This article is all about** Liquid State**. So today here we will be talking about the structure of the liquid. We will also be discussing the Four Important **Properties Of Liquid** **State** in details. We will also learn how to measure the **vapour pressure**, **viscosity**, **surface tension** and **refractive index** of the **liquid state**.

**LIQUID STATE**

The structure of liquids lies somewhere between the completely disordered gaseous state and the highly ordered crystalline state.

**Structure of Liquids**

A given amount of liquid has a fixed volume but assumes the shape of its container. At the molecular level, however, liquids do possess some degree of structure, or order, as evidenced by several physical measurements. Liquids possess short-range order but lack long-range order. Even its short-range order is disrupted by an increase in the kinetic energy of the atoms when the temperature is raised.

**Four important properties of liquids: **

**Vapour Pressure**

**Viscosity**

**Surface Tension and **

**Refractive Index**

**Vapour Pressure**

While deriving kinetic gas equation it was assumed that, at a particular temperature, the gaseous molecules have a particular velocity known as the root mean square velocity. This is so in the case of liquid molecules as well. Only a few liquid molecules have lower or higher velocities, i.e., lower or higher kinetic energies. The energy distribution of molecules in a liquid is shown in Fig.

It is evident from the figure that the number of molecules with high kinetic energies, as shown by the shaded area ABCD below the dotted curve, is small. This number, however, increases with the rise in temperature, as shown by the shaded area FBCE below the bold line curve. The molecules with higher energies are of importance in determining the tendency of a liquid to escape as vapour into a free space if available.

In order to understand this, imagine a liquid contained in an evacuated vessel connected to a manometer so that any pressure that is developed in the free space above the liquid can be measured. The entire system is placed in a thermostat maintained at a constant temperature.

Consider a molecule somewhere in the body of the liquid. It is being attracted by the molecules surrounding it. Since the attractive forces act equally in all directions, the net effect is zero and, therefore, the translatory motion of the molecule is not affected at all. Now, consider a similar molecule near the surface of the liquid. In this case, the attractive forces operate more strongly in the downward direction because there are many more molecules below than in the space above it. This unbalanced attractive force tends to pull the molecule downwards towards the main bulk of the liquid. Thus, the tendency of the molecule, as a result of its translational energy, to pass into the free space above the surface of the liquid, is being prevented by the inward molecular attraction.

However, if this molecule is the one associated with, a higher kinetic energy corresponding to the shaded portion ABCD of the graph at a given temperature, it will be able to break through the forces of molecular attraction and escape into the free space as vapour. Thus, the molecules of a liquid with energy higher than the average energy have a greater tendency to pass into the vapour state. Since the fraction of such molecules increases with the rise in temperature (cf. shaded portion FBCE), it follows that a liquid has a greater tendency to pass into vapour state with the rise in temperature. The escape of liquid molecules into the vapour state constitutes a change of phase.

Let us suppose that in this phase-change process, all the molecules with high kinetic energies represented by the shaded portion of the graph in Fig. escape from the liquid into the vapour phase. The average kinetic energy of the remaining molecules in the liquid phase will, evidently, go down. Hence, the temperature of the liquid shall fall. We conclude, therefore, that a liquid on evaporation cools itself.

Some of the escaping molecules may return to the body of the liquid, i.e., may change back into liquid state. Ultimately, equilibrium is established at each temperature so that the number of molecules leaving the surface in a given time is equal to the number of molecules returning to it. This is called **phase equilibrium**. The vapour molecules confined in the space above the liquid strike against the walls of the vessel and thus register pressure on the manometer attached to the vessel. This pressure at the time when phase equilibrium has been established is found to be constant at a given temperature and is known as **vapour pressure**. Thus, the** vapour pressure** of a liquid at a given temperature is defined as the pressure of the vapour in equilibrium with the liquid at that temperature.

The vapour pressure measures the ease with which a liquid can be converted into vapour, i.e., it is a measure of the volatility of the liquid. Stated in other terms, it is a measure of the escaping tendency of molecules from the surface of the liquid.

As the temperature rises, the number of molecules escaping from the liquid surface increases and there is an increase in the number of vapour molecules in the space above the liquid when phase equilibrium is attained. Hence, the vapour pressure of a liquid increases with the rise in temperature.

**Viscosity**

The viscosity of a ﬂuid—that is, a gas, a pure liquid, or a solution—is an index of its resistance to ﬂow. A viscometer is a device used to measure viscosity. Common viscometers monitor the ease with which ﬂuids ﬂow through capillary tubing. Let us derive an expression relating the viscosity of a liquid, η, to the experimental parameters. Consider a certain liquid ﬂowing through a capillary tube of radius R and length L under constant pressure, P. The velocity of the liquid is zero at the wall and increases toward the centre of the tube, reaching a maximum at the centre. Imagine two concentric cylinders of radii r and (r + dr). The frictional drag, F, between these two cylindrical layers is

F = -η(2πrL)dυ/dr …..(1)

where 2πrL is the surface area of the inner cylinder, and dυ/dr is the velocity gradient. Because the velocity decreases as r increases, dυ/dr is a negative quantity, and a negative sign has been included in Equation (1) to make F a positive number. For steady-state ﬂow, the frictional drag must be exactly balanced by the downward force, which is given by the product of pressure, P, and area, πr^{2}. Thus,

P(πr^{2}) = -η(2πrL)dυ/dr

dυ = – (P/2ηL) r dr

Integration between υ = 0 (at r = R) and υ = υ (at r = r) yields

_{ 0}∫^{υ}dυ = – (P/2ηL)_{ R}∫^{r} r dr

Hence, υ = (P/4ηL) (R^{2} – r^{2}) ……….(2) 0 ≤ r ≤ R

The velocity of ﬂow anywhere in the tube is a parabolic function of r. Equation (2) holds only for laminar ﬂow, which requires small diameters and low ﬂow rates. Without these conditions, Equation (2) is not valid, and turbulent ﬂow may result.

Our next step is to calculate the total ﬂow rate of the liquid through the capillary as a function of viscosity. The volume of liquid that ﬂows through a cross-sectional element, 2πrdr, per second is simply (2πrdr)υ, and the total volume of the liquid ﬂowing per second, Q, is given by

Q = V/ t =_{ 0}∫^{R} υ(2πrdr) = (2πP/4ηL) _{0}∫^{R} (R^{2 }– r^{2})r dr

= πPR^{4}/8ηL ……..(3)

where V is the total volume, and t is the ﬂow time. Equation (3), known as Poiseuille’s law (after the French physician Jean Poiseuille, 1799–1869), applies to both liquids and gases.

A relatively simple apparatus for measuring viscosity is the Ostwald viscometer. It consists of a bulb (A) with markings x and y, attached to a capillary tube (B) and a reservoir bulb (C). A definite volume of the liquid under study is introduced into C and drawn into A, and the time (t) the liquid takes to ﬂow between x and y is recorded. Rearranging Equation (3) gives

η = πPR^{4}t/8VL …….(4)

The pressure, P, at any instant driving the liquid through B, is equal to hρg, where h is the difference in height between the levels of the liquid in the two limbs, ρ is the density of the liquid, and g is the acceleration due to gravity. This pressure varies during the experiment because h decreases. But because the initial and final values of h are the same in every case and g is a constant, the applied pressure is proportional to the density of the liquid.

The viscosity of a liquid is most conveniently determined by comparison with a reference liquid of accurately known viscosity, as follows. The ratio of the viscosities of a sample and a reference liquid is given by

η_{sample}/η_{reference} = πR^{4}(Pt)_{sample}/8VL × 8VL/πR^{4}(Pt)_{reference}

Because V, L, and R values are the same if we use the same viscometer and P = constant × ρ, the preceding equation reduces to

η_{sample}/η_{reference} =(ρt)_{sample}/(ρt)_{reference} …….(5)

Thus, the viscosity of the sample can be obtained readily from the densities of the liquids and the times of ﬂow if η_{reference} is known.

Generally, the viscosity of a solution is greater than that of the pure solvent. The presence of solute molecules disrupts the smooth ﬂow pattern, or velocity gradient, of the ﬂuid, resulting in an increase in viscosity. The viscosities of most liquids decrease with increasing temperature. A molecular interpretation is that liquids possess a number of holes or vacancies and molecules are continually moving into these vacancies. This process permits a liquid to ﬂow but requires energy. To be able to move into a vacancy, a molecule must possess sufficient activation energy to overcome the repulsion by the molecules that surround the vacancy. At higher temperatures, more molecules possess the necessary activation energy, so the liquid ﬂows more easily.

**Surface Tension**

When the surface of a liquid expands, molecules that were originally in the interior region are brought out to the exterior. Work must be done to counteract the attractive forces among these molecules and their neighbours. This process is somewhat similar to the vaporization of a liquid. In vaporization, however, the molecules are completely removed from the liquid, whereas molecules in a surface layer are still under the inﬂuence of strong intermolecular forces, except that the forces are away from the direction of the vapour phase. This unbalanced interaction experienced by surface-layer molecules results in a tendency for the liquid to minimize its surface area. For this reason, a small drop of liquid assumes a spherical shape.

Consider a thin film, such as a soap film, stretched on a wire frame that has a movable side (called the piston) of length l. The force (F) required to stretch the film is proportional to the length, l. Because the film has two sides (i.e., two surfaces), the total dimension of the film is 2l, so

**F ****∝**** 2l**

** = 2γl** …….(6)

where the proportionality constant γ is the surface tension of the liquid. Thus, surface tension can be viewed as the force exerted by a surface of unit length; it has the units Nm^{-1}. Because Nm^{-1} is equivalent to J m^{-2}, we can also interpret surface tension in terms of surface energy. The mechanical work done by moving the piston a distance dx is Fdx, and the change in surface area is 2ldx. The ratio of work done over the increase in area is

** Fdx/****2ldx = 2γldx/2ldx = γ** ……(7)

Surface tension can also be defined as the surface energy per unit area.

**The Capillary-Rise Method**

The capillary-rise method provides a simple means for measuring the surface tension of liquids. In this arrangement, a capillary tube of radius r is dipped into the liquid under study. The force acting downward is the gravitational pull on the liquid, given by πr^{2}hρg, where πr^{2}h is the volume, ρ is the density of the liquid, and g is the acceleration due to gravity. This weight must be balanced by an upward force caused by the liquid’s surface tension. Acting along the periphery of the cylindrical bore, between the liquid and the glass wall, this force is given by 2πrγ cos θ, where 2πr is the circumference of the bore, θ is the angle of contact between the liquid and the capillary tube in the meniscus, and cos θ gives the vertical ((upward) component of the force. Equating the upward and downward forces, we write

**πr**^{2}**hρg ****= 2πrγ cos θ
or**

** γ = rhρg/2 cos θ** …….(8)

Although the rise of liquids up a capillary tube is commonly observed, it is by no means a universal phenomenon. For example, when a capillary tube is dipped into liquid mercury, the upper level of the liquid in the tube is actually lower than the surface of the free liquid. These two divergent behaviours can be understood by considering the intermolecular attraction between like molecules in the liquid, called *cohesion*, and the attraction between the liquid and the glass wall called *adhesion*. If adhesion is stronger than cohesion, the walls become wettable, and the liquid will rise along the walls. Because the vapour-liquid interface resists being stretched, the liquid in the centre of the column also rises. Conversely, if cohesion is greater than adhesion, the liquid in the capillary forms a depression.

The surface tension of aqueous solutions is generally close to that of pure water if the solutes are salts, such as NaCl, or sucrose and other substances that do not preferentially collect at the air-water interface. On the other hand, surface tension can dramatically decrease if the dissolved substance is a fatty acid or a lipid. These molecules consist of two regions: a hydrophilic (water-loving) polar group such as 2COOH at one end, and a long hydrocarbon chain that is nonpolar and therefore hydrophobic (water-fearing) at the other end. The nonpolar groups tend to line up together along the surface of the water with the polar groups pointing toward the interior of the solution. Consequently, surface tension decreases.

**REFRACTION**

**Refractive Index or Index of Refraction**

When a ray of light passes from one medium to another, it suffers refraction, that is, a change of direction. If it passes from a less dense to a more dense medium, as from air to water, it is refracted towards the normal so that the angle of refraction r is less than the angle of incidence i. The refractive index n_{r} of the second medium with respect to the first is then given by the relation

** n _{r} = sin i/sin r ** ……(9)

The refractive index of a medium may also be defined as the ratio of the velocity of light in the vacuum to that in the medium. Refractive indices can be measured easily with a high degree of accuracy.

The values depend upon the temperature as well as the wavelength of light used. Instruments used for measuring refractive indices are known as refractometers. The refractive index of a liquid varies with the temperature. The magnitude of variation, however, is not as large as in the case of surface tension and viscosity.

**Specific Refraction:** The term specific refraction (R), introduced by Lorenz and Lorentz, may be defined as

**R = (n _{r}^{2} – 1) / ρ(n_{r}^{2} + 2)** …….(10)

where p is the density and n, as usual, is the refractive index of the liquid. The advantage of this term is that it is independent of temperature. The variation in n_{r} with the change in temperature is compensated by the variation in ρ, the density of the liquid.

**Molar Refraction: **The product of molar mass (M) of the liquid and specific refraction (R) is called molar refraction (R_{m}). Thus,

**R _{m }= M(n_{r}^{2} – 1) / ρ(n_{r}^{2} + 2)** …….(11)

Molar refraction of a solid is determined by dissolving it first in a suitable solvent so as to get a solution of a known concentration. The refractive index and the density of the solution are then determined experimentally. The molar refraction of the solution R_{m, sol }is given by

** R _{m, sol }= (n_{r}^{2} – 1) / (n_{r}^{2} + 2) [x_{1}M’ +x_{2}M”/ ρ]** …………..(12)

where M’ and M” are the molar masses of the solvent and the solute, respectively and x_{1} and x_{2 }are their respective mole fractions, while n_{r} and ρ are the refractive index and density, respectively, of the solution. Since all the quantities on the right-hand side of Eq. (12) are known, R_{m, sol }can be evaluated. The molar refraction of the solution R_{m, sol }is related to molar refractions R_{1},_{m} and R_{2},_{m} of the solvent and the solute, respectively, by the following equation :

** R _{m, sol }= x_{1}R_{1},_{m} + x_{2}R_{2},_{m}**

_{ }………(13)

From Eq. (13), the molar refraction of the solid solute, R_{2},_{m }can be easily calculated.