the other atom and acquires partial positive charge (δ+)**

**Hence there is an electrostatic force between positively charged atom of one molecule and negatively charged atom of neighbouring molecule which results in the formation of hydrogen bond.**

**In this way, we can define hydrogen bond as the attractive force which binds the hydrogen atom of one molecule with electronegative atom (F,O,N) of another molecule.**

**Note:-**

**The hydrogen bond may be between two different molecules or within the same molecule.**

**If the hydrogen bonding happens****between molecules****having either same or other compounds then it is called as****Intermolecular hydrogen bonding.**

**If the hydrogen bonding happens****within the same molecule****, then it is called as****Intramolecular hydrogen bonding.**

**For example:**

**Two HF molecules are joined together due to dipole-dipole interaction viz., called as Intermolecular H-bonding as shown in fig.**

**While the hydrogen bonding within o-hydroxybenzoic acid is Intramolecular hydrogen bonding as shown in fig.**

**Repulsive Intermolecular Forces **

**When two molecules come closer then the interactions occur between the nuclei and electrons of the molecules.**

**At Large distances,**

**the attractive forces operate between two molecules.**

**While, ****at very small distances,**

**the nuclei and electrons of the molecules repel each other.**

**At this stage, the repulsive forces begin to dominate the attractive forces.**

**Repulsive forces vary inversely as the 12th power of intermolecular distance i.e., \(\propto\) \(\frac{1}{r^{12}}\) **

**Hence, the repulsive forces increase sharply with decrease in the distance between molecules.**

**Mathematically, the magnitude of repulsive interaction energy is given by **

**\(V_{repulsion} = \frac{B}{r^{12}}\)**

**where B= constant (depending upon the nature of substance)**

**Total Energy of Interaction between a Pair of Molecules **

**or The ‘Lennard-Jones Potential’**

**The total energy of interaction between a pair of molecules is the sum of all attractive and repulsive forces.**

**i.e., It is the sum of following interaction energies:**

**Dipole-Dipole interaction energy **

**\(V_1 =-\frac{2}{3kT}\mu_1^2\, \mu_2^2 ×\frac{1}{r^6}\)**

**Dipole-Induced dipole interaction energy **

**\(V_2 =-2 \alpha \mu_1^2 × \frac{1}{r^6}\)**

**Induced dipole-Induced dipole interaction energy**

**\(V_3 =-\frac{3}{2} \alpha_1 \alpha_2 \frac{I_1 I_2}{I_1 + I_2} × \frac{1}{r^6} \)**

**Repulsive interaction energy **

**\(V_{repulsion} = \frac{B}{r^{12}}\)**

**Hence, Total Potential Energy = Total attractive forces + Total repulsive forces**

**=\([ V_1 + V_2 + V_3 ] + V_r \)**

**= \(-\frac{2}{3kT}\mu_1^2\, \mu_2^2 ×\frac{1}{r^6}\) + \([-2 \alpha \mu_1^2 × \frac{1}{r^6}]\) + \([-\frac{3}{2} \alpha_1 \alpha_2 \frac{I_1 I_2}{I_1 + I_2} × \frac{1}{r^6} \)] + \(\frac{B}{r^12}\)**

**$$V= -[\frac{2}{3} \frac{\mu_1^2 \mu_2^2}{kT} + 2 \alpha \mu_1^2 +\frac{3}{2} \alpha_1 \alpha_2 [\frac{I_1 I_2}{I_1 + I_2}]] \frac{1}{r^6} + \frac{B}{r^{12}}$$**

**\(\implies V=-\frac{A}{r^6} + \frac{B}{r^{12}}\)**

**where, A and B are constants.**

**The potential energy of interaction is usually expressed in a standard form known as ****Lennard-Jones potential.**

**Linnard-Jones Potential is the special case of ****Mie Potential energy ****with ****m=6 and n=12**

**Mie Potential Energy **

**It is a function of the distance between two particles (r) and is written as**

**\(V(r) = C ε [( \frac{r_0}{r})^{12} – (\frac{r_0}{r})^6] \)**

**where, \(C=\frac{n}{n-m}(\frac{n}{m})^{\frac{m}{n-m}}\)**

**ε= maximum energy of attraction ( depth of the well)**

**r _{0} = closest distance between two molecules at which V=0**

**At m=6 and n=12,**

**\(V= 4ε [( \frac{r_0}{r})^{12} – (\frac{r_0}{r})^6]\)**

**viz., the Lennard Jones potential.**

**Linnard-Jones Potential is also reffered to as ****6-12 Potential**** because VWL attractive forces fall of as 6th power of intermolecular distance and the repulsive forces vary inversely as the 12th power of the intermolecular distance.**

**Linnard-Jones Potential Energy Curve:-**

**The energy of Interaction is given by the derivative of V(r) w.r.t. r**

**$$V= – \frac{ \partial V} {\partial \,r}$$**

**If \(\frac{ \partial V} {\partial \,r}\) = +ve , then the interaction energy = -ve**

**\(\Rightarrow\) the molecules are attracted towards each other.**

**If \(\frac{ \partial V} {\partial \,r}\) = -ve , then the interaction energy = +ve**

**\(\Rightarrow\) the molecules repel each other.**